Daily Papers

As Multimodal Large Language Models (MLLMs) continue to evolve, their cognitive and reasoning capabilities have seen remarkable progress. However, challenges in visual fine-grained perception and commonsense causal inference persist. This paper introduces Argus Inspection, a multimodal benchmark with two levels of difficulty, emphasizing detailed visual recognition while incorporating real-world commonsense understanding to evaluate causal reasoning abilities. Expanding on it, we present the Eye of Panoptes framework, which integrates a binary parametric Sigmoid metric with an indicator function, enabling a more holistic evaluation of MLLMs' responses in opinion-based reasoning tasks. Experiments conducted on 26 mainstream MLLMs reveal that the highest performance in visual fine-grained reasoning reaches only 0.46, highlighting considerable potential for enhancement. Our research offers valuable perspectives for the continued refinement of MLLMs.

While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the computational efficiency through the random projection, yet they suffer from low accuracy if the number of projections is not sufficiently large, because the majority of projections result in trivially small values. In this work, we propose a new family of distance metrics, called augmented sliced Wasserstein distances (ASWDs), constructed by first mapping samples to higher-dimensional hypersurfaces parameterized by neural networks. It is derived from a key observation that (random) linear projections of samples residing on these hypersurfaces would translate to much more flexible nonlinear projections in the original sample space, so they can capture complex structures of the data distribution. We show that the hypersurfaces can be optimized by gradient ascent efficiently. We provide the condition under which the ASWD is a valid metric and show that this can be obtained by an injective neural network architecture. Numerical results demonstrate that the ASWD significantly outperforms other Wasserstein variants for both synthetic and real-world problems.

Quantized neural networks employ reduced precision representations for both weights and activations. This quantization process significantly reduces the memory requirements and computational complexity of the network. Binary Neural Networks (BNNs) are the extreme quantization case, representing values with just one bit. Since the sign function is typically used to map real values to binary values, smooth approximations are introduced to mimic the gradients during error backpropagation. Thus, the mismatch between the forward and backward models corrupts the direction of the gradient, causing training inconsistency problems and performance degradation. In contrast to current BNN approaches, we propose to employ a binary periodic (BiPer) function during binarization. Specifically, we use a square wave for the forward pass to obtain the binary values and employ the trigonometric sine function with the same period of the square wave as a differentiable surrogate during the backward pass. We demonstrate that this approach can control the quantization error by using the frequency of the periodic function and improves network performance. Extensive experiments validate the effectiveness of BiPer in benchmark datasets and network architectures, with improvements of up to 1% and 0.69% with respect to state-of-the-art methods in the classification task over CIFAR-10 and ImageNet, respectively. Our code is publicly available at https://github.com/edmav4/BiPer.

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's theoretical advantages of optimization stability, convergence speed and generalization performance.

Many evaluation metrics can be used to assess the performance of models in binary classification tasks. However, most of them are derived from a confusion matrix in a non-differentiable form, making it very difficult to generate a differentiable loss function that could directly optimize them. The lack of solutions to bridge this challenge not only hinders our ability to solve difficult tasks, such as imbalanced learning, but also requires the deployment of computationally expensive hyperparameter search processes in model selection. In this paper, we propose a general-purpose approach that transforms any confusion matrix-based metric into a loss function, AnyLoss, that is available in optimization processes. To this end, we use an approximation function to make a confusion matrix represented in a differentiable form, and this approach enables any confusion matrix-based metric to be directly used as a loss function. The mechanism of the approximation function is provided to ensure its operability and the differentiability of our loss functions is proved by suggesting their derivatives. We conduct extensive experiments under diverse neural networks with many datasets, and we demonstrate their general availability to target any confusion matrix-based metrics. Our method, especially, shows outstanding achievements in dealing with imbalanced datasets, and its competitive learning speed, compared to multiple baseline models, underscores its efficiency.

This paper proposes a new metric to measure the calibration error of probabilistic binary classifiers, called test-based calibration error (TCE). TCE incorporates a novel loss function based on a statistical test to examine the extent to which model predictions differ from probabilities estimated from data. It offers (i) a clear interpretation, (ii) a consistent scale that is unaffected by class imbalance, and (iii) an enhanced visual representation with repect to the standard reliability diagram. In addition, we introduce an optimality criterion for the binning procedure of calibration error metrics based on a minimal estimation error of the empirical probabilities. We provide a novel computational algorithm for optimal bins under bin-size constraints. We demonstrate properties of TCE through a range of experiments, including multiple real-world imbalanced datasets and ImageNet 1000.

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Binary Neural Network (BNN) represents convolution weights with 1-bit values, which enhances the efficiency of storage and computation. This paper is motivated by a previously revealed phenomenon that the binary kernels in successful BNNs are nearly power-law distributed: their values are mostly clustered into a small number of codewords. This phenomenon encourages us to compact typical BNNs and obtain further close performance through learning non-repetitive kernels within a binary kernel subspace. Specifically, we regard the binarization process as kernel grouping in terms of a binary codebook, and our task lies in learning to select a smaller subset of codewords from the full codebook. We then leverage the Gumbel-Sinkhorn technique to approximate the codeword selection process, and develop the Permutation Straight-Through Estimator (PSTE) that is able to not only optimize the selection process end-to-end but also maintain the non-repetitive occupancy of selected codewords. Experiments verify that our method reduces both the model size and bit-wise computational costs, and achieves accuracy improvements compared with state-of-the-art BNNs under comparable budgets.

Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. In this work, we (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. We show that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. Our theoretical results provide new insight in understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, we provide an algorithm to compute the metric by leveraging Sinkhorn divergences and validate our findings through a simulation study.

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations -- usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. The source code is available at https://github.com/htdt/hyp_metric.

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Systems based on artificial neural networks (ANNs) have achieved state-of-the-art results in many natural language processing tasks. Although ANNs do not require manually engineered features, ANNs have many hyperparameters to be optimized. The choice of hyperparameters significantly impacts models' performances. However, the ANN hyperparameters are typically chosen by manual, grid, or random search, which either requires expert experiences or is computationally expensive. Recent approaches based on Bayesian optimization using Gaussian processes (GPs) is a more systematic way to automatically pinpoint optimal or near-optimal machine learning hyperparameters. Using a previously published ANN model yielding state-of-the-art results for dialog act classification, we demonstrate that optimizing hyperparameters using GP further improves the results, and reduces the computational time by a factor of 4 compared to a random search. Therefore it is a useful technique for tuning ANN models to yield the best performances for natural language processing tasks.

We present Semantify: a self-supervised method that utilizes the semantic power of CLIP language-vision foundation model to simplify the control of 3D morphable models. Given a parametric model, training data is created by randomly sampling the model's parameters, creating various shapes and rendering them. The similarity between the output images and a set of word descriptors is calculated in CLIP's latent space. Our key idea is first to choose a small set of semantically meaningful and disentangled descriptors that characterize the 3DMM, and then learn a non-linear mapping from scores across this set to the parametric coefficients of the given 3DMM. The non-linear mapping is defined by training a neural network without a human-in-the-loop. We present results on numerous 3DMMs: body shape models, face shape and expression models, as well as animal shapes. We demonstrate how our method defines a simple slider interface for intuitive modeling, and show how the mapping can be used to instantly fit a 3D parametric body shape to in-the-wild images.

The growth of generative adversarial network (GAN) models has increased the ability of image processing and provides numerous industries with the technology to produce realistic image transformations. However, with the field being recently established there are new evaluation metrics that can further this research. Previous research has shown the Fr\'echet Inception Distance (FID) to be an effective metric when testing these image-to-image GANs in real-world applications. Signed Inception Distance (SID), a founded metric in 2023, expands on FID by allowing unsigned distances. This paper uses public datasets that consist of facades, cityscapes, and maps within Pix2Pix and CycleGAN models. After training these models are evaluated on both inception distance metrics which measure the generating performance of the trained models. Our findings indicate that usage of the metric SID incorporates an efficient and effective metric to complement, or even exceed the ability shown using the FID for the image-to-image GANs

Stochastic neurons and hard non-linearities can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such stochastic or non-smooth neurons? I.e., can we "back-propagate" through these stochastic neurons? We examine this question, existing approaches, and compare four families of solutions, applicable in different settings. One of them is the minimum variance unbiased gradient estimator for stochatic binary neurons (a special case of the REINFORCE algorithm). A second approach, introduced here, decomposes the operation of a binary stochastic neuron into a stochastic binary part and a smooth differentiable part, which approximates the expected effect of the pure stochatic binary neuron to first order. A third approach involves the injection of additive or multiplicative noise in a computational graph that is otherwise differentiable. A fourth approach heuristically copies the gradient with respect to the stochastic output directly as an estimator of the gradient with respect to the sigmoid argument (we call this the straight-through estimator). To explore a context where these estimators are useful, we consider a small-scale version of {\em conditional computation}, where sparse stochastic units form a distributed representation of gaters that can turn off in combinatorially many ways large chunks of the computation performed in the rest of the neural network. In this case, it is important that the gating units produce an actual 0 most of the time. The resulting sparsity can be potentially be exploited to greatly reduce the computational cost of large deep networks for which conditional computation would be useful.

Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space with intrinsic non-Euclidean geometry, the primary challenge in representation learning is to respect this underlying geometric structure. Drawing inspiration from the success of Euclidean deep learning, researchers have developed neural networks on the SPD manifolds for more faithful covariance embedding learning. A notable advancement in this area is the implementation of Riemannian batch normalization (RBN), which has been shown to improve the performance of SPD network models. Nonetheless, the Riemannian metric beneath the existing RBN might fail to effectively deal with the ill-conditioned SPD matrices (ICSM), undermining the effectiveness of RBN. In contrast, the Bures-Wasserstein metric (BWM) demonstrates superior performance for ill-conditioning. In addition, the recently introduced Generalized BWM (GBWM) parameterizes the vanilla BWM via an SPD matrix, allowing for a more nuanced representation of vibrant geometries of the SPD manifold. Therefore, we propose a novel RBN algorithm based on the GBW geometry, incorporating a learnable metric parameter. Moreover, the deformation of GBWM by matrix power is also introduced to further enhance the representational capacity of GBWM-based RBN. Experimental results on different datasets validate the effectiveness of our proposed method.

The field of image generation has made significant progress thanks to the introduction of Diffusion Models, which learn to progressively reverse a given image corruption. Recently, a few studies introduced alternative ways of corrupting images in Diffusion Models, with an emphasis on blurring. However, these studies are purely empirical and it remains unclear what is the optimal procedure for corrupting an image. In this work, we hypothesize that the optimal procedure minimizes the length of the path taken when corrupting an image towards a given final state. We propose the Fisher metric for the path length, measured in the space of probability distributions. We compute the shortest path according to this metric, and we show that it corresponds to a combination of image sharpening, rather than blurring, and noise deblurring. While the corruption was chosen arbitrarily in previous work, our Shortest Path Diffusion (SPD) determines uniquely the entire spatiotemporal structure of the corruption. We show that SPD improves on strong baselines without any hyperparameter tuning, and outperforms all previous Diffusion Models based on image blurring. Furthermore, any small deviation from the shortest path leads to worse performance, suggesting that SPD provides the optimal procedure to corrupt images. Our work sheds new light on observations made in recent works and provides a new approach to improve diffusion models on images and other types of data.

Deep metric learning, which learns discriminative features to process image clustering and retrieval tasks, has attracted extensive attention in recent years. A number of deep metric learning methods, which ensure that similar examples are mapped close to each other and dissimilar examples are mapped farther apart, have been proposed to construct effective structures for loss functions and have shown promising results. In this paper, different from the approaches on learning the loss structures, we propose a robust SNR distance metric based on Signal-to-Noise Ratio (SNR) for measuring the similarity of image pairs for deep metric learning. By exploring the properties of our SNR distance metric from the view of geometry space and statistical theory, we analyze the properties of our metric and show that it can preserve the semantic similarity between image pairs, which well justify its suitability for deep metric learning. Compared with Euclidean distance metric, our SNR distance metric can further jointly reduce the intra-class distances and enlarge the inter-class distances for learned features. Leveraging our SNR distance metric, we propose Deep SNR-based Metric Learning (DSML) to generate discriminative feature embeddings. By extensive experiments on three widely adopted benchmarks, including CARS196, CUB200-2011 and CIFAR10, our DSML has shown its superiority over other state-of-the-art methods. Additionally, we extend our SNR distance metric to deep hashing learning, and conduct experiments on two benchmarks, including CIFAR10 and NUS-WIDE, to demonstrate the effectiveness and generality of our SNR distance metric.

Deep face recognition has achieved great success due to large-scale training databases and rapidly developing loss functions. The existing algorithms devote to realizing an ideal idea: minimizing the intra-class distance and maximizing the inter-class distance. However, they may neglect that there are also low quality training images which should not be optimized in this strict way. Considering the imperfection of training databases, we propose that intra-class and inter-class objectives can be optimized in a moderate way to mitigate overfitting problem, and further propose a novel loss function, named sigmoid-constrained hypersphere loss (SFace). Specifically, SFace imposes intra-class and inter-class constraints on a hypersphere manifold, which are controlled by two sigmoid gradient re-scale functions respectively. The sigmoid curves precisely re-scale the intra-class and inter-class gradients so that training samples can be optimized to some degree. Therefore, SFace can make a better balance between decreasing the intra-class distances for clean examples and preventing overfitting to the label noise, and contributes more robust deep face recognition models. Extensive experiments of models trained on CASIA-WebFace, VGGFace2, and MS-Celeb-1M databases, and evaluated on several face recognition benchmarks, such as LFW, MegaFace and IJB-C databases, have demonstrated the superiority of SFace.

In most machine learning tasks, we evaluate a model M on a given data population S by measuring a population-level metric F(S;M). Examples of such evaluation metric F include precision/recall for (binary) recognition, the F1 score for multi-class classification, and the BLEU metric for language generation. On the other hand, the model M is trained by optimizing a sample-level loss G(S_t;M) at each learning step t, where S_t is a subset of S (a.k.a. the mini-batch). Popular choices of G include cross-entropy loss, the Dice loss, and sentence-level BLEU scores. A fundamental assumption behind this paradigm is that the mean value of the sample-level loss G, if averaged over all possible samples, should effectively represent the population-level metric F of the task, such as, that E[ G(S_t;M) ] approx F(S;M). In this paper, we systematically investigate the above assumption in several NLP tasks. We show, both theoretically and experimentally, that some popular designs of the sample-level loss G may be inconsistent with the true population-level metric F of the task, so that models trained to optimize the former can be substantially sub-optimal to the latter, a phenomenon we call it, Simpson's bias, due to its deep connections with the classic paradox known as Simpson's reversal paradox in statistics and social sciences.

We present a class of novel optimisers for training neural networks that makes use of the Riemannian metric naturally induced when the loss landscape is embedded in higher-dimensional space. This is the same metric that underlies common visualisations of loss landscapes. By taking this geometric perspective literally and using the induced metric, we develop a new optimiser and compare it to existing methods, namely: SGD, Adam, AdamW, and Muon, across a range of tasks and architectures. Empirically, we conclude that this new class of optimisers is highly effective in low dimensional examples, and provides slight improvement over state-of-the-art methods for training neural networks. These new optimisers have theoretically desirable properties. In particular, the effective learning rate is automatically decreased in regions of high curvature acting as a smoothed out form of gradient clipping. Similarly, one variant of these optimisers can also be viewed as inducing an effective scheduled learning rate and decoupled weight decay is the natural choice from our geometric perspective. The basic method can be used to modify any existing preconditioning method. The new optimiser has a computational complexity comparable to that of Adam.

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells).

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural implicit surfaces to simple parametric domains like spheres and polycubes. Our method allows users to specify the number of cubes in the parametric domain, learning a configuration that closely resembles the target 3D object's geometry. It computes bi-directional deformation between the object and the domain using a forward mapping from the object's zero level set and an inverse deformation for backward mapping. We ensure nearly bijective mapping with a cycle loss and optimize deformation smoothness. The parameterization quality, assessed by angle and area distortions, is guaranteed using a Laplacian regularizer and an optimized learned parametric domain. Our framework integrates with existing neural rendering pipelines, using multi-view images of a single object or multiple objects of similar geometries to reconstruct 3D geometry and compute texture maps automatically, eliminating the need for any prior information. We demonstrate the method's effectiveness on images of human heads and man-made objects.

Gravitational-wave approximants are essential for gravitational-wave astronomy, allowing the coverage binary black hole parameter space for inference or match filtering without costly numerical relativity (NR) simulations, but generally trading some accuracy for computational efficiency. To reduce this trade-off, NR surrogate models can be constructed using interpolation within NR waveform space. We present a 2-stage training approach for neural network-based NR surrogate models. Initially trained on approximant-generated waveforms and then fine-tuned with NR data, these dual-stage artificial neural surrogate (DANSur) models offer rapid and competitively accurate waveform generation, generating millions in under 20ms on a GPU while keeping mean mismatches with NR around 10^{-4}. Implemented in the bilby framework, we show they can be used for parameter estimation tasks.

Optimization of Top-1 ImageNet promotes enormous networks that may be impractical in inference settings. Binary neural networks (BNNs) have the potential to significantly lower the compute intensity but existing models suffer from low quality. To overcome this deficiency, we propose PokeConv, a binary convolution block which improves quality of BNNs by techniques such as adding multiple residual paths, and tuning the activation function. We apply it to ResNet-50 and optimize ResNet's initial convolutional layer which is hard to binarize. We name the resulting network family PokeBNN. These techniques are chosen to yield favorable improvements in both top-1 accuracy and the network's cost. In order to enable joint optimization of the cost together with accuracy, we define arithmetic computation effort (ACE), a hardware- and energy-inspired cost metric for quantized and binarized networks. We also identify a need to optimize an under-explored hyper-parameter controlling the binarization gradient approximation. We establish a new, strong state-of-the-art (SOTA) on top-1 accuracy together with commonly-used CPU64 cost, ACE cost and network size metrics. ReActNet-Adam, the previous SOTA in BNNs, achieved a 70.5% top-1 accuracy with 7.9 ACE. A small variant of PokeBNN achieves 70.5% top-1 with 2.6 ACE, more than 3x reduction in cost; a larger PokeBNN achieves 75.6% top-1 with 7.8 ACE, more than 5% improvement in accuracy without increasing the cost. PokeBNN implementation in JAX/Flax and reproduction instructions are available in AQT repository: https://github.com/google/aqt

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

Neural architecture search (NAS) can have a significant impact in computer vision by automatically designing optimal neural network architectures for various tasks. A variant, binarized neural architecture search (BNAS), with a search space of binarized convolutions, can produce extremely compressed models. Unfortunately, this area remains largely unexplored. BNAS is more challenging than NAS due to the learning inefficiency caused by optimization requirements and the huge architecture space. To address these issues, we introduce channel sampling and operation space reduction into a differentiable NAS to significantly reduce the cost of searching. This is accomplished through a performance-based strategy used to abandon less potential operations. Two optimization methods for binarized neural networks are used to validate the effectiveness of our BNAS. Extensive experiments demonstrate that the proposed BNAS achieves a performance comparable to NAS on both CIFAR and ImageNet databases. An accuracy of 96.53% vs. 97.22% is achieved on the CIFAR-10 dataset, but with a significantly compressed model, and a 40% faster search than the state-of-the-art PC-DARTS.

We introduce a model-based asynchronous multi-fidelity method for hyperparameter and neural architecture search that combines the strengths of asynchronous Hyperband and Gaussian process-based Bayesian optimization. At the heart of our method is a probabilistic model that can simultaneously reason across hyperparameters and resource levels, and supports decision-making in the presence of pending evaluations. We demonstrate the effectiveness of our method on a wide range of challenging benchmarks, for tabular data, image classification and language modelling, and report substantial speed-ups over current state-of-the-art methods. Our new methods, along with asynchronous baselines, are implemented in a distributed framework which will be open sourced along with this publication.

Binarization of neural networks is a dominant paradigm in neural networks compression. The pioneering work BinaryConnect uses Straight Through Estimator (STE) to mimic the gradients of the sign function, but it also causes the crucial inconsistency problem. Most of the previous methods design different estimators instead of STE to mitigate it. However, they ignore the fact that when reducing the estimating error, the gradient stability will decrease concomitantly. These highly divergent gradients will harm the model training and increase the risk of gradient vanishing and gradient exploding. To fully take the gradient stability into consideration, we present a new perspective to the BNNs training, regarding it as the equilibrium between the estimating error and the gradient stability. In this view, we firstly design two indicators to quantitatively demonstrate the equilibrium phenomenon. In addition, in order to balance the estimating error and the gradient stability well, we revise the original straight through estimator and propose a power function based estimator, Rectified Straight Through Estimator (ReSTE for short). Comparing to other estimators, ReSTE is rational and capable of flexibly balancing the estimating error with the gradient stability. Extensive experiments on CIFAR-10 and ImageNet datasets show that ReSTE has excellent performance and surpasses the state-of-the-art methods without any auxiliary modules or losses.

A digital twin is a virtual replica of a real-world physical phenomena that uses mathematical modeling to characterize and simulate its defining features. By constructing digital twins for disease processes, we can perform in-silico simulations that mimic patients' health conditions and counterfactual outcomes under hypothetical interventions in a virtual setting. This eliminates the need for invasive procedures or uncertain treatment decisions. In this paper, we propose a method to identify digital twin model parameters using only noninvasive patient health data. We approach the digital twin modeling as a composite inverse problem, and observe that its structure resembles pretraining and finetuning in self-supervised learning (SSL). Leveraging this, we introduce a physics-informed SSL algorithm that initially pretrains a neural network on the pretext task of solving the physical model equations. Subsequently, the model is trained to reconstruct low-dimensional health measurements from noninvasive modalities while being constrained by the physical equations learned in pretraining. We apply our method to identify digital twins of cardiac hemodynamics using noninvasive echocardiogram videos, and demonstrate its utility in unsupervised disease detection and in-silico clinical trials.

Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing hypernetworks are often challenging to train. Training typically converges far more slowly than for non-hypernetwork models, and the rate of convergence can be very sensitive to hyperparameter choices. In this work, we identify a fundamental and previously unidentified problem that contributes to the challenge of training hypernetworks: a magnitude proportionality between the inputs and outputs of the hypernetwork. We demonstrate both analytically and empirically that this can lead to unstable optimization, thereby slowing down convergence, and sometimes even preventing any learning. We present a simple solution to this problem using a revised hypernetwork formulation that we call Magnitude Invariant Parametrizations (MIP). We demonstrate the proposed solution on several hypernetwork tasks, where it consistently stabilizes training and achieves faster convergence. Furthermore, we perform a comprehensive ablation study including choices of activation function, normalization strategies, input dimensionality, and hypernetwork architecture; and find that MIP improves training in all scenarios. We provide easy-to-use code that can turn existing networks into MIP-based hypernetworks.

We investigate the relationship between representation geometry and neural network performance. Analyzing 52 pretrained ImageNet models across 13 architecture families, we show that effective dimension -- an unsupervised geometric metric -- strongly predicts accuracy. Output effective dimension achieves partial r=0.75 (p < 10^(-10)) after controlling for model capacity, while total compression achieves partial r=-0.72. These findings replicate across ImageNet and CIFAR-10, and generalize to NLP: effective dimension predicts performance for 8 encoder models on SST-2/MNLI and 15 decoder-only LLMs on AG News (r=0.69, p=0.004), while model size does not (r=0.07). We establish bidirectional causality: degrading geometry via noise causes accuracy loss (r=-0.94, p < 10^(-9)), while improving geometry via PCA maintains accuracy across architectures (-0.03pp at 95% variance). This relationship is noise-type agnostic -- Gaussian, Uniform, Dropout, and Salt-and-pepper noise all show |r| > 0.90. These results establish that effective dimension provides domain-agnostic predictive and causal information about neural network performance, computed entirely without labels.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

Binary Neural Networks (BNNs) have emerged as a promising solution for reducing the memory footprint and compute costs of deep neural networks. BNNs, on the other hand, suffer from information loss because binary activations are limited to only two values, resulting in reduced accuracy. To improve the accuracy, previous studies have attempted to control the distribution of binary activation by manually shifting the threshold of the activation function or making the shift amount trainable. During the process, they usually depended on statistical information computed from a batch. We argue that using statistical data from a batch fails to capture the crucial information for each input instance in BNN computations, and the differences between statistical information computed from each instance need to be considered when determining the binary activation threshold of each instance. Based on the concept, we propose the Binary Neural Network with INSTAnce-aware threshold (INSTA-BNN), which decides the activation threshold value considering the difference between statistical data computed from a batch and each instance. The proposed INSTA-BNN outperforms the baseline by 2.5% and 2.3% on the ImageNet classification task with comparable computing cost, achieving 68.0% and 71.7% top-1 accuracy on ResNet-18 and MobileNetV1 based models, respectively.

While existing work on neural architecture search (NAS) tunes hyperparameters in a separate post-processing step, we demonstrate that architectural choices and other hyperparameter settings interact in a way that can render this separation suboptimal. Likewise, we demonstrate that the common practice of using very few epochs during the main NAS and much larger numbers of epochs during a post-processing step is inefficient due to little correlation in the relative rankings for these two training regimes. To combat both of these problems, we propose to use a recent combination of Bayesian optimization and Hyperband for efficient joint neural architecture and hyperparameter search.

Asymmetrical distance structures (quasimetrics) are ubiquitous in our lives and are gaining more attention in machine learning applications. Imposing such quasimetric structures in model representations has been shown to improve many tasks, including reinforcement learning (RL) and causal relation learning. In this work, we present four desirable properties in such quasimetric models, and show how prior works fail at them. We propose Interval Quasimetric Embedding (IQE), which is designed to satisfy all four criteria. On three quasimetric learning experiments, IQEs show strong approximation and generalization abilities, leading to better performance and improved efficiency over prior methods. Project Page: https://www.tongzhouwang.info/interval_quasimetric_embedding Quasimetric Learning Code Package: https://www.github.com/quasimetric-learning/torch-quasimetric

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean geometry, mostly because of the absence of corresponding hyperbolic neural network layers. This makes it hard to use hyperbolic embeddings in downstream tasks. Here, we bridge this gap in a principled manner by combining the formalism of Möbius gyrovector spaces with the Riemannian geometry of the Poincaré model of hyperbolic spaces. As a result, we derive hyperbolic versions of important deep learning tools: multinomial logistic regression, feed-forward and recurrent neural networks such as gated recurrent units. This allows to embed sequential data and perform classification in the hyperbolic space. Empirically, we show that, even if hyperbolic optimization tools are limited, hyperbolic sentence embeddings either outperform or are on par with their Euclidean variants on textual entailment and noisy-prefix recognition tasks.

Existing methods for evaluating graph generative models primarily rely on Maximum Mean Discrepancy (MMD) metrics based on graph descriptors. While these metrics can rank generative models, they do not provide an absolute measure of performance. Their values are also highly sensitive to extrinsic parameters, namely kernel and descriptor parametrization, making them incomparable across different graph descriptors. We introduce PolyGraph Discrepancy (PGD), a new evaluation framework that addresses these limitations. It approximates the Jensen-Shannon distance of graph distributions by fitting binary classifiers to distinguish between real and generated graphs, featurized by these descriptors. The data log-likelihood of these classifiers approximates a variational lower bound on the JS distance between the two distributions. Resulting metrics are constrained to the unit interval [0,1] and are comparable across different graph descriptors. We further derive a theoretically grounded summary metric that combines these individual metrics to provide a maximally tight lower bound on the distance for the given descriptors. Thorough experiments demonstrate that PGD provides a more robust and insightful evaluation compared to MMD metrics. The PolyGraph framework for benchmarking graph generative models is made publicly available at https://github.com/BorgwardtLab/polygraph-benchmark.

The ability to automatically estimate the quality and coverage of the samples produced by a generative model is a vital requirement for driving algorithm research. We present an evaluation metric that can separately and reliably measure both of these aspects in image generation tasks by forming explicit, non-parametric representations of the manifolds of real and generated data. We demonstrate the effectiveness of our metric in StyleGAN and BigGAN by providing several illustrative examples where existing metrics yield uninformative or contradictory results. Furthermore, we analyze multiple design variants of StyleGAN to better understand the relationships between the model architecture, training methods, and the properties of the resulting sample distribution. In the process, we identify new variants that improve the state-of-the-art. We also perform the first principled analysis of truncation methods and identify an improved method. Finally, we extend our metric to estimate the perceptual quality of individual samples, and use this to study latent space interpolations.

We propose two efficient approximations to standard convolutional neural networks: Binary-Weight-Networks and XNOR-Networks. In Binary-Weight-Networks, the filters are approximated with binary values resulting in 32x memory saving. In XNOR-Networks, both the filters and the input to convolutional layers are binary. XNOR-Networks approximate convolutions using primarily binary operations. This results in 58x faster convolutional operations and 32x memory savings. XNOR-Nets offer the possibility of running state-of-the-art networks on CPUs (rather than GPUs) in real-time. Our binary networks are simple, accurate, efficient, and work on challenging visual tasks. We evaluate our approach on the ImageNet classification task. The classification accuracy with a Binary-Weight-Network version of AlexNet is only 2.9% less than the full-precision AlexNet (in top-1 measure). We compare our method with recent network binarization methods, BinaryConnect and BinaryNets, and outperform these methods by large margins on ImageNet, more than 16% in top-1 accuracy.

Determining the optimal data mixture for large language model training remains a challenging problem with an outsized impact on performance. In practice, language model developers continue to rely on heuristic exploration since no learning-based approach has emerged as a reliable solution. In this work, we propose to view the selection of training data mixtures as a black-box hyperparameter optimization problem, for which Bayesian Optimization is a well-established class of appropriate algorithms. Firstly, we cast data mixture learning as a sequential decision-making problem, in which we aim to find a suitable trade-off between the computational cost of training exploratory (proxy-) models and final mixture performance. Secondly, we systematically explore the properties of transferring mixtures learned at a small scale to larger-scale experiments, providing insights and highlighting opportunities for research at a modest scale. By proposing Multi-fidelity Bayesian Optimization as a suitable method in this common scenario, we introduce a natural framework to balance experiment cost with model fit, avoiding the risks of overfitting to smaller scales while minimizing the number of experiments at high cost. We present results for pre-training and instruction finetuning across models ranging from 1 million to 7 billion parameters, varying from simple architectures to state-of-the-art models and benchmarks spanning dozens of datasets. We demonstrate consistently strong results relative to a wide range of baselines, resulting inspeed-ups of over 500% in determining the best data mixture on our largest experiments. In addition, we broaden access to research by sharing ADMIRE IFT Runs, a dataset of 460 full training & evaluation runs worth over 13,000 GPU hours, greatly reducing the cost of conducting research in this area.

Purpose: Accurate segmentation of clinical target volumes (CTV) and organs-at-risk is crucial for optimizing gynecologic brachytherapy (GYN-BT) treatment planning. However, anatomical variability, low soft-tissue contrast in CT imaging, and limited annotated datasets pose significant challenges. This study presents GynBTNet, a novel multi-stage learning framework designed to enhance segmentation performance through self-supervised pretraining and hierarchical fine-tuning strategies. Methods: GynBTNet employs a three-stage training strategy: (1) self-supervised pretraining on large-scale CT datasets using sparse submanifold convolution to capture robust anatomical representations, (2) supervised fine-tuning on a comprehensive multi-organ segmentation dataset to refine feature extraction, and (3) task-specific fine-tuning on a dedicated GYN-BT dataset to optimize segmentation performance for clinical applications. The model was evaluated against state-of-the-art methods using the Dice Similarity Coefficient (DSC), 95th percentile Hausdorff Distance (HD95), and Average Surface Distance (ASD). Results: Our GynBTNet achieved superior segmentation performance, significantly outperforming nnU-Net and Swin-UNETR. Notably, it yielded a DSC of 0.837 +/- 0.068 for CTV, 0.940 +/- 0.052 for the bladder, 0.842 +/- 0.070 for the rectum, and 0.871 +/- 0.047 for the uterus, with reduced HD95 and ASD compared to baseline models. Self-supervised pretraining led to consistent performance improvements, particularly for structures with complex boundaries. However, segmentation of the sigmoid colon remained challenging, likely due to anatomical ambiguities and inter-patient variability. Statistical significance analysis confirmed that GynBTNet's improvements were significant compared to baseline models.

Devising indicative evaluation metrics for the image generation task remains an open problem. The most widely used metric for measuring the similarity between real and generated images has been the Fr\'echet Inception Distance (FID) score. Because it does not differentiate the fidelity and diversity aspects of the generated images, recent papers have introduced variants of precision and recall metrics to diagnose those properties separately. In this paper, we show that even the latest version of the precision and recall metrics are not reliable yet. For example, they fail to detect the match between two identical distributions, they are not robust against outliers, and the evaluation hyperparameters are selected arbitrarily. We propose density and coverage metrics that solve the above issues. We analytically and experimentally show that density and coverage provide more interpretable and reliable signals for practitioners than the existing metrics. Code: https://github.com/clovaai/generative-evaluation-prdc.

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

Neural networks achieve remarkable performance through superposition: encoding multiple features as overlapping directions in activation space rather than dedicating individual neurons to each feature. This challenges interpretability, yet we lack principled methods to measure superposition. We present an information-theoretic framework measuring a neural representation's effective degrees of freedom. We apply Shannon entropy to sparse autoencoder activations to compute the number of effective features as the minimum neurons needed for interference-free encoding. Equivalently, this measures how many "virtual neurons" the network simulates through superposition. When networks encode more effective features than actual neurons, they must accept interference as the price of compression. Our metric strongly correlates with ground truth in toy models, detects minimal superposition in algorithmic tasks, and reveals systematic reduction under dropout. Layer-wise patterns mirror intrinsic dimensionality studies on Pythia-70M. The metric also captures developmental dynamics, detecting sharp feature consolidation during grokking. Surprisingly, adversarial training can increase effective features while improving robustness, contradicting the hypothesis that superposition causes vulnerability. Instead, the effect depends on task complexity and network capacity: simple tasks with ample capacity allow feature expansion (abundance regime), while complex tasks or limited capacity force reduction (scarcity regime). By defining superposition as lossy compression, this work enables principled measurement of how neural networks organize information under computational constraints, connecting superposition to adversarial robustness.

Deep neural networks have delivered remarkable performance and have been widely used in various visual tasks. However, their huge size causes significant inconvenience for transmission and storage. Many previous studies have explored model size compression. However, these studies often approach various lossy and lossless compression methods in isolation, leading to challenges in achieving high compression ratios efficiently. This work proposes a post-training model size compression method that combines lossy and lossless compression in a unified way. We first propose a unified parametric weight transformation, which ensures different lossy compression methods can be performed jointly in a post-training manner. Then, a dedicated differentiable counter is introduced to guide the optimization of lossy compression to arrive at a more suitable point for later lossless compression. Additionally, our method can easily control a desired global compression ratio and allocate adaptive ratios for different layers. Finally, our method can achieve a stable 10times compression ratio without sacrificing accuracy and a 20times compression ratio with minor accuracy loss in a short time. Our code is available at https://github.com/ModelTC/L2_Compression .

Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal transport-based differentiable Sinkhorn sorting algorithms to making classic sorting networks differentiable. One problem of current differentiable sorting methods is that they are non-monotonic. To address this issue, we propose a novel relaxation of conditional swap operations that guarantees monotonicity in differentiable sorting networks. We introduce a family of sigmoid functions and prove that they produce differentiable sorting networks that are monotonic. Monotonicity ensures that the gradients always have the correct sign, which is an advantage in gradient-based optimization. We demonstrate that monotonic differentiable sorting networks improve upon previous differentiable sorting methods.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by exponentiating a weighted sum of rectified and exponentiated components and a constant. We optimize the parameters of the full transformation (linear transform, exponents, weights, constant) over a database of natural images, directly minimizing the negentropy of the responses. The optimized transformation substantially Gaussianizes the data, achieving a significantly smaller mutual information between transformed components than alternative methods including ICA and radial Gaussianization. The transformation is differentiable and can be efficiently inverted, and thus induces a density model on images. We show that samples of this model are visually similar to samples of natural image patches. We demonstrate the use of the model as a prior probability density that can be used to remove additive noise. Finally, we show that the transformation can be cascaded, with each layer optimized using the same Gaussianization objective, thus offering an unsupervised method of optimizing a deep network architecture.

In the last decade, zero-cost metrics have gained prominence in neural architecture search (NAS) due to their ability to evaluate architectures without training. These metrics are significantly faster and less computationally expensive than traditional NAS methods and provide insights into neural architectures' internal workings. This paper introduces epsinas, a novel zero-cost NAS metric that assesses architecture potential using two constant shared weight initialisations and the statistics of their outputs. We show that the dispersion of raw outputs, normalised by their average magnitude, strongly correlates with trained accuracy. This effect holds across image classification and language tasks on NAS-Bench-101, NAS-Bench-201, and NAS-Bench-NLP. Our method requires no data labels, operates on a single minibatch, and eliminates the need for gradient computation, making it independent of training hyperparameters, loss metrics, and human annotations. It evaluates a network in a fraction of a GPU second and integrates seamlessly into existing NAS frameworks. The code supporting this study can be found on GitHub at https://github.com/egracheva/epsinas.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

Generating synthetic tabular data is critical in machine learning, especially when real data is limited or sensitive. Traditional generative models often face challenges due to the unique characteristics of tabular data, such as mixed data types and varied distributions, and require complex preprocessing or large pretrained models. In this paper, we introduce a novel, lossless binary transformation method that converts any tabular data into fixed-size binary representations, and a corresponding new generative model called Binary Diffusion, specifically designed for binary data. Binary Diffusion leverages the simplicity of XOR operations for noise addition and removal and employs binary cross-entropy loss for training. Our approach eliminates the need for extensive preprocessing, complex noise parameter tuning, and pretraining on large datasets. We evaluate our model on several popular tabular benchmark datasets, demonstrating that Binary Diffusion outperforms existing state-of-the-art models on Travel, Adult Income, and Diabetes datasets while being significantly smaller in size.

The performance of many machine learning models depends on their hyper-parameter settings. Bayesian Optimization has become a successful tool for hyper-parameter optimization of machine learning algorithms, which aims to identify optimal hyper-parameters during an iterative sequential process. However, most of the Bayesian Optimization algorithms are designed to select models for effectiveness only and ignore the important issue of model training efficiency. Given that both model effectiveness and training time are important for real-world applications, models selected for effectiveness may not meet the strict training time requirements necessary to deploy in a production environment. In this work, we present a unified Bayesian Optimization framework for jointly optimizing models for both prediction effectiveness and training efficiency. We propose an objective that captures the tradeoff between these two metrics and demonstrate how we can jointly optimize them in a principled Bayesian Optimization framework. Experiments on model selection for recommendation tasks indicate models selected this way significantly improves model training efficiency while maintaining strong effectiveness as compared to state-of-the-art Bayesian Optimization algorithms.

Recent findings suggest that the consecutive layers of ReLU neural networks can be understood geometrically as space folding transformations of the input space, revealing patterns of self-similarity. In this paper, we present the first quantitative analysis of this space folding phenomenon in ReLU neural networks. Our approach focuses on examining how straight paths in the Euclidean input space are mapped to their counterparts in the Hamming activation space. In this process, the convexity of straight lines is generally lost, giving rise to non-convex folding behavior. To quantify this effect, we introduce a novel measure based on range metrics, similar to those used in the study of random walks, and provide the proof for the equivalence of convexity notions between the input and activation spaces. Furthermore, we provide empirical analysis on a geometrical analysis benchmark (CantorNet) as well as an image classification benchmark (MNIST). Our work advances the understanding of the activation space in ReLU neural networks by leveraging the phenomena of geometric folding, providing valuable insights on how these models process input information.

Widely observed neural scaling laws, in which error falls off as a power of the training set size, model size, or both, have driven substantial performance improvements in deep learning. However, these improvements through scaling alone require considerable costs in compute and energy. Here we focus on the scaling of error with dataset size and show how in theory we can break beyond power law scaling and potentially even reduce it to exponential scaling instead if we have access to a high-quality data pruning metric that ranks the order in which training examples should be discarded to achieve any pruned dataset size. We then test this improved scaling prediction with pruned dataset size empirically, and indeed observe better than power law scaling in practice on ResNets trained on CIFAR-10, SVHN, and ImageNet. Next, given the importance of finding high-quality pruning metrics, we perform the first large-scale benchmarking study of ten different data pruning metrics on ImageNet. We find most existing high performing metrics scale poorly to ImageNet, while the best are computationally intensive and require labels for every image. We therefore developed a new simple, cheap and scalable self-supervised pruning metric that demonstrates comparable performance to the best supervised metrics. Overall, our work suggests that the discovery of good data-pruning metrics may provide a viable path forward to substantially improved neural scaling laws, thereby reducing the resource costs of modern deep learning.

Despite the remarkable capabilities, Large Language Models (LLMs) face deployment challenges due to their extensive size. Pruning methods drop a subset of weights to accelerate, but many of them require retraining, which is prohibitively expensive and computationally demanding. Recently, post-training pruning approaches introduced novel metrics, enabling the pruning of LLMs without retraining. However, these metrics require the involvement of human experts and tedious trial and error. To efficiently identify superior pruning metrics, we develop an automatic framework for searching symbolic pruning metrics using genetic programming. In particular, we devise an elaborate search space encompassing the existing pruning metrics to discover the potential symbolic pruning metric. We propose an opposing operation simplification strategy to increase the diversity of the population. In this way, Pruner-Zero allows auto-generation of symbolic pruning metrics. Based on the searched results, we explore the correlation between pruning metrics and performance after pruning and summarize some principles. Extensive experiments on LLaMA and LLaMA-2 on language modeling and zero-shot tasks demonstrate that our Pruner-Zero obtains superior performance than SOTA post-training pruning methods. Code at: https://github.com/pprp/Pruner-Zero.

Modern semantic search and retrieval-augmented generation (RAG) systems rely predominantly on in-memory approximate nearest neighbor (ANN) indexes over high-precision floating-point vectors, resulting in escalating operational cost and inherent trade-offs between latency, throughput, and retrieval accuracy. This paper analyzes the architectural limitations of the dominant "HNSW + float32 + cosine similarity" stack and evaluates existing cost-reduction strategies, including storage disaggregation and lossy vector quantization, which inevitably sacrifice either performance or accuracy. We introduce and empirically evaluate an alternative information-theoretic architecture based on maximally informative binarization (MIB), efficient bitwise distance metrics, and an information-theoretic scoring (ITS) mechanism. Unlike conventional ANN systems, this approach enables exhaustive search over compact binary representations, allowing deterministic retrieval and eliminating accuracy degradation under high query concurrency. Using the MAIR benchmark across 14 datasets and 10,038 queries, we compare this architecture against Elasticsearch, Pinecone, PGVector, and Qdrant. Results demonstrate retrieval quality comparable to full-precision systems, while achieving substantially lower latency and maintaining constant throughput at high request rates. We show that this architectural shift enables a truly serverless, cost-per-query deployment model, challenging the necessity of large in-memory ANN indexes for high-quality semantic search.

We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approximate Partial Differential Equations (PDEs) on manifolds, (iii) learn solution maps for Laplace-Beltrami (LB) operators, and (iv) to solve Bayesian inverse problems for identifying manifold shapes. The methods allow for handling geometries of general shape including point-cloud representations. The developed GNPs provide approaches for incorporating the roles of geometry in data-driven learning of operators.

While Minimum Bayes Risk (MBR) decoding using metrics such as COMET or MetricX has outperformed traditional decoding methods such as greedy or beam search, it introduces a challenge we refer to as metric bias. As MBR decoding aims to produce translations that score highly according to a specific utility metric, this very process makes it impossible to use the same metric for both decoding and evaluation, as improvements might simply be due to reward hacking rather than reflecting real quality improvements. In this work we find that compared to human ratings, neural metrics not only overestimate the quality of MBR decoding when the same metric is used as the utility metric, but they also overestimate the quality of MBR/QE decoding with other neural utility metrics as well. We also show that the metric bias issue can be mitigated by using an ensemble of utility metrics during MBR decoding: human evaluations show that MBR decoding using an ensemble of utility metrics outperforms a single utility metric.

Novel architectures have recently improved generative image synthesis leading to excellent visual quality in various tasks. Much of this success is due to the scalability of these architectures and hence caused by a dramatic increase in model complexity and in the computational resources invested in training these models. Our work questions the underlying paradigm of compressing large training data into ever growing parametric representations. We rather present an orthogonal, semi-parametric approach. We complement comparably small diffusion or autoregressive models with a separate image database and a retrieval strategy. During training we retrieve a set of nearest neighbors from this external database for each training instance and condition the generative model on these informative samples. While the retrieval approach is providing the (local) content, the model is focusing on learning the composition of scenes based on this content. As demonstrated by our experiments, simply swapping the database for one with different contents transfers a trained model post-hoc to a novel domain. The evaluation shows competitive performance on tasks which the generative model has not been trained on, such as class-conditional synthesis, zero-shot stylization or text-to-image synthesis without requiring paired text-image data. With negligible memory and computational overhead for the external database and retrieval we can significantly reduce the parameter count of the generative model and still outperform the state-of-the-art.

The discrepancy between the cost function used for training a speech enhancement model and human auditory perception usually makes the quality of enhanced speech unsatisfactory. Objective evaluation metrics which consider human perception can hence serve as a bridge to reduce the gap. Our previously proposed MetricGAN was designed to optimize objective metrics by connecting the metric with a discriminator. Because only the scores of the target evaluation functions are needed during training, the metrics can even be non-differentiable. In this study, we propose a MetricGAN+ in which three training techniques incorporating domain-knowledge of speech processing are proposed. With these techniques, experimental results on the VoiceBank-DEMAND dataset show that MetricGAN+ can increase PESQ score by 0.3 compared to the previous MetricGAN and achieve state-of-the-art results (PESQ score = 3.15).

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input to a neural network that outputs a second, interdependent distribution. Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models; however it is conceptually simpler in that no forward process is required. Discrete and continuous-time loss functions are derived for continuous, discretised and discrete data, along with sample generation procedures. Notably, the network inputs for discrete data lie on the probability simplex, and are therefore natively differentiable, paving the way for gradient-based sample guidance and few-step generation in discrete domains such as language modelling. The loss function directly optimises data compression and places no restrictions on the network architecture. In our experiments BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

Uniformity plays a crucial role in the assessment of learned representations, contributing to a deeper comprehension of self-supervised learning. The seminal work by Wang2020UnderstandingCR introduced a uniformity metric that quantitatively measures the collapse degree of learned representations. Directly optimizing this metric together with alignment proves to be effective in preventing constant collapse. However, we present both theoretical and empirical evidence revealing that this metric lacks sensitivity to dimensional collapse, highlighting its limitations. To address this limitation and design a more effective uniformity metric, this paper identifies five fundamental properties, some of which the existing uniformity metric fails to meet. We subsequently introduce a novel uniformity metric that satisfies all of these desiderata and exhibits sensitivity to dimensional collapse. When applied as an auxiliary loss in various established self-supervised methods, our proposed uniformity metric consistently enhances their performance in downstream tasks.Our code was released at https://github.com/sunset-clouds/WassersteinUniformityMetric.

This work focuses on addressing two major challenges in the context of large-scale nonconvex Bi-Level Optimization (BLO) problems, which are increasingly applied in machine learning due to their ability to model nested structures. These challenges involve ensuring computational efficiency and providing theoretical guarantees. While recent advances in scalable BLO algorithms have primarily relied on lower-level convexity simplification, our work specifically tackles large-scale BLO problems involving nonconvexity in both the upper and lower levels. We simultaneously address computational and theoretical challenges by introducing an innovative single-loop gradient-based algorithm, utilizing the Moreau envelope-based reformulation, and providing non-asymptotic convergence analysis for general nonconvex BLO problems. Notably, our algorithm relies solely on first-order gradient information, enhancing its practicality and efficiency, especially for large-scale BLO learning tasks. We validate our approach's effectiveness through experiments on various synthetic problems, two typical hyper-parameter learning tasks, and a real-world neural architecture search application, collectively demonstrating its superior performance.

Current model quantization methods have shown their promising capability in reducing storage space and computation complexity. However, due to the diversity of quantization forms supported by different hardware, one limitation of existing solutions is that usually require repeated optimization for different scenarios. How to construct a model with flexible quantization forms has been less studied. In this paper, we explore a one-shot network quantization regime, named Elastic Quantization Neural Networks (EQ-Net), which aims to train a robust weight-sharing quantization supernet. First of all, we propose an elastic quantization space (including elastic bit-width, granularity, and symmetry) to adapt to various mainstream quantitative forms. Secondly, we propose the Weight Distribution Regularization Loss (WDR-Loss) and Group Progressive Guidance Loss (GPG-Loss) to bridge the inconsistency of the distribution for weights and output logits in the elastic quantization space gap. Lastly, we incorporate genetic algorithms and the proposed Conditional Quantization-Aware Accuracy Predictor (CQAP) as an estimator to quickly search mixed-precision quantized neural networks in supernet. Extensive experiments demonstrate that our EQ-Net is close to or even better than its static counterparts as well as state-of-the-art robust bit-width methods. Code can be available at https://github.com/xuke225/EQ-Net.git{https://github.com/xuke225/EQ-Net}.

Classical convergence guarantees for gradient-based learning in games require the pseudo-gradient to be (strongly) monotone in Euclidean geometry as shown by rosen(1965), a condition that often fails even in simple games with strong cross-player couplings. We introduce Small-Gain Nash (SGN), a block small-gain condition in a custom block-weighted geometry. SGN converts local curvature and cross-player Lipschitz coupling bounds into a tractable certificate of contraction. It constructs a weighted block metric in which the pseudo-gradient becomes strongly monotone on any region where these bounds hold, even when it is non-monotone in the Euclidean sense. The continuous flow is exponentially contracting in this designed geometry, and projected Euler and RK4 discretizations converge under explicit step-size bounds derived from the SGN margin and a local Lipschitz constant. Our analysis reveals a certified ``timescale band'', a non-asymptotic, metric-based certificate that plays a TTUR-like role: rather than forcing asymptotic timescale separation via vanishing, unequal step sizes, SGN identifies a finite band of relative metric weights for which a single-step-size dynamics is provably contractive. We validate the framework on quadratic games where Euclidean monotonicity analysis fails to predict convergence, but SGN successfully certifies it, and extend the construction to mirror/Fisher geometries for entropy-regularized policy gradient in Markov games. The result is an offline certification pipeline that estimates curvature, coupling, and Lipschitz parameters on compact regions, optimizes block weights to enlarge the SGN margin, and returns a structural, computable convergence certificate consisting of a metric, contraction rate, and safe step-sizes for non-monotone games.

In many neural networks, different values of the parameters may result in the same loss value. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm's success is not well understood. In this paper, we show that teleportation not only speeds up optimization in the short-term, but gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minimum and generalization ability. Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.

In this paper, we show that a binary latent space can be explored for compact yet expressive image representations. We model the bi-directional mappings between an image and the corresponding latent binary representation by training an auto-encoder with a Bernoulli encoding distribution. On the one hand, the binary latent space provides a compact discrete image representation of which the distribution can be modeled more efficiently than pixels or continuous latent representations. On the other hand, we now represent each image patch as a binary vector instead of an index of a learned cookbook as in discrete image representations with vector quantization. In this way, we obtain binary latent representations that allow for better image quality and high-resolution image representations without any multi-stage hierarchy in the latent space. In this binary latent space, images can now be generated effectively using a binary latent diffusion model tailored specifically for modeling the prior over the binary image representations. We present both conditional and unconditional image generation experiments with multiple datasets, and show that the proposed method performs comparably to state-of-the-art methods while dramatically improving the sampling efficiency to as few as 16 steps without using any test-time acceleration. The proposed framework can also be seamlessly scaled to 1024 times 1024 high-resolution image generation without resorting to latent hierarchy or multi-stage refinements.

In Neural Architecture Search (NAS), reducing the cost of architecture evaluation remains one of the most crucial challenges. Among a plethora of efforts to bypass training of each candidate architecture to convergence for evaluation, the Neural Tangent Kernel (NTK) is emerging as a promising theoretical framework that can be utilized to estimate the performance of a neural architecture at initialization. In this work, we revisit several at-initialization metrics that can be derived from the NTK and reveal their key shortcomings. Then, through the empirical analysis of the time evolution of NTK, we deduce that modern neural architectures exhibit highly non-linear characteristics, making the NTK-based metrics incapable of reliably estimating the performance of an architecture without some amount of training. To take such non-linear characteristics into account, we introduce Label-Gradient Alignment (LGA), a novel NTK-based metric whose inherent formulation allows it to capture the large amount of non-linear advantage present in modern neural architectures. With minimal amount of training, LGA obtains a meaningful level of rank correlation with the post-training test accuracy of an architecture. Lastly, we demonstrate that LGA, complemented with few epochs of training, successfully guides existing search algorithms to achieve competitive search performances with significantly less search cost. The code is available at: https://github.com/nutellamok/DemystifyingNTK.

We discuss methods for modeling eclipsing binary stars using the "physical", "simplified" and "phenomenological" models. There are few realizations of the "physical" Wilson-Devinney (1971) code and its improvements, e.g. Binary Maker, Phoebe. A parameter search using the Monte-Carlo method was realized by Zola et al. (2010), which is efficient in expense of too many evaluations of the test function. We compare existing algorithms of minimization of multi-parametric functions and propose to use a "combined" algorithm, depending on if the Hessian matrix is positively determined. To study methods, a simply fast-computed function resembling the "complete" test function for the physical model. Also we adopt a simplified model of an eclipsing binary at a circular orbit assuming spherical components with an uniform brightness distribution. This model resembles more advanced models in a sense of correlated parameter estimates due to a similar topology of the test function. Such a model may be applied to detached Algol-type systems, where the tidal distortion of components is negligible.

We introduce the Bittensor Language Model, called "BTLM-3B-8K", a new state-of-the-art 3 billion parameter open-source language model. BTLM-3B-8K was trained on 627B tokens from the SlimPajama dataset with a mixture of 2,048 and 8,192 context lengths. BTLM-3B-8K outperforms all existing 3B parameter models by 2-5.5% across downstream tasks. BTLM-3B-8K is even competitive with some 7B parameter models. Additionally, BTLM-3B-8K provides excellent long context performance, outperforming MPT-7B-8K and XGen-7B-8K on tasks up to 8,192 context length. We trained the model on a cleaned and deduplicated SlimPajama dataset; aggressively tuned the \textmu P hyperparameters and schedule; used ALiBi position embeddings; and adopted the SwiGLU nonlinearity. On Hugging Face, the most popular models have 7B parameters, indicating that users prefer the quality-size ratio of 7B models. Compacting the 7B parameter model to one with 3B parameters, with little performance impact, is an important milestone. BTLM-3B-8K needs only 3GB of memory with 4-bit precision and takes 2.5x less inference compute than 7B models, helping to open up access to a powerful language model on mobile and edge devices. BTLM-3B-8K is available under an Apache 2.0 license on Hugging Face: https://huggingface.co/cerebras/btlm-3b-8k-base.

Machine learning models are often tuned by nesting optimization of model weights inside the optimization of hyperparameters. We give a method to collapse this nested optimization into joint stochastic optimization of weights and hyperparameters. Our process trains a neural network to output approximately optimal weights as a function of hyperparameters. We show that our technique converges to locally optimal weights and hyperparameters for sufficiently large hypernetworks. We compare this method to standard hyperparameter optimization strategies and demonstrate its effectiveness for tuning thousands of hyperparameters.

Next generations of radio surveys are expected to identify tens of millions of new sources, and identifying and classifying their morphologies will require novel and more efficient methods. Self-Organising Maps (SOMs), a type of unsupervised machine learning, can be used to address this problem. We map 251,259 multi-Gaussian sources from Rapid ASKAP Continuum Survey (RACS) onto a SOM with discrete neurons. Similarity metrics, such as Euclidean distances, can be used to identify the best-matching neuron or unit (BMU) for each input image. We establish a reliability threshold by visually inspecting a subset of input images and their corresponding BMU. We label the individual neurons based on observed morphologies and these labels are included in our value-added catalogue of RACS sources. Sources for which the Euclidean distance to their BMU is lesssim 5 (accounting for approximately 79% of sources) have an estimated >90% reliability for their SOM-derived morphological labels. This reliability falls to less than 70% at Euclidean distances gtrsim 7. Beyond this threshold it is unlikely that the morphological label will accurately describe a given source. Our catalogue of complex radio sources from RACS with their SOM-derived morphological labels from this work will be made publicly available.

We propose a tuning-free dynamic SGD step size formula, which we call Distance over Gradients (DoG). The DoG step sizes depend on simple empirical quantities (distance from the initial point and norms of gradients) and have no ``learning rate'' parameter. Theoretically, we show that a slight variation of the DoG formula enjoys strong parameter-free convergence guarantees for stochastic convex optimization assuming only locally bounded stochastic gradients. Empirically, we consider a broad range of vision and language transfer learning tasks, and show that DoG's performance is close to that of SGD with tuned learning rate. We also propose a per-layer variant of DoG that generally outperforms tuned SGD, approaching the performance of tuned Adam. A PyTorch implementation is available at https://github.com/formll/dog

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised deep-learning applications, these methods tend to be less adequate when there is large intra-class variance and low inter-class variance in input data distribution. Deep Metric Learning seeks to develop methods that aim to measure the similarity between data samples by learning a representation function that maps these data samples into a representative embedding space. It leverages carefully designed sampling strategies and loss functions that aid in optimizing the generation of a discriminative embedding space even for distributions having low inter-class and high intra-class variances. In this chapter, we will provide an overview of recent progress in this area and discuss state-of-the-art Deep Metric Learning approaches.

For many evaluation metrics commonly used as benchmarks for unconditional image generation, trivially memorizing the training set attains a better score than models which are considered state-of-the-art; we consider this problematic. We clarify a necessary condition for an evaluation metric not to behave this way: estimating the function must require a large sample from the model. In search of such a metric, we turn to neural network divergences (NNDs), which are defined in terms of a neural network trained to distinguish between distributions. The resulting benchmarks cannot be "won" by training set memorization, while still being perceptually correlated and computable only from samples. We survey past work on using NNDs for evaluation and implement an example black-box metric based on these ideas. Through experimental validation we show that it can effectively measure diversity, sample quality, and generalization.

In this paper, we aim to bridge test-time-training with a new type of parametric memory that can be flexibly offloaded from or merged into model parameters. We present Locas, a Locally-Supported parametric memory that shares the design of FFN blocks in modern transformers, allowing it to be flexibly permanentized into the model parameters while supporting efficient continual learning. We discuss two major variants of Locas: one with a conventional two-layer MLP design that has a clearer theoretical guarantee; the other one shares the same GLU-FFN structure with SOTA LLMs, and can be easily attached to existing models for both parameter-efficient and computation-efficient continual learning. Crucially, we show that proper initialization of such low-rank sideway-FFN-style memories -- performed in a principled way by reusing model parameters, activations and/or gradients -- is essential for fast convergence, improved generalization, and catastrophic forgetting prevention. We validate the proposed memory mechanism on the PG-19 whole-book language modeling and LoCoMo long-context dialogue question answering tasks. With only 0.02\% additional parameters in the lowest case, Locas-GLU is capable of storing the information from past context while maintaining a much smaller context window. In addition, we also test the model's general capability loss after memorizing the whole book with Locas, through comparative MMLU evaluation. Results show the promising ability of Locas to permanentize past context into parametric knowledge with minimized catastrophic forgetting of the model's existing internal knowledge.

Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact best-response for a shallow linear network with L2-regularized Jacobian can be represented by a similar gating mechanism. We fit this model using a gradient-based hyperparameter optimization algorithm which alternates between approximating the best-response around the current hyperparameters and optimizing the hyperparameters using the approximate best-response function. Unlike other gradient-based approaches, we do not require differentiating the training loss with respect to the hyperparameters, allowing us to tune discrete hyperparameters, data augmentation hyperparameters, and dropout probabilities. Because the hyperparameters are adapted online, our approach discovers hyperparameter schedules that can outperform fixed hyperparameter values. Empirically, our approach outperforms competing hyperparameter optimization methods on large-scale deep learning problems. We call our networks, which update their own hyperparameters online during training, Self-Tuning Networks (STNs).

Various tasks in data science are modeled utilizing the variational regularization approach, where manually selecting regularization parameters presents a challenge. The difficulty gets exacerbated when employing regularizers involving a large number of hyperparameters. To overcome this challenge, bilevel learning can be employed to learn such parameters from data. However, neither exact function values nor exact gradients with respect to the hyperparameters are attainable, necessitating methods that only rely on inexact evaluation of such quantities. State-of-the-art inexact gradient-based methods a priori select a sequence of the required accuracies and cannot identify an appropriate step size since the Lipschitz constant of the hypergradient is unknown. In this work, we propose an algorithm with backtracking line search that only relies on inexact function evaluations and hypergradients and show convergence to a stationary point. Furthermore, the proposed algorithm determines the required accuracy dynamically rather than manually selected before running it. Our numerical experiments demonstrate the efficiency and feasibility of our approach for hyperparameter estimation on a range of relevant problems in imaging and data science such as total variation and field of experts denoising and multinomial logistic regression. Particularly, the results show that the algorithm is robust to its own hyperparameters such as the initial accuracies and step size.

As with many machine learning problems, the progress of image generation methods hinges on good evaluation metrics. One of the most popular is the Frechet Inception Distance (FID). FID estimates the distance between a distribution of Inception-v3 features of real images, and those of images generated by the algorithm. We highlight important drawbacks of FID: Inception's poor representation of the rich and varied content generated by modern text-to-image models, incorrect normality assumptions, and poor sample complexity. We call for a reevaluation of FID's use as the primary quality metric for generated images. We empirically demonstrate that FID contradicts human raters, it does not reflect gradual improvement of iterative text-to-image models, it does not capture distortion levels, and that it produces inconsistent results when varying the sample size. We also propose an alternative new metric, CMMD, based on richer CLIP embeddings and the maximum mean discrepancy distance with the Gaussian RBF kernel. It is an unbiased estimator that does not make any assumptions on the probability distribution of the embeddings and is sample efficient. Through extensive experiments and analysis, we demonstrate that FID-based evaluations of text-to-image models may be unreliable, and that CMMD offers a more robust and reliable assessment of image quality.

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support exact inference. While standard GP surrogates have been well-established in Bayesian optimization, Bayesian neural networks (BNNs) have recently become practical function approximators, with many benefits over standard GPs such as the ability to naturally handle non-stationarity and learn representations for high-dimensional data. In this paper, we study BNNs as alternatives to standard GP surrogates for optimization. We consider a variety of approximate inference procedures for finite-width BNNs, including high-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics such as deep ensembles. We also consider infinite-width BNNs and partially stochastic models such as deep kernel learning. We evaluate this collection of surrogate models on diverse problems with varying dimensionality, number of objectives, non-stationarity, and discrete and continuous inputs. We find: (i) the ranking of methods is highly problem dependent, suggesting the need for tailored inductive biases; (ii) HMC is the most successful approximate inference procedure for fully stochastic BNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is relatively competitive; (iv) infinite-width BNNs are particularly promising, especially in high dimensions.

Our world is full of asymmetries. Gravity and wind can make reaching a place easier than coming back. Social artifacts such as genealogy charts and citation graphs are inherently directed. In reinforcement learning and control, optimal goal-reaching strategies are rarely reversible (symmetrical). Distance functions supported on these asymmetrical structures are called quasimetrics. Despite their common appearance, little research has been done on the learning of quasimetrics. Our theoretical analysis reveals that a common class of learning algorithms, including unconstrained multilayer perceptrons (MLPs), provably fails to learn a quasimetric consistent with training data. In contrast, our proposed Poisson Quasimetric Embedding (PQE) is the first quasimetric learning formulation that both is learnable with gradient-based optimization and enjoys strong performance guarantees. Experiments on random graphs, social graphs, and offline Q-learning demonstrate its effectiveness over many common baselines.

We propose a simple pairwise sigmoid loss for image-text pre-training. Unlike standard contrastive learning with softmax normalization, the sigmoid loss operates solely on image-text pairs and does not require a global view of the pairwise similarities for normalization. The sigmoid loss simultaneously allows further scaling up the batch size, while also performing better at smaller batch sizes. With only four TPUv4 chips, we can train a Base CLIP model at 4k batch size and a Large LiT model at 20k batch size, the latter achieves 84.5% ImageNet zero-shot accuracy in two days. This disentanglement of the batch size from the loss further allows us to study the impact of examples vs pairs and negative to positive ratio. Finally, we push the batch size to the extreme, up to one million, and find that the benefits of growing batch size quickly diminish, with a more reasonable batch size of 32k being sufficient. We hope our research motivates further explorations in improving the quality and efficiency of language-image pre-training.

Precision and Recall are two prominent metrics of generative performance, which were proposed to separately measure the fidelity and diversity of generative models. Given their central role in comparing and improving generative models, understanding their limitations are crucially important. To that end, in this work, we identify a critical flaw in the common approximation of these metrics using k-nearest-neighbors, namely, that the very interpretations of fidelity and diversity that are assigned to Precision and Recall can fail in high dimensions, resulting in very misleading conclusions. Specifically, we empirically and theoretically show that as the number of dimensions grows, two model distributions with supports at equal point-wise distance from the support of the real distribution, can have vastly different Precision and Recall regardless of their respective distributions, hence an emergent asymmetry in high dimensions. Based on our theoretical insights, we then provide simple yet effective modifications to these metrics to construct symmetric metrics regardless of the number of dimensions. Finally, we provide experiments on real-world datasets to illustrate that the identified flaw is not merely a pathological case, and that our proposed metrics are effective in alleviating its impact.

Prevailing Multimodal Large Language Models (MLLMs) encode the input image(s) as vision tokens and feed them into the language backbone, similar to how Large Language Models (LLMs) process the text tokens. However, the number of vision tokens increases quadratically as the image resolutions, leading to huge computational costs. In this paper, we consider improving MLLM's efficiency from two scenarios, (I) Reducing computational cost without degrading the performance. (II) Improving the performance with given budgets. We start with our main finding that the ranking of each vision token sorted by attention scores is similar in each layer except the first layer. Based on it, we assume that the number of essential top vision tokens does not increase along layers. Accordingly, for Scenario I, we propose a greedy search algorithm (G-Search) to find the least number of vision tokens to keep at each layer from the shallow to the deep. Interestingly, G-Search is able to reach the optimal reduction strategy based on our assumption. For Scenario II, based on the reduction strategy from G-Search, we design a parametric sigmoid function (P-Sigmoid) to guide the reduction at each layer of the MLLM, whose parameters are optimized by Bayesian Optimization. Extensive experiments demonstrate that our approach can significantly accelerate those popular MLLMs, e.g. LLaVA, and InternVL2 models, by more than 2 times without performance drops. Our approach also far outperforms other token reduction methods when budgets are limited, achieving a better trade-off between efficiency and effectiveness.

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

Serving Large Language Models (LLMs) is costly. However, post-training weight quantization can address this problem by both compressing their sizes for limited memory and saving bandwidth for acceleration. As not all weight dimensions are equally important, those methods typically rely on a sensitivity metric, which indicates the element-wise influence of weights on loss function and is used to preprocess original weights for better quantization. In this work, we conduct an empirical study on the accuracy of the sensitivity metric, and find that existing gradient and Hessian based metrics are very inaccurate: they underestimate quantization's impact on the loss function by orders of magnitude, mainly due to the small convergence radius of local 2nd order approximation, \ie, gradient and Hessian term in Taylor's formula. To tackle this problem, we propose Post-quantization Integral (PQI), an accurate metric to estimate posterior sensitivity in a fine-grained manner. To leverage this accurate metric, we further propose ReQuant, a simple yet powerful framework that mainly consists of two Dense-and-Sparse detach components: self-adaptive outlier selection and step-wise significant weights detach. Results show that ReQuant boosts state-of-the-art post-training quantization methods, with a pronounced improvement of 2.66 perplexity gain on Llama 3.2 1B with QTIP.

Perceptual similarity metrics have progressively become more correlated with human judgments on perceptual similarity; however, despite recent advances, the addition of an imperceptible distortion can still compromise these metrics. In our study, we systematically examine the robustness of these metrics to imperceptible adversarial perturbations. Following the two-alternative forced-choice experimental design with two distorted images and one reference image, we perturb the distorted image closer to the reference via an adversarial attack until the metric flips its judgment. We first show that all metrics in our study are susceptible to perturbations generated via common adversarial attacks such as FGSM, PGD, and the One-pixel attack. Next, we attack the widely adopted LPIPS metric using spatial-transformation-based adversarial perturbations (stAdv) in a white-box setting to craft adversarial examples that can effectively transfer to other similarity metrics in a black-box setting. We also combine the spatial attack stAdv with PGD (ell_infty-bounded) attack to increase transferability and use these adversarial examples to benchmark the robustness of both traditional and recently developed metrics. Our benchmark provides a good starting point for discussion and further research on the robustness of metrics to imperceptible adversarial perturbations.

Dynamic model pruning is a recent direction that allows for the inference of a different sub-network for each input sample during deployment. However, current dynamic methods rely on learning a continuous channel gating through regularization by inducing sparsity loss. This formulation introduces complexity in balancing different losses (e.g task loss, regularization loss). In addition, regularization based methods lack transparent tradeoff hyperparameter selection to realize a computational budget. Our contribution is two-fold: 1) decoupled task and pruning losses. 2) Simple hyperparameter selection that enables FLOPs reduction estimation before training. Inspired by the Hebbian theory in Neuroscience: "neurons that fire together wire together", we propose to predict a mask to process k filters in a layer based on the activation of its previous layer. We pose the problem as a self-supervised binary classification problem. Each mask predictor module is trained to predict if the log-likelihood for each filter in the current layer belongs to the top-k activated filters. The value k is dynamically estimated for each input based on a novel criterion using the mass of heatmaps. We show experiments on several neural architectures, such as VGG, ResNet and MobileNet on CIFAR and ImageNet datasets. On CIFAR, we reach similar accuracy to SOTA methods with 15% and 24% higher FLOPs reduction. Similarly in ImageNet, we achieve lower drop in accuracy with up to 13% improvement in FLOPs reduction.

This paper establishes a mathematical foundation for the Adam optimizer, elucidating its connection to natural gradient descent through Riemannian and information geometry. We rigorously analyze the diagonal empirical Fisher information matrix (FIM) in Adam, clarifying all detailed approximations and advocating for the use of log probability functions as loss, which should be based on discrete distributions, due to the limitations of empirical FIM. Our analysis uncovers flaws in the original Adam algorithm, leading to proposed corrections such as enhanced momentum calculations, adjusted bias corrections, and gradient clipping. We refine the weight decay term based on our theoretical framework. Our modified algorithm, Fisher Adam (FAdam), demonstrates superior performance across diverse domains including LLM, ASR, and VQ-VAE, achieving state-of-the-art results in ASR.

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their statistical efficiency or quantified estimator uncertainty in data-limited regimes. Here, we derive upper and lower bounds on the worst-case convergence of standard estimators of shape distancex2014a measure of representational dissimilarity proposed by Williams et al. (2021).These bounds reveal the challenging nature of the problem in high-dimensional feature spaces. To overcome these challenges, we introduce a new method-of-moments estimator with a tunable bias-variance tradeoff. We show that this estimator achieves substantially lower bias than standard estimators in simulation and on neural data, particularly in high-dimensional settings. Thus, we lay the foundation for a rigorous statistical theory for high-dimensional shape analysis, and we contribute a new estimation method that is well-suited to practical scientific settings.

Recent studies show that paddings in convolutional neural networks encode absolute position information which can negatively affect the model performance for certain tasks. However, existing metrics for quantifying the strength of positional information remain unreliable and frequently lead to erroneous results. To address this issue, we propose novel metrics for measuring (and visualizing) the encoded positional information. We formally define the encoded information as PPP (Position-information Pattern from Padding) and conduct a series of experiments to study its properties as well as its formation. The proposed metrics measure the presence of positional information more reliably than the existing metrics based on PosENet and a test in F-Conv. We also demonstrate that for any extant (and proposed) padding schemes, PPP is primarily a learning artifact and is less dependent on the characteristics of the underlying padding schemes.

In the domain of medical imaging, many supervised learning based methods for segmentation face several challenges such as high variability in annotations from multiple experts, paucity of labelled data and class imbalanced datasets. These issues may result in segmentations that lack the requisite precision for clinical analysis and can be misleadingly overconfident without associated uncertainty quantification. We propose the PULASki for biomedical image segmentation that accurately captures variability in expert annotations, even in small datasets. Our approach makes use of an improved loss function based on statistical distances in a conditional variational autoencoder structure (Probabilistic UNet), which improves learning of the conditional decoder compared to the standard cross-entropy particularly in class imbalanced problems. We analyse our method for two structurally different segmentation tasks (intracranial vessel and multiple sclerosis (MS) lesion) and compare our results to four well-established baselines in terms of quantitative metrics and qualitative output. Empirical results demonstrate the PULASKi method outperforms all baselines at the 5\% significance level. The generated segmentations are shown to be much more anatomically plausible than in the 2D case, particularly for the vessel task. Our method can also be applied to a wide range of multi-label segmentation tasks and and is useful for downstream tasks such as hemodynamic modelling (computational fluid dynamics and data assimilation), clinical decision making, and treatment planning.

Population Based Training (PBT) is an efficient hyperparameter optimization algorithm. PBT is a single-objective algorithm, but many real-world hyperparameter optimization problems involve two or more conflicting objectives. In this work, we therefore introduce a multi-objective version of PBT, MO-PBT. Our experiments on diverse multi-objective hyperparameter optimization problems (Precision/Recall, Accuracy/Fairness, Accuracy/Adversarial Robustness) show that MO-PBT outperforms random search, single-objective PBT, and the state-of-the-art multi-objective hyperparameter optimization algorithm MO-ASHA.

With the advancement of diffusion models (DMs) and the substantially increased computational requirements, quantization emerges as a practical solution to obtain compact and efficient low-bit DMs. However, the highly discrete representation leads to severe accuracy degradation, hindering the quantization of diffusion models to ultra-low bit-widths. In this paper, we propose BinaryDM, a novel accurate quantization-aware training approach to push the weights of diffusion models towards the limit of 1-bit. Firstly, we present a Learnable Multi-basis Binarizer (LMB) to recover the representations generated by the binarized DM, which improves the information in details of representations crucial to the DM. Secondly, a Low-rank Representation Mimicking (LRM) is applied to enhance the binarization-aware optimization of the DM, alleviating the optimization direction ambiguity caused by fine-grained alignment. Moreover, a progressive initialization strategy is applied to training DMs to avoid convergence difficulties. Comprehensive experiments demonstrate that BinaryDM achieves significant accuracy and efficiency gains compared to SOTA quantization methods of DMs under ultra-low bit-widths. As the first binarization method for diffusion models, BinaryDM achieves impressive 16.0 times FLOPs and 27.1 times storage savings with 1-bit weight and 4-bit activation, showcasing its substantial advantages and potential for deploying DMs on resource-limited scenarios.

Binarization, which converts weight parameters to binary values, has emerged as an effective strategy to reduce the size of large language models (LLMs). However, typical binarization techniques significantly diminish linguistic effectiveness of LLMs. To address this issue, we introduce a novel binarization technique called Mixture of Scales (BinaryMoS). Unlike conventional methods, BinaryMoS employs multiple scaling experts for binary weights, dynamically merging these experts for each token to adaptively generate scaling factors. This token-adaptive approach boosts the representational power of binarized LLMs by enabling contextual adjustments to the values of binary weights. Moreover, because this adaptive process only involves the scaling factors rather than the entire weight matrix, BinaryMoS maintains compression efficiency similar to traditional static binarization methods. Our experimental results reveal that BinaryMoS surpasses conventional binarization techniques in various natural language processing tasks and even outperforms 2-bit quantization methods, all while maintaining similar model size to static binarization techniques.

Neural architecture search (NAS) has become a key component of AutoML and a standard tool to automate the design of deep neural networks. Recently, training-free NAS as an emerging paradigm has successfully reduced the search costs of standard training-based NAS by estimating the true architecture performance with only training-free metrics. Nevertheless, the estimation ability of these metrics typically varies across different tasks, making it challenging to achieve robust and consistently good search performance on diverse tasks with only a single training-free metric. Meanwhile, the estimation gap between training-free metrics and the true architecture performances limits training-free NAS to achieve superior performance. To address these challenges, we propose the robustifying and boosting training-free NAS (RoBoT) algorithm which (a) employs the optimized combination of existing training-free metrics explored from Bayesian optimization to develop a robust and consistently better-performing metric on diverse tasks, and (b) applies greedy search, i.e., the exploitation, on the newly developed metric to bridge the aforementioned gap and consequently to boost the search performance of standard training-free NAS further. Remarkably, the expected performance of our RoBoT can be theoretically guaranteed, which improves over the existing training-free NAS under mild conditions with additional interesting insights. Our extensive experiments on various NAS benchmark tasks yield substantial empirical evidence to support our theoretical results.

We propose a novel neural deformable model (NDM) targeting at the reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D sparse cardiac magnetic resonance (CMR) imaging data. We model the bi-ventricular shape using blended deformable superquadrics, which are parameterized by a set of geometric parameter functions and are capable of deforming globally and locally. While global geometric parameter functions and deformations capture gross shape features from visual data, local deformations, parameterized as neural diffeomorphic point flows, can be learned to recover the detailed heart shape.Different from iterative optimization methods used in conventional deformable model formulations, NDMs can be trained to learn such geometric parameter functions, global and local deformations from a shape distribution manifold. Our NDM can learn to densify a sparse cardiac point cloud with arbitrary scales and generate high-quality triangular meshes automatically. It also enables the implicit learning of dense correspondences among different heart shape instances for accurate cardiac shape registration. Furthermore, the parameters of NDM are intuitive, and can be used by a physician without sophisticated post-processing. Experimental results on a large CMR dataset demonstrate the improved performance of NDM over conventional methods.

Automatic metrics are now central to evaluating text-to-image models, often substituting for human judgment in benchmarking and large-scale filtering. However, it remains unclear whether these metrics truly prioritize semantic correctness or instead favor visually and socially prototypical images learned from biased data distributions. We identify and study prototypicality bias as a systematic failure mode in multimodal evaluation. We introduce a controlled contrastive benchmark ProtoBias (Prototypical Bias), spanning Animals, Objects, and Demography images, where semantically correct but non-prototypical images are paired with subtly incorrect yet prototypical adversarial counterparts. This setup enables a directional evaluation of whether metrics follow textual semantics or default to prototypes. Our results show that widely used metrics, including CLIPScore, PickScore, and VQA-based scores, frequently misrank these pairs, while even LLM-as-Judge systems exhibit uneven robustness in socially grounded cases. Human evaluations consistently favour semantic correctness with larger decision margins. Motivated by these findings, we propose ProtoScore, a robust 7B-parameter metric that substantially reduces failure rates and suppresses misranking, while running at orders of magnitude faster than the inference time of GPT-5, approaching the robustness of much larger closed-source judges.

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.

Computing a Gaussian process (GP) posterior has a computational cost cubical in the number of historical points. A reformulation of the same GP posterior highlights that this complexity mainly depends on how many unique historical points are considered. This can have important implication in active learning settings, where the set of historical points is constructed sequentially by the learner. We show that sequential black-box optimization based on GPs (GP-Opt) can be made efficient by sticking to a candidate solution for multiple evaluation steps and switch only when necessary. Limiting the number of switches also limits the number of unique points in the history of the GP. Thus, the efficient GP reformulation can be used to exactly and cheaply compute the posteriors required to run the GP-Opt algorithms. This approach is especially useful in real-world applications of GP-Opt with high switch costs (e.g. switching chemicals in wet labs, data/model loading in hyperparameter optimization). As examples of this meta-approach, we modify two well-established GP-Opt algorithms, GP-UCB and GP-EI, to switch candidates as infrequently as possible adapting rules from batched GP-Opt. These versions preserve all the theoretical no-regret guarantees while improving practical aspects of the algorithms such as runtime, memory complexity, and the ability of batching candidates and evaluating them in parallel.

Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced k-Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP\&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP\&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probablistic_precision_recall.

Recent work has shown that the training of a one-hidden-layer, scalar-output fully-connected ReLU neural network can be reformulated as a finite-dimensional convex program. Unfortunately, the scale of such a convex program grows exponentially in data size. In this work, we prove that a stochastic procedure with a linear complexity well approximates the exact formulation. Moreover, we derive a convex optimization approach to efficiently solve the "adversarial training" problem, which trains neural networks that are robust to adversarial input perturbations. Our method can be applied to binary classification and regression, and provides an alternative to the current adversarial training methods, such as Fast Gradient Sign Method (FGSM) and Projected Gradient Descent (PGD). We demonstrate in experiments that the proposed method achieves a noticeably better adversarial robustness and performance than the existing methods.

We present a Non-parametric Network for 3D point cloud analysis, Point-NN, which consists of purely non-learnable components: farthest point sampling (FPS), k-nearest neighbors (k-NN), and pooling operations, with trigonometric functions. Surprisingly, it performs well on various 3D tasks, requiring no parameters or training, and even surpasses existing fully trained models. Starting from this basic non-parametric model, we propose two extensions. First, Point-NN can serve as a base architectural framework to construct Parametric Networks by simply inserting linear layers on top. Given the superior non-parametric foundation, the derived Point-PN exhibits a high performance-efficiency trade-off with only a few learnable parameters. Second, Point-NN can be regarded as a plug-and-play module for the already trained 3D models during inference. Point-NN captures the complementary geometric knowledge and enhances existing methods for different 3D benchmarks without re-training. We hope our work may cast a light on the community for understanding 3D point clouds with non-parametric methods. Code is available at https://github.com/ZrrSkywalker/Point-NN.

We focus on the problem of black-box adversarial attacks, where the aim is to generate adversarial examples for deep learning models solely based on information limited to output label~(hard label) to a queried data input. We propose a simple and efficient Bayesian Optimization~(BO) based approach for developing black-box adversarial attacks. Issues with BO's performance in high dimensions are avoided by searching for adversarial examples in a structured low-dimensional subspace. We demonstrate the efficacy of our proposed attack method by evaluating both ell_infty and ell_2 norm constrained untargeted and targeted hard label black-box attacks on three standard datasets - MNIST, CIFAR-10 and ImageNet. Our proposed approach consistently achieves 2x to 10x higher attack success rate while requiring 10x to 20x fewer queries compared to the current state-of-the-art black-box adversarial attacks.

Neural architecture search (NAS) has allowed for the automatic creation of new and effective neural network architectures, offering an alternative to the laborious process of manually designing complex architectures. However, traditional NAS algorithms are slow and require immense amounts of computing power. Recent research has investigated training-free NAS metrics for image classification architectures, drastically speeding up search algorithms. In this paper, we investigate training-free NAS metrics for recurrent neural network (RNN) and BERT-based transformer architectures, targeted towards language modeling tasks. First, we develop a new training-free metric, named hidden covariance, that predicts the trained performance of an RNN architecture and significantly outperforms existing training-free metrics. We experimentally evaluate the effectiveness of the hidden covariance metric on the NAS-Bench-NLP benchmark. Second, we find that the current search space paradigm for transformer architectures is not optimized for training-free neural architecture search. Instead, a simple qualitative analysis can effectively shrink the search space to the best performing architectures. This conclusion is based on our investigation of existing training-free metrics and new metrics developed from recent transformer pruning literature, evaluated on our own benchmark of trained BERT architectures. Ultimately, our analysis shows that the architecture search space and the training-free metric must be developed together in order to achieve effective results.

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current decomposition methods -- decomposes neural network parameters into a sum of sparsely used vectors in parameter space. However, the current main method in this framework, Attribution-based Parameter Decomposition (APD), is impractical on account of its computational cost and sensitivity to hyperparameters. In this work, we introduce Stochastic Parameter Decomposition (SPD), a method that is more scalable and robust to hyperparameters than APD, which we demonstrate by decomposing models that are slightly larger and more complex than was possible to decompose with APD. We also show that SPD avoids other issues, such as shrinkage of the learned parameters, and better identifies ground truth mechanisms in toy models. By bridging causal mediation analysis and network decomposition methods, this demonstration opens up new research possibilities in mechanistic interpretability by removing barriers to scaling linear parameter decomposition methods to larger models. We release a library for running SPD and reproducing our experiments at https://github.com/goodfire-ai/spd.

Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound). However, model scores are often not aligned with the true positivity rate. This is especially true when the training involves a differential sampling across classes or there is distributional drift between train and test settings. In this paper, we provide theoretical analysis and empirical evidence of the dependence of model score estimation bias on both uncertainty and score itself. Further, we formulate the decision boundary selection in terms of both model score and uncertainty, prove that it is NP-hard, and present algorithms based on dynamic programming and isotonic regression. Evaluation of the proposed algorithms on three real-world datasets yield 25%-40% gain in recall at high precision bounds over the traditional approach of using model score alone, highlighting the benefits of leveraging uncertainty.

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

We introduce a Cascaded Diffusion Model (Cas-DM) that improves a Denoising Diffusion Probabilistic Model (DDPM) by effectively incorporating additional metric functions in training. Metric functions such as the LPIPS loss have been proven highly effective in consistency models derived from the score matching. However, for the diffusion counterparts, the methodology and efficacy of adding extra metric functions remain unclear. One major challenge is the mismatch between the noise predicted by a DDPM at each step and the desired clean image that the metric function works well on. To address this problem, we propose Cas-DM, a network architecture that cascades two network modules to effectively apply metric functions to the diffusion model training. The first module, similar to a standard DDPM, learns to predict the added noise and is unaffected by the metric function. The second cascaded module learns to predict the clean image, thereby facilitating the metric function computation. Experiment results show that the proposed diffusion model backbone enables the effective use of the LPIPS loss, leading to state-of-the-art image quality (FID, sFID, IS) on various established benchmarks.

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of parametric PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parametrizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that compares the physics of the generated PINN to the requested PDE and uses the discrepancy to generate a "delta" PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves over 100x gain in average L_2 loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems with significantly improved accuracy and reduced computational cost.

To bridge the ever increasing gap between deep neural networks' complexity and hardware capability, network quantization has attracted more and more research attention. The latest trend of mixed precision quantization takes advantage of hardware's multiple bit-width arithmetic operations to unleash the full potential of network quantization. However, this also results in a difficult integer programming formulation, and forces most existing approaches to use an extremely time-consuming search process even with various relaxations. Instead of solving a problem of the original integer programming, we propose to optimize a proxy metric, the concept of network orthogonality, which is highly correlated with the loss of the integer programming but also easy to optimize with linear programming. This approach reduces the search time and required data amount by orders of magnitude, with little compromise on quantization accuracy. Specifically, we achieve 72.08% Top-1 accuracy on ResNet-18 with 6.7Mb, which does not require any searching iterations. Given the high efficiency and low data dependency of our algorithm, we used it for the post-training quantization, which achieve 71.27% Top-1 accuracy on MobileNetV2 with only 1.5Mb. Our code is available at https://github.com/MAC-AutoML/OMPQ.

Recently, a race towards the simplification of deep networks has begun, showing that it is effectively possible to reduce the size of these models with minimal or no performance loss. However, there is a general lack in understanding why these pruning strategies are effective. In this work, we are going to compare and analyze pruned solutions with two different pruning approaches, one-shot and gradual, showing the higher effectiveness of the latter. In particular, we find that gradual pruning allows access to narrow, well-generalizing minima, which are typically ignored when using one-shot approaches. In this work we also propose PSP-entropy, a measure to understand how a given neuron correlates to some specific learned classes. Interestingly, we observe that the features extracted by iteratively-pruned models are less correlated to specific classes, potentially making these models a better fit in transfer learning approaches.