Daily Papers

Fully Homomorphic Encryption (FHE) is an encryption scheme that allows for computation to be performed directly on encrypted data, effectively closing the loop on secure and outsourced computing. Data is encrypted not only during rest and transit, but also during processing. However, FHE provides a limited instruction set: SIMD addition, SIMD multiplication, and cyclic rotation of 1-D vectors. This restriction makes performing multi-dimensional tensor operations challenging. Practitioners must pack these tensors into 1-D vectors and map tensor operations onto this one-dimensional layout rather than their traditional nested structure. And while prior systems have made significant strides in automating this process, they often hide critical packing decisions behind layers of abstraction, making debugging, optimizing, and building on top of these systems difficult. In this work, we approach multi-dimensional tensor operations in FHE through Einstein summation (einsum) notation. Einsum notation explicitly encodes dimensional structure and operations in its syntax, naturally exposing how tensors should be packed and transformed. We decompose einsum expressions into a fixed set of FHE-friendly operations. We implement our design and present EinHops, a minimalist system that factors einsum expressions into a fixed sequence of FHE operations. EinHops enables developers to perform encrypted tensor operations using FHE while maintaining full visibility into the underlying packing strategy. We evaluate EinHops on a range of tensor operations from a simple transpose to complex multi-dimensional contractions. We show that the explicit nature of einsum notation allows us to build an FHE tensor system that is simple, general, and interpretable. We open-source EinHops at the following repository: https://github.com/baahl-nyu/einhops.

Implicit Neural Representation (INR) has emerged as a powerful tool for encoding discrete signals into continuous, differentiable functions using neural networks. However, these models often have an unfortunate reliance on monolithic architectures to represent high-dimensional data, leading to prohibitive computational costs as dimensionality grows. We propose F-INR, a framework that reformulates INR learning through functional tensor decomposition, breaking down high-dimensional tasks into lightweight, axis-specific sub-networks. Each sub-network learns a low-dimensional data component (e.g., spatial or temporal). Then, we combine these components via tensor operations, reducing forward pass complexity while improving accuracy through specialized learning. F-INR is modular and, therefore, architecture-agnostic, compatible with MLPs, SIREN, WIRE, or other state-of-the-art INR architecture. It is also decomposition-agnostic, supporting CP, TT, and Tucker modes with user-defined rank for speed-accuracy control. In our experiments, F-INR trains 100times faster than existing approaches on video tasks while achieving higher fidelity (+3.4 dB PSNR). Similar gains hold for image compression, physics simulations, and 3D geometry reconstruction. Through this, F-INR offers a new scalable, flexible solution for high-dimensional signal modeling.

We present a complete system for real-time rendering of scenes with complex appearance previously reserved for offline use. This is achieved with a combination of algorithmic and system level innovations. Our appearance model utilizes learned hierarchical textures that are interpreted using neural decoders, which produce reflectance values and importance-sampled directions. To best utilize the modeling capacity of the decoders, we equip the decoders with two graphics priors. The first prior -- transformation of directions into learned shading frames -- facilitates accurate reconstruction of mesoscale effects. The second prior -- a microfacet sampling distribution -- allows the neural decoder to perform importance sampling efficiently. The resulting appearance model supports anisotropic sampling and level-of-detail rendering, and allows baking deeply layered material graphs into a compact unified neural representation. By exposing hardware accelerated tensor operations to ray tracing shaders, we show that it is possible to inline and execute the neural decoders efficiently inside a real-time path tracer. We analyze scalability with increasing number of neural materials and propose to improve performance using code optimized for coherent and divergent execution. Our neural material shaders can be over an order of magnitude faster than non-neural layered materials. This opens up the door for using film-quality visuals in real-time applications such as games and live previews.

Advancing research in the emerging field of deep graph learning requires new tools to support tensor computation over graphs. In this paper, we present the design principles and implementation of Deep Graph Library (DGL). DGL distills the computational patterns of GNNs into a few generalized sparse tensor operations suitable for extensive parallelization. By advocating graph as the central programming abstraction, DGL can perform optimizations transparently. By cautiously adopting a framework-neutral design, DGL allows users to easily port and leverage the existing components across multiple deep learning frameworks. Our evaluation shows that DGL significantly outperforms other popular GNN-oriented frameworks in both speed and memory consumption over a variety of benchmarks and has little overhead for small scale workloads.

Layer-wise Relevance Propagation (LRP) provides principled attribution for neural networks through conservation properties and foundations in Deep Taylor Decomposition. However, existing implementations operate at the module level, requiring architecture-specific propagation rules and modifications. These limit the generality of target model and sustainability of implementations as architectures evolve. We introduce DynamicLRP, a model-agnostic LRP framework operating at the tensor operation level. By decomposing attribution to individual operations within computation graphs and introducing a novel mechanism for deferred activation resolution, named the Promise System, our approach achieves true architecture agnosticity while maintaining LRP's theoretical guarantees. This design operates independently of backpropagation machinery, enabling operation on arbitrary computation graphs without model modification and side-by-side execution with gradient backpropagation. Being based on computation graphs, this method is theoretically extensible to other deep learning libraries that support auto-differentiation. We demonstrate faithfulness matching or exceeding specialized implementations (1.77 vs 1.69 ABPC on VGG, equivalent performance on ViT, 93.70\% and 95.06\% top-1 attribution accuracy for explaining RoBERTa-large and Flan-T5-large answers on SQuADv2, respectively) while maintaining practical efficiency on models with hundreds of millions of parameters. We achieved 99.92\% node coverage across 31,465 computation graph nodes from 15 diverse architectures, including state-space models (Mamba), audio transformers (Whisper), and multimodal systems (DePlot) without any model-specific code with rules for 47 fundamental operations implemented. Our operation-level decomposition and Promise System establish a sustainable, extensible foundation for LRP across evolving architectures.

Estimating probability distribution is one of the core issues in the NLP field. However, in both deep learning (DL) and pre-DL eras, unlike the vast applications of linear-chain CRF in sequence labeling tasks, very few works have applied tree-structure CRF to constituency parsing, mainly due to the complexity and inefficiency of the inside-outside algorithm. This work presents a fast and accurate neural CRF constituency parser. The key idea is to batchify the inside algorithm for loss computation by direct large tensor operations on GPU, and meanwhile avoid the outside algorithm for gradient computation via efficient back-propagation. We also propose a simple two-stage bracketing-then-labeling parsing approach to improve efficiency further. To improve the parsing performance, inspired by recent progress in dependency parsing, we introduce a new scoring architecture based on boundary representation and biaffine attention, and a beneficial dropout strategy. Experiments on PTB, CTB5.1, and CTB7 show that our two-stage CRF parser achieves new state-of-the-art performance on both settings of w/o and w/ BERT, and can parse over 1,000 sentences per second. We release our code at https://github.com/yzhangcs/crfpar.

In this paper, we propose a novel top-down instance segmentation framework based on explicit shape encoding, named ESE-Seg. It largely reduces the computational consumption of the instance segmentation by explicitly decoding the multiple object shapes with tensor operations, thus performs the instance segmentation at almost the same speed as the object detection. ESE-Seg is based on a novel shape signature Inner-center Radius (IR), Chebyshev polynomial fitting and the strong modern object detectors. ESE-Seg with YOLOv3 outperforms the Mask R-CNN on Pascal VOC 2012 at mAP^[email protected] while 7 times faster.

The demand for inference on extremely large scale LLMs has seen enormous growth in the recent months. It made evident the colossal shortage of dedicated hardware capable of efficient and fast processing of the involved compute and memory movement. The problem is aggravated by the exploding raise in the lengths of the sequences being processed, since those require efficient on-chip storage of the KV-cache of size proportional to the sequence length. To make the required compute feasible and fit the involved data into available memory, numerous quantization techniques have been proposed that allow accurate quantization for both weights and activations. One of the main recent breakthroughs in this direction was introduction of the family of Block Floating Point (BFP) formats characterized by a block of mantissas with a shared scale factor. These enable memory- power-, and compute- efficient hardware support of the tensor operations and provide extremely good quantization accuracy. The main issues preventing widespread application of block formats is caused by the presence of outliers in weights and activations since those affect the accuracy of the other values in the same block. In this paper, we focus on the most critical problem of limited KV-cache storage. We propose a novel approach enabling usage of low precision BFP formats without compromising the resulting model accuracy. We exploit the common channel-wise patterns exhibited by the outliers to rearrange them in such a way, that their quantization quality is significantly improved. The methodology yields 2x savings in the memory footprint without significant degradation of the model's accuracy. Importantly, the rearrangement of channels happens at the compile time and thus has no impact on the inference latency.

By integrating tools from external APIs, Large Language Models (LLMs) have expanded their promising capabilities in a diverse spectrum of complex real-world tasks. However, testing, evaluation, and analysis of LLM tool use remain in their early stages. Most existing benchmarks rely on manually collected test cases, many of which cannot be automatically checked for semantic correctness and instead depend on static methods such as string matching. Additionally, these benchmarks often overlook the complex interactions that occur between sequential API calls, which are common in real-world applications. To fill the gap, in this paper, we introduce StateGen, an automated framework designed to generate diverse coding tasks involving sequential API interactions. StateGen combines state-machine-based API constraint solving and validation, energy-based sampling, and control-flow injection to generate executable programs. These programs are then translated into human-like natural language task descriptions through a collaboration of two LLM agents. Utilizing StateGen, we construct StateEval, a benchmark encompassing 120 verified test cases spanning across three representative scenarios: Session Service, Tensor Operation, and ElevenLabs MCP. Experimental results confirm that StateGen can effectively generate challenging and realistic API-oriented tasks, highlighting areas for improvement in current LLMs incorporating APIs.We make our framework and benchmark publicly available to support future research.

Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP, whose layers perform mean-field variational inference over an MLN. It can be plugged into any off-the-shelf neural network to encode FOLCs while retaining modularity and efficiency. By exploiting the structure and symmetries in MLNs, we theoretically demonstrate that our well-designed, efficient mean-field iterations effectively mitigate the difficulty of MLN inference, reducing the inference from sequential calculation to a series of parallel tensor operations. Empirical results in three kinds of tasks over graphs, images, and text show that LogicMP outperforms advanced competitors in both performance and efficiency.

This document presents a vision for a novel AI infrastructure design that has been initially validated through inference simulations on state-of-the-art large language models. Advancements in deep learning and specialized hardware have driven the rapid growth of large language models (LLMs) and generative AI systems. However, traditional GPU-centric architectures face scalability challenges for inference workloads due to limitations in memory capacity, bandwidth, and interconnect scaling. To address these issues, the FengHuang Platform, a disaggregated AI infrastructure platform, is proposed to overcome memory and communication scaling limits for AI inference. FengHuang features a multi-tier shared-memory architecture combining high-speed local memory with centralized disaggregated remote memory, enhanced by active tensor paging and near-memory compute for tensor operations. Simulations demonstrate that FengHuang achieves up to 93% local memory capacity reduction, 50% GPU compute savings, and 16x to 70x faster inter-GPU communication compared to conventional GPU scaling. Across workloads such as GPT-3, Grok-1, and QWEN3-235B, FengHuang enables up to 50% GPU reductions while maintaining end-user performance, offering a scalable, flexible, and cost-effective solution for AI inference infrastructure. FengHuang provides an optimal balance as a rack-level AI infrastructure scale-up solution. Its open, heterogeneous design eliminates vendor lock-in and enhances supply chain flexibility, enabling significant infrastructure and power cost reductions.

E(3)-equivariant neural networks have demonstrated success across a wide range of 3D modelling tasks. A fundamental operation in these networks is the tensor product, which interacts two geometric features in an equivariant manner to create new features. Due to the high computational complexity of the tensor product, significant effort has been invested to optimize the runtime of this operation. For example, Luo et al. (2024) recently proposed the Gaunt tensor product (GTP) which promises a significant speedup. In this work, we provide a careful, systematic analysis of a number of tensor product operations. In particular, we emphasize that different tensor products are not performing the same operation. The reported speedups typically come at the cost of expressivity. We introduce measures of expressivity and interactability to characterize these differences. In addition, we realized the original implementation of GTP can be greatly simplified by directly using a spherical grid at no cost in asymptotic runtime. This spherical grid approach is faster on our benchmarks and in actual training of the MACE interatomic potential by 30%. Finally, we provide the first systematic microbenchmarks of the various tensor product operations. We find that the theoretical runtime guarantees can differ wildly from empirical performance, demonstrating the need for careful application-specific benchmarking. Code is available at https://github.com/atomicarchitects/PriceofFreedom.

In multi-task learning, the conventional approach involves training a model on multiple tasks simultaneously. However, the training signals from different tasks can interfere with one another, potentially leading to negative transfer. To mitigate this, we investigate if modular language models can facilitate positive transfer and systematic generalization. Specifically, we propose a novel modular language model (TensorPoly), that balances parameter efficiency with nuanced routing methods. For modules, we reparameterize Low-Rank Adaptation (LoRA) by employing an entangled tensor through the use of tensor product operations and name the resulting approach TLoRA. For routing function, we tailor two innovative routing functions according to the granularity: TensorPoly-I which directs to each rank within the entangled tensor while TensorPoly-II offers a finer-grained routing approach targeting each order of the entangled tensor. The experimental results from the multi-task T0-benchmark demonstrate that: 1) all modular LMs surpass the corresponding dense approaches, highlighting the potential of modular language models to mitigate negative inference in multi-task learning and deliver superior outcomes. 2) TensorPoly-I achieves higher parameter efficiency in adaptation and outperforms other modular LMs, which shows the potential of our approach in multi-task transfer learning.

Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity multiplication L-Mul algorithm that approximates floating point number multiplication with integer addition operations. The new algorithm costs significantly less computation resource than 8-bit floating point multiplication but achieves higher precision. Compared to 8-bit floating point multiplications, the proposed method achieves higher precision but consumes significantly less bit-level computation. Since multiplying floating point numbers requires substantially higher energy compared to integer addition operations, applying the L-Mul operation in tensor processing hardware can potentially reduce 95% energy cost by element-wise floating point tensor multiplications and 80% energy cost of dot products. We calculated the theoretical error expectation of L-Mul, and evaluated the algorithm on a wide range of textual, visual, and symbolic tasks, including natural language understanding, structural reasoning, mathematics, and commonsense question answering. Our numerical analysis experiments agree with the theoretical error estimation, which indicates that L-Mul with 4-bit mantissa achieves comparable precision as float8_e4m3 multiplications, and L-Mul with 3-bit mantissa outperforms float8_e5m2. Evaluation results on popular benchmarks show that directly applying L-Mul to the attention mechanism is almost lossless. We further show that replacing all floating point multiplications with 3-bit mantissa L-Mul in a transformer model achieves equivalent precision as using float8_e4m3 as accumulation precision in both fine-tuning and inference.

Hamiltonian matrix prediction is pivotal in computational chemistry, serving as the foundation for determining a wide range of molecular properties. While SE(3) equivariant graph neural networks have achieved remarkable success in this domain, their substantial computational cost--driven by high-order tensor product (TP) operations--restricts their scalability to large molecular systems with extensive basis sets. To address this challenge, we introduce SPHNet, an efficient and scalable equivariant network, that incorporates adaptive SParsity into Hamiltonian prediction. SPHNet employs two innovative sparse gates to selectively constrain non-critical interaction combinations, significantly reducing tensor product computations while maintaining accuracy. To optimize the sparse representation, we develop a Three-phase Sparsity Scheduler, ensuring stable convergence and achieving high performance at sparsity rates of up to 70%. Extensive evaluations on QH9 and PubchemQH datasets demonstrate that SPHNet achieves state-of-the-art accuracy while providing up to a 7x speedup over existing models. Beyond Hamiltonian prediction, the proposed sparsification techniques also hold significant potential for improving the efficiency and scalability of other SE(3) equivariant networks, further broadening their applicability and impact. Our code can be found at https://github.com/microsoft/SPHNet.

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from O(L^6) to O(L^3), where L is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach.

Design of neural networks that incorporate symmetry is crucial for geometric deep learning. Central to this effort is the development of invariant and equivariant operations. This works presents a systematic method for constructing valid invariant and equivariant operations. It can handle inputs and outputs in the form of Cartesian tensors with different rank, as well as spherical tensors with different types. In addition, our method features a graphical representation utilizing the symmetric tensor network, which simplifies both the proofs and constructions related to invariant and equivariant functions. We also apply this approach to design the equivariant interaction message for the geometry graph neural network, and equivariant machine learning model to learn the constitutive law of materials.

SO(3)-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks in which CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of SO(3)-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the O(L^3) CG paths into a single shared parameter set without compromising equivariance, where L is the maximum angular degree. The resulting layer acts as a plug-and-play replacement for tensor products in existing networks, and the computational complexity of tensor products is reduced from O(L^6) to O(L^4). We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots. We also use existing datasets, including OC20, and OC22. Results show that TDNs achieve competitive performance with dramatic speedup in computations. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS/tree/main/OpenMol/TDN{https://github.com/divelab/AIRS/}).

We analyse perception and memory, using mathematical models for knowledge graphs and tensors, to gain insights into the corresponding functionalities of the human mind. Our discussion is based on the concept of propositional sentences consisting of subject-predicate-object (SPO) triples for expressing elementary facts. SPO sentences are the basis for most natural languages but might also be important for explicit perception and declarative memories, as well as intra-brain communication and the ability to argue and reason. A set of SPO sentences can be described as a knowledge graph, which can be transformed into an adjacency tensor. We introduce tensor models, where concepts have dual representations as indices and associated embeddings, two constructs we believe are essential for the understanding of implicit and explicit perception and memory in the brain. We argue that a biological realization of perception and memory imposes constraints on information processing. In particular, we propose that explicit perception and declarative memories require a semantic decoder, which, in a simple realization, is based on four layers: First, a sensory memory layer, as a buffer for sensory input, second, an index layer representing concepts, third, a memoryless representation layer for the broadcasting of information ---the "blackboard", or the "canvas" of the brain--- and fourth, a working memory layer as a processing center and data buffer. We discuss the operations of the four layers and relate them to the global workspace theory. In a Bayesian brain interpretation, semantic memory defines the prior for observable triple statements. We propose that ---in evolution and during development--- semantic memory, episodic memory, and natural language evolved as emergent properties in agents' process to gain a deeper understanding of sensory information.

Tensor computations, with matrix multiplication being the primary operation, serve as the fundamental basis for data analysis, physics, machine learning, and deep learning. As the scale and complexity of data continue to grow rapidly, the demand for tensor computations has also increased significantly. To meet this demand, several research institutions have started developing dedicated hardware for tensor computations. To further improve the computational performance of tensor process units, we have reexamined the issue of computation reuse that was previously overlooked in existing architectures. As a result, we propose a novel EN-T architecture that can reduce chip area and power consumption. Furthermore, our method is compatible with existing tensor processing units. We evaluated our method on prevalent microarchitectures, the results demonstrate an average improvement in area efficiency of 8.7\%, 12.2\%, and 11.0\% for tensor computing units at computational scales of 256 GOPS, 1 TOPS, and 4 TOPS, respectively. Similarly, there were energy efficiency enhancements of 13.0\%, 17.5\%, and 15.5\%.

Tensor Cores have been an important unit to accelerate Fused Matrix Multiplication Accumulation (MMA) in all NVIDIA GPUs since Volta Architecture. To program Tensor Cores, users have to use either legacy wmma APIs or current mma APIs. Legacy wmma APIs are more easy-to-use but can only exploit limited features and power of Tensor Cores. Specifically, wmma APIs support fewer operand shapes and can not leverage the new sparse matrix multiplication feature of the newest Ampere Tensor Cores. However, the performance of current programming interface has not been well explored. Furthermore, the computation numeric behaviors of low-precision floating points (TF32, BF16, and FP16) supported by the newest Ampere Tensor Cores are also mysterious. In this paper, we explore the throughput and latency of current programming APIs. We also intuitively study the numeric behaviors of Tensor Cores MMA and profile the intermediate operations including multiplication, addition of inner product, and accumulation. All codes used in this work can be found in https://github.com/sunlex0717/DissectingTensorCores.

Progress in AI is hindered by the lack of a programming language with all the requisite features. Libraries like PyTorch and TensorFlow provide automatic differentiation and efficient GPU implementation, but are additions to Python, which was never intended for AI. Their lack of support for automated reasoning and knowledge acquisition has led to a long and costly series of hacky attempts to tack them on. On the other hand, AI languages like LISP an Prolog lack scalability and support for learning. This paper proposes tensor logic, a language that solves these problems by unifying neural and symbolic AI at a fundamental level. The sole construct in tensor logic is the tensor equation, based on the observation that logical rules and Einstein summation are essentially the same operation, and all else can be reduced to them. I show how to elegantly implement key forms of neural, symbolic and statistical AI in tensor logic, including transformers, formal reasoning, kernel machines and graphical models. Most importantly, tensor logic makes new directions possible, such as sound reasoning in embedding space. This combines the scalability and learnability of neural networks with the reliability and transparency of symbolic reasoning, and is potentially a basis for the wider adoption of AI.

As large language model (LLM) inference demands ever-greater resources, there is a rapid growing trend of using low-bit weights to shrink memory usage and boost inference efficiency. However, these low-bit LLMs introduce the need for mixed-precision matrix multiplication (mpGEMM), which is a crucial yet under-explored operation that involves multiplying lower-precision weights with higher-precision activations. Unfortunately, current hardware does not natively support mpGEMM, resulting in indirect and inefficient dequantization-based implementations. To address the mpGEMM requirements in low-bit LLMs, we explored the lookup table (LUT)-based approach for mpGEMM. However, a conventional LUT implementation falls short of its potential. To fully harness the power of LUT-based mpGEMM, we introduce LUT Tensor Core, a software-hardware co-design optimized for low-bit LLM inference. Specifically, we introduce software-based operator fusion and table symmetrization techniques to optimize table precompute and table storage, respectively. Then, LUT Tensor Core proposes the hardware design featuring an elongated tiling shape design to enhance table reuse and a bit-serial design to support various precision combinations in mpGEMM. Moreover, we design an end-to-end compilation stack with new instructions for LUT-based mpGEMM, enabling efficient LLM compilation and optimizations. The evaluation on low-bit LLMs (e.g., BitNet, LLAMA) shows that LUT Tensor Core achieves more than a magnitude of improvements on both compute density and energy efficiency.

In this work, we demonstrate that a simple two-layer neural network with standard activation functions can learn an arbitrary word operation in any finite group, provided sufficient width is available and exhibits grokking while doing so. To explain the mechanism by which this is achieved, we reframe the problem as that of learning a particular 3-tensor, which we show is typically of low rank. A key insight is that low-rank implementations of this tensor can be obtained by decomposing it along triplets of basic self-conjugate representations of the group and leveraging the fusion structure to rule out many components. Focusing on a phenomenologically similar but more tractable surrogate model, we show that the network is able to find such low-rank implementations (or approximations thereof), thereby using limited width to approximate the word-tensor in a generalizable way. In the case of the simple multiplication word, we further elucidate the form of these low-rank implementations, showing that the network effectively implements efficient matrix multiplication in the sense of Strassen. Our work also sheds light on the mechanism by which a network reaches such a solution under gradient descent.

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that leverages Cartesian tensor representations. By using Cartesian tensor atomic embeddings, feature mixing is simplified through matrix product operations. Furthermore, the cost-effective decomposition of these tensors into rotation group irreducible representations allows for the separate processing of scalars, vectors, and tensors when necessary. Compared to higher-rank spherical tensor models, TensorNet demonstrates state-of-the-art performance with significantly fewer parameters. For small molecule potential energies, this can be achieved even with a single interaction layer. As a result of all these properties, the model's computational cost is substantially decreased. Moreover, the accurate prediction of vector and tensor molecular quantities on top of potential energies and forces is possible. In summary, TensorNet's framework opens up a new space for the design of state-of-the-art equivariant models.

Benefiting from the capability of building inter-dependencies among channels or spatial locations, attention mechanisms have been extensively studied and broadly used in a variety of computer vision tasks recently. In this paper, we investigate light-weight but effective attention mechanisms and present triplet attention, a novel method for computing attention weights by capturing cross-dimension interaction using a three-branch structure. For an input tensor, triplet attention builds inter-dimensional dependencies by the rotation operation followed by residual transformations and encodes inter-channel and spatial information with negligible computational overhead. Our method is simple as well as efficient and can be easily plugged into classic backbone networks as an add-on module. We demonstrate the effectiveness of our method on various challenging tasks including image classification on ImageNet-1k and object detection on MSCOCO and PASCAL VOC datasets. Furthermore, we provide extensive in-sight into the performance of triplet attention by visually inspecting the GradCAM and GradCAM++ results. The empirical evaluation of our method supports our intuition on the importance of capturing dependencies across dimensions when computing attention weights. Code for this paper can be publicly accessed at https://github.com/LandskapeAI/triplet-attention

A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.

Evolutionary multiobjective optimization (EMO) has made significant strides over the past two decades. However, as problem scales and complexities increase, traditional EMO algorithms face substantial performance limitations due to insufficient parallelism and scalability. While most work has focused on algorithm design to address these challenges, little attention has been given to hardware acceleration, thereby leaving a clear gap between EMO algorithms and advanced computing devices, such as GPUs. To bridge the gap, we propose to parallelize EMO algorithms on GPUs via the tensorization methodology. By employing tensorization, the data structures and operations of EMO algorithms are transformed into concise tensor representations, which seamlessly enables automatic utilization of GPU computing. We demonstrate the effectiveness of our approach by applying it to three representative EMO algorithms: NSGA-III, MOEA/D, and HypE. To comprehensively assess our methodology, we introduce a multiobjective robot control benchmark using a GPU-accelerated physics engine. Our experiments show that the tensorized EMO algorithms achieve speedups of up to 1113x compared to their CPU-based counterparts, while maintaining solution quality and effectively scaling population sizes to hundreds of thousands. Furthermore, the tensorized EMO algorithms efficiently tackle complex multiobjective robot control tasks, producing high-quality solutions with diverse behaviors. Source codes are available at https://github.com/EMI-Group/evomo.

Vision transformers have shown great success due to their high model capabilities. However, their remarkable performance is accompanied by heavy computation costs, which makes them unsuitable for real-time applications. In this paper, we propose a family of high-speed vision transformers named EfficientViT. We find that the speed of existing transformer models is commonly bounded by memory inefficient operations, especially the tensor reshaping and element-wise functions in MHSA. Therefore, we design a new building block with a sandwich layout, i.e., using a single memory-bound MHSA between efficient FFN layers, which improves memory efficiency while enhancing channel communication. Moreover, we discover that the attention maps share high similarities across heads, leading to computational redundancy. To address this, we present a cascaded group attention module feeding attention heads with different splits of the full feature, which not only saves computation cost but also improves attention diversity. Comprehensive experiments demonstrate EfficientViT outperforms existing efficient models, striking a good trade-off between speed and accuracy. For instance, our EfficientViT-M5 surpasses MobileNetV3-Large by 1.9% in accuracy, while getting 40.4% and 45.2% higher throughput on Nvidia V100 GPU and Intel Xeon CPU, respectively. Compared to the recent efficient model MobileViT-XXS, EfficientViT-M2 achieves 1.8% superior accuracy, while running 5.8x/3.7x faster on the GPU/CPU, and 7.4x faster when converted to ONNX format. Code and models are available at https://github.com/microsoft/Cream/tree/main/EfficientViT.

We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch-Gordan tensor products. This is achieved by introducing a set of new efficient and powerful SO(2)-equivariant operations and performing all off-diagonal feature updates and message passing within SO(2) local frames, thereby eliminating the need of SO(3) tensor products. Moreover, a continuous SO(2) tensor product is performed within the SO(2) local frame at each node to fuse node features, mimicking the symmetric contraction operation. Extensive experiments on the large QH9 and MD17 datasets demonstrate that our model achieves superior performance across a wide range of molecular structures and trajectories, highlighting its strong generalization capability. The proposed SO(2) operations on SO(2) local frames offer a promising direction for scalable and symmetry-aware learning of electronic structures. Our code will be released as part of the AIRS library https://github.com/divelab/AIRS.

Attention, as a core layer of the ubiquitous Transformer architecture, is the bottleneck for large language models and long-context applications. FlashAttention elaborated an approach to speed up attention on GPUs through minimizing memory reads/writes. However, it has yet to take advantage of new capabilities present in recent hardware, with FlashAttention-2 achieving only 35% utilization on the H100 GPU. We develop three main techniques to speed up attention on Hopper GPUs: exploiting asynchrony of the Tensor Cores and TMA to (1) overlap overall computation and data movement via warp-specialization and (2) interleave block-wise matmul and softmax operations, and (3) block quantization and incoherent processing that leverages hardware support for FP8 low-precision. We demonstrate that our method, FlashAttention-3, achieves speedup on H100 GPUs by 1.5-2.0times with FP16 reaching up to 740 TFLOPs/s (75% utilization), and with FP8 reaching close to 1.2 PFLOPs/s. We validate that FP8 FlashAttention-3 achieves 2.6times lower numerical error than a baseline FP8 attention.

This work presents Kornia, an open source computer vision library built upon a set of differentiable routines and modules that aims to solve generic computer vision problems. The package uses PyTorch as its main backend, not only for efficiency but also to take advantage of the reverse auto-differentiation engine to define and compute the gradient of complex functions. Inspired by OpenCV, Kornia is composed of a set of modules containing operators that can be integrated into neural networks to train models to perform a wide range of operations including image transformations,camera calibration, epipolar geometry, and low level image processing techniques, such as filtering and edge detection that operate directly on high dimensional tensor representations on graphical processing units, generating faster systems. Examples of classical vision problems implemented using our framework are provided including a benchmark comparing to existing vision libraries.