Daily Papers

Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given precision level. One challenge in PCG solvers is the selection of preconditioners, as different problem-dependent systems can benefit from different preconditioners. We present a new method to introduce inductive bias in preconditioning conjugate gradient algorithm. Given a system matrix and a set of solution vectors arise from an underlying distribution, we train a graph neural network to obtain an approximate decomposition to the system matrix to be used as a preconditioner in the context of PCG solvers. We conduct extensive experiments to demonstrate the efficacy and generalizability of our proposed approach in solving various 2D and 3D linear second-order PDEs.

We consider a family of linear systems A_mu alpha=C with system matrix A_mu depending on a parameter mu and for simplicity parameter-independent right-hand side C. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form A_muapproxsum_{m}beta_m(mu)A_{mu_m} for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices A_{mu_m}. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for partial differential equations. Algorithms for approximating the solution to these systems are often the bottleneck in problems that require their solution, particularly for modern applications that require many millions of unknowns. Indeed, numerical linear algebra techniques have been investigated for many decades to alleviate this computational burden. Recently, data-driven techniques have also shown promise for these problems. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search directions. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We train the network using unsupervised learning with a loss function equal to the L^2 difference between an input and the system matrix times the network evaluation, where the unspecified constant in the approximate inverse is accounted for. We demonstrate the efficacy of our approach on spatially discretized Poisson equations with millions of degrees of freedom arising in computational fluid dynamics applications. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

The utilization of Large Language Models (LLMs) for the construction of AI systems has garnered significant attention across diverse fields. The extension of LLMs to the domain of fashion holds substantial commercial potential but also inherent challenges due to the intricate semantic interactions in fashion-related generation. To address this issue, we developed a hierarchical AI system called Fashion Matrix dedicated to editing photos by just talking. This system facilitates diverse prompt-driven tasks, encompassing garment or accessory replacement, recoloring, addition, and removal. Specifically, Fashion Matrix employs LLM as its foundational support and engages in iterative interactions with users. It employs a range of Semantic Segmentation Models (e.g., Grounded-SAM, MattingAnything, etc.) to delineate the specific editing masks based on user instructions. Subsequently, Visual Foundation Models (e.g., Stable Diffusion, ControlNet, etc.) are leveraged to generate edited images from text prompts and masks, thereby facilitating the automation of fashion editing processes. Experiments demonstrate the outstanding ability of Fashion Matrix to explores the collaborative potential of functionally diverse pre-trained models in the domain of fashion editing.

Large matrix multiplication is a cornerstone of modern machine learning workloads, yet traditional approaches suffer from cubic computational complexity (e.g., O(n^3) for a matrix of size ntimes n). We present Low-Rank GEMM, a novel approach that leverages low-rank matrix approximations to achieve sub-quadratic complexity while maintaining hardware-accelerated performance through FP8 precision and intelligent kernel selection. On a NVIDIA RTX 4090, our implementation achieves up to 378 TFLOPS on matrices up to N=20480, providing 75\% memory savings and 7.8times speedup over PyTorch FP32 for large matrices. The system automatically adapts to hardware capabilities, selecting optimal decomposition methods (SVD, randomized SVD) and precision levels based on matrix characteristics and available accelerators. Comprehensive benchmarking on NVIDIA RTX 4090 demonstrates that Low-Rank GEMM becomes the fastest approach for matrices Ngeq10240, surpassing traditional cuBLAS implementations through memory bandwidth optimization rather than computational shortcuts.

Sparse matrices, more specifically SpGEMM kernels, are commonly found in a wide range of applications, spanning graph-based path-finding to machine learning algorithms (e.g., neural networks). A particular challenge in implementing SpGEMM kernels has been the pressure placed on DRAM memory. One approach to tackle this problem is to use an inner product method for the SpGEMM kernel implementation. While the inner product produces fewer intermediate results, it can end up saturating the memory bandwidth, given the high number of redundant fetches of the input matrix elements. Using an outer product-based SpGEMM kernel can reduce redundant fetches, but at the cost of increased overhead due to extra computation and memory accesses for producing/managing partial products. In this thesis, we introduce a novel SpGEMM kernel implementation based on the row-wise product approach. We leverage atomic instructions to merge intermediate partial products as they are generated. The use of atomic instructions eliminates the need to create partial product matrices. To evaluate our row-wise product approach, we map an optimized SpGEMM kernel to a custom accelerator designed to accelerate graph-based applications. The targeted accelerator is an experimental system named PIUMA, being developed by Intel. PIUMA provides several attractive features, including fast context switching, user-configurable caches, globally addressable memory, non-coherent caches, and asynchronous pipelines. We tailor our SpGEMM kernel to exploit many of the features of the PIUMA fabric. This thesis compares our SpGEMM implementation against prior solutions, all mapped to the PIUMA framework. We briefly describe some of the PIUMA architecture features and then delve into the details of our optimized SpGEMM kernel. Our SpGEMM kernel can achieve 9.4x speedup as compared to competing approaches.

We present The Matrix, the first foundational realistic world simulator capable of generating continuous 720p high-fidelity real-scene video streams with real-time, responsive control in both first- and third-person perspectives, enabling immersive exploration of richly dynamic environments. Trained on limited supervised data from AAA games like Forza Horizon 5 and Cyberpunk 2077, complemented by large-scale unsupervised footage from real-world settings like Tokyo streets, The Matrix allows users to traverse diverse terrains -- deserts, grasslands, water bodies, and urban landscapes -- in continuous, uncut hour-long sequences. Operating at 16 FPS, the system supports real-time interactivity and demonstrates zero-shot generalization, translating virtual game environments to real-world contexts where collecting continuous movement data is often infeasible. For example, The Matrix can simulate a BMW X3 driving through an office setting--an environment present in neither gaming data nor real-world sources. This approach showcases the potential of AAA game data to advance robust world models, bridging the gap between simulations and real-world applications in scenarios with limited data.

Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in graphs such as large conjugated molecules, and social networks due to oversmoothing and oversquashing. Although Spectral GNNs and traditional neural networks such as recurrent neural networks and transformers mitigate these challenges, they often lack generalizability, or fail to capture detailed structural relationships or symmetries in the data. To address these concerns, we introduce Matrix Function Neural Networks (MFNs), a novel architecture that parameterizes non-local interactions through analytic matrix equivariant functions. Employing resolvent expansions offers a straightforward implementation and the potential for linear scaling with system size. The MFN architecture achieves stateof-the-art performance in standard graph benchmarks, such as the ZINC and TU datasets, and is able to capture intricate non-local interactions in quantum systems, paving the way to new state-of-the-art force fields.

A central challenge of video prediction lies where the system has to reason the objects' future motions from image frames while simultaneously maintaining the consistency of their appearances across frames. This work introduces an end-to-end trainable two-stream video prediction framework, Motion-Matrix-based Video Prediction (MMVP), to tackle this challenge. Unlike previous methods that usually handle motion prediction and appearance maintenance within the same set of modules, MMVP decouples motion and appearance information by constructing appearance-agnostic motion matrices. The motion matrices represent the temporal similarity of each and every pair of feature patches in the input frames, and are the sole input of the motion prediction module in MMVP. This design improves video prediction in both accuracy and efficiency, and reduces the model size. Results of extensive experiments demonstrate that MMVP outperforms state-of-the-art systems on public data sets by non-negligible large margins (about 1 db in PSNR, UCF Sports) in significantly smaller model sizes (84% the size or smaller).

The weather forecasting system is important for science and society, and significant achievements have been made in applying artificial intelligence (AI) to medium-range weather forecasting. However, existing AI-based weather forecasting models rely on analysis or reanalysis products from traditional numerical weather prediction (NWP) systems as initial conditions for making predictions. Initial states are typically generated by traditional data assimilation components, which are computational expensive and time-consuming. Here we present an AI-based data assimilation model, i.e., Adas, for global weather variables. By introducing the confidence matrix, Adas employs gated convolution to handle sparse observations and gated cross-attention for capturing the interactions between the background and observations. Further, we combine Adas with the advanced AI-based forecasting model (i.e., FengWu) to construct the first end-to-end AI-based global weather forecasting system: FengWu-Adas. We demonstrate that Adas can assimilate global observations to produce high-quality analysis, enabling the system operate stably for long term. Moreover, we are the first to apply the methods to real-world scenarios, which is more challenging and has considerable practical application potential. We have also achieved the forecasts based on the analyses generated by AI with a skillful forecast lead time exceeding that of the IFS for the first time.

Large language models (LLMs) face low hardware efficiency during decoding, especially for long-context reasoning tasks. This paper introduces Step-3, a 321B-parameter VLM with hardware-aware model-system co-design optimized for minimizing decoding costs. Step-3 innovates in two key dimensions: (1) A novel Multi-Matrix Factorization Attention (MFA) mechanism that significantly reduces both KV cache size and computation while maintaining high attention expressiveness, and (2) Attention-FFN Disaggregation (AFD), a distributed inference system that decouples attention and Feed-Forward Network (FFN) layers into specialized subsystems. This co-design achieves unprecedented cost efficiency: Step-3 significantly reduces theoretical decoding costs compared with models like DeepSeek-V3 and Qwen3 MoE 235B, with the gains widening at longer context. Step-3 achieves low cost while activating 38B parameters per token (more than DeepSeek-V3 and Qwen3 MoE 235B), demonstrating that hardware-aligned attention arithmetic intensity, MoE sparsity, and AFD are critical to cost-effectiveness. We perform a head-to-head comparison with DeepSeek-V3 in its favorable scenarios. Our implementation on Hopper GPUs achieves a decoding throughput of up to 4,039 tokens per second per GPU under 50ms TPOT SLA (4K context, FP8, no MTP). It is higher than DeepSeek-V3's 2,324 in the same setup and sets a new Pareto frontier for LLM decoding.

In this paper, we propose CUDA-L2, a system that combines large language models (LLMs) and reinforcement learning (RL) to automatically optimize Half-precision General Matrix Multiply (HGEMM) CUDA kernels. Using CUDA execution speed as the RL reward, CUDA-L2 automatically optimizes HGEMM kernels across 1,000 configurations. CUDA-L2 systematically outperforms major matmul baselines to date, from the widely-used {\it torch.matmul} to state-of-the-art Nvidia's closed-source libraries, i.e., {\it cuBLAS}, {\it cuBLASLt}. In offline mode, where kernels are executed consecutively without time intervals, CUDA-L2 yields +22.0\% over {\it torch.matmul} on average; +19.2\% over {\it cuBLAS} using the optimal layout configuration (normal-normal NN and transposed-normal TN); +16.8\% over {\it cuBLASLt-heuristic}, which queries {\it cuBLASLt} library and selects the algorithm based on the heuristic's suggestion; and +11.4\% over the most competitive {\it cuBLASLt-AutoTuning} model, which selects the fastest algorithm from up to 100 candidates from {\it cuBLASLt}'s suggestions. In server mode, where kernels are executed at random intervals simulating real-time inference, the speedups further increase to +28.7\%, +26.0\%, +22.4\%, and +15.9\% for {\it torch.matmul}, {\it cuBLAS}, {\it cuBLASLt-heuristic}, and {\it cuBLASLt-AutoTuning} respectively. CUDA-L2 shows that even the most performance-critical, heavily-optimized kernels like HGEMM can be improved through LLM-guided RL automation by systematically exploring configuration spaces at scales impractical for humans. Project and code can be found at github.com/deepreinforce-ai/CUDA-L2

Large Language Model (LLM) inference requires substantial computational resources, yet CPU-based inference remains essential for democratizing AI due to the widespread availability of CPUs compared to specialized accelerators. However, efficient LLM inference on CPUs faces two fundamental challenges: (1) existing CPU architectures struggle with low-precision arithmetic required by quantized models, where optimal bit precision varies across models and layers; and (2) the memory-bound nature of the token generation phase creates severe performance bottlenecks. To address these challenges, we propose SAIL (SRAM-Accelerated Inference of LLMs), a CPU-based inference solution that efficiently supports arbitrary bit precisions with minimal overhead. SAIL integrates three key innovations: First, we introduce Batched LUT-based General Matrix-Vector Multiplication (LUT-GEMV) with SRAM-based processing-in-memory, enabling high data reuse through lookup tables and reducing memory movement. Second, our Pattern-Aware LUT optimization identifies and exploits redundancy in input activation patterns, reducing computation cycles by 13.8\%. Third, we develop an in-memory type conversion algorithm that leverages PIM's parallelism for efficient de-/quantization operations, alleviating pressure on CPU's vector units. Our architecture requires only 2\% hardware overhead and a single new instruction, while maintaining dual functionality as both compute and storage units. Experimental evaluations using a modified gem5 simulator demonstrate that SAIL achieves up to 10.7x speedup and 19.9x higher tokens per dollar compared to ARM Neoverse-N1 CPU baselines, and up to 7.04x better cost efficiency than NVIDIA V100 GPUs, establishing a practical path for efficient CPU-based LLM inference.

The Eigenstate Thermalization Hypothesis (ETH) has been established as a cornerstone for understanding thermalization in quantum many-body systems. Recently, there has been growing interest in the full ETH, which extends the framework of the conventional ETH and postulates a smooth function to describe the multi-point correlations among matrix elements. Within this framework, free cumulants play a central role, and most previous studies have primarily focused on closed systems. In this paper, we extend the analysis to a system-bath setup, considering both an idealized case with a random-matrix bath and a more realistic scenario where the bath is modeled as a defect Ising chain. In both cases, we uncover a universal scaling of microcanonical free cumulants of system observables with respect to the interaction strength. Furthermore we establish a connection between this scaling behavior and the thermalization dynamics of the thermal free cumulants of corresponding observables.

Large Language Models (LLMs) demonstrate exceptional performance but entail significant memory and computational costs, restricting their practical deployment. While existing INT4/INT8 quantization reduces these costs, they often degrade accuracy or lack optimal efficiency. INT6 quantization offers a superior trade-off between model accuracy and inference efficiency, but lacks hardware support in modern GPUs, forcing emulation via higher-precision arithmetic units that limit acceleration. In this paper, we propose FlexQ, a novel post-training INT6 quantization framework combining algorithmic innovation with system-level optimizations. FlexQ employs uniform 6-bit weight quantization across all layers, with adaptive retention of 8-bit activations in layers identified through layer-wise sensitivity analysis. To maximize hardware efficiency, we develop a specialized high-performance GPU kernel supporting matrix multiplication for W6A6 and W6A8 representations via Binary Tensor Core (BTC) equivalents, effectively bypassing the lack of native INT6 tensor cores. Evaluations on LLaMA models show FlexQ maintains near-FP16 accuracy, with perplexity increases of no more than 0.05. The proposed kernel achieves an average 1.39times speedup over ABQ-LLM on LLaMA-2-70B linear layers. End-to-end, FlexQ delivers 1.33times inference acceleration and 1.21times memory savings over SmoothQuant. Code is released at https://github.com/FlyFoxPlayer/FlexQ.

While Large Language Models (LLMs) become ever more dominant, classic pre-trained word embeddings sustain their relevance through computational efficiency and nuanced linguistic interpretation. Drawing from recent studies demonstrating that the convergence of GloVe and word2vec optimizations all tend towards log-co-occurrence matrix variants, we construct a novel word representation system called Bit-cipher that eliminates the need of backpropagation while leveraging contextual information and hyper-efficient dimensionality reduction techniques based on unigram frequency, providing strong interpretability, alongside efficiency. We use the bit-cipher algorithm to train word vectors via a two-step process that critically relies on a hyperparameter -- bits -- that controls the vector dimension. While the first step trains the bit-cipher, the second utilizes it under two different aggregation modes -- summation or concatenation -- to produce contextually rich representations from word co-occurrences. We extend our investigation into bit-cipher's efficacy, performing probing experiments on part-of-speech (POS) tagging and named entity recognition (NER) to assess its competitiveness with classic embeddings like word2vec and GloVe. Additionally, we explore its applicability in LM training and fine-tuning. By replacing embedding layers with cipher embeddings, our experiments illustrate the notable efficiency of cipher in accelerating the training process and attaining better optima compared to conventional training paradigms. Experiments on the integration of bit-cipher embedding layers with Roberta, T5, and OPT, prior to or as a substitute for fine-tuning, showcase a promising enhancement to transfer learning, allowing rapid model convergence while preserving competitive performance.

We propose a distributed bundle adjustment (DBA) method using the exact Levenberg-Marquardt (LM) algorithm for super large-scale datasets. Most of the existing methods partition the global map to small ones and conduct bundle adjustment in the submaps. In order to fit the parallel framework, they use approximate solutions instead of the LM algorithm. However, those methods often give sub-optimal results. Different from them, we utilize the exact LM algorithm to conduct global bundle adjustment where the formation of the reduced camera system (RCS) is actually parallelized and executed in a distributed way. To store the large RCS, we compress it with a block-based sparse matrix compression format (BSMC), which fully exploits its block feature. The BSMC format also enables the distributed storage and updating of the global RCS. The proposed method is extensively evaluated and compared with the state-of-the-art pipelines using both synthetic and real datasets. Preliminary results demonstrate the efficient memory usage and vast scalability of the proposed method compared with the baselines. For the first time, we conducted parallel bundle adjustment using LM algorithm on a real datasets with 1.18 million images and a synthetic dataset with 10 million images (about 500 times that of the state-of-the-art LM-based BA) on a distributed computing system.

Computer-use agent (CUA) frameworks, powered by large language models (LLMs) or multimodal LLMs (MLLMs), are rapidly maturing as assistants that can perceive context, reason, and act directly within software environments. Among their most critical applications is operating system (OS) control. As CUAs in the OS domain become increasingly embedded in daily operations, it is imperative to examine their real-world security implications, specifically whether CUAs can be misused to perform realistic, security-relevant attacks. Existing works exhibit four major limitations: Missing attacker-knowledge model on tactics, techniques, and procedures (TTP), Incomplete coverage for end-to-end kill chains, unrealistic environment without multi-host and encrypted user credentials, and unreliable judgment dependent on LLM-as-a-Judge. To address these gaps, we propose AdvCUA, the first benchmark aligned with real-world TTPs in MITRE ATT&CK Enterprise Matrix, which comprises 140 tasks, including 40 direct malicious tasks, 74 TTP-based malicious tasks, and 26 end-to-end kill chains, systematically evaluates CUAs under a realistic enterprise OS security threat in a multi-host environment sandbox by hard-coded evaluation. We evaluate the existing five mainstream CUAs, including ReAct, AutoGPT, Gemini CLI, Cursor CLI, and Cursor IDE based on 8 foundation LLMs. The results demonstrate that current frontier CUAs do not adequately cover OS security-centric threats. These capabilities of CUAs reduce dependence on custom malware and deep domain expertise, enabling even inexperienced attackers to mount complex enterprise intrusions, which raises social concern about the responsibility and security of CUAs.

We utilize a recently developed topic modeling method called SeNMFk, extending the standard Non-negative Matrix Factorization (NMF) methods by incorporating the semantic structure of the text, and adding a robust system for determining the number of topics. With SeNMFk, we were able to extract coherent topics validated by human experts. From these topics, a few are relatively general and cover broad concepts, while the majority can be precisely mapped to specific scientific effects or measurement techniques. The topics also differ by ubiquity, with only three topics prevalent in almost 40 percent of the abstract, while each specific topic tends to dominate a small subset of the abstracts. These results demonstrate the ability of SeNMFk to produce a layered and nuanced analysis of large scientific corpora.

Multi-turn dialogues are essential in many real-world applications of large language models, such as chatbots and virtual assistants. As conversation histories become longer, existing large language models face increasing computational and memory challenges, which hinder their ability to provide efficient and responsive interactions. Most current acceleration methods either compress the context or optimize key value caching, but they often rely on fixed or position-based heuristics that do not adapt well to the dynamic and unpredictable patterns found in actual multi-turn conversations. In this paper, we present LoopServe, an adaptive dual-phase inference acceleration framework for large language models in multi-turn dialogues. LoopServe introduces two main innovations. First, it performs online sparsification during the prefilling phase by dynamically selecting the most important parts of the attention matrix for each new input. Second, it uses progressive key value compression during decoding by adaptively maintaining a relevant and efficient cache based on the most recently generated output tokens. We also propose a https://huggingface.co/datasets/TreeAILab/Multi-turn_Long-context_Benchmark_for_LLMs{new benchmark} with eleven multi-turn datasets that reflect realistic query positions and conversational dependencies. Extensive experiments demonstrate that LoopServe consistently achieves superior effectiveness compared to existing baselines and significantly accelerates LLM inference across a wide range of long-context dialogue tasks.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

We explore the non-equilibrium dynamics of a one-dimensional Fermi-Hubbard system as a sensitive testbed for the capabilities of the time-dependent two-particle reduced density matrix (TD2RDM) theory to accurately describe time-dependent correlated systems. We follow the time evolution of the out-of-equilibrium finite-size Fermi-Hubbard model initialized by a quench over extended periods of time. By comparison with exact calculations for small systems and with matrix product state (MPS) calculations for larger systems but limited to short times, we demonstrate that the TD2RDM theory can accurately account for the non-equilibrium dynamics in the regime from weak to moderately strong inter-particle correlations. We find that the quality of the approximate reconstruction of the three-particle cumulant (or correlation) required for the closure of the equations of motion for the reduced density matrix is key to the accuracy of the numerical TD2RDM results. We identify the size of the dynamically induced three-particle correlations and the amplitude of cross correlations between the two- and three-particle cumulants as critical parameters that control the accuracy of the TD2RDM theory when current state-of-the art reconstruction functionals are employed.

Analytical framework for predicting General Matrix Multiplication (GEMM) performance on modern GPUs, focusing on runtime, power consumption, and energy efficiency. Our study employs two approaches: a custom-implemented tiled matrix multiplication kernel for fundamental analysis, and NVIDIA's CUTLASS library for comprehensive performance data collection across advanced configurations. Using the NVIDIA RTX 4070 as our experimental platform, we developed a Random Forest-based prediction model with multi-output regression capability. Through analysis of both naive tiled matrix multiplication with varying tile sizes (1 to 32) and 16,128 CUTLASS GEMM operations across diverse configurations, we identified critical performance patterns related to matrix dimensions, thread block configurations, and memory access patterns. Our framework achieved exceptional accuracy with an R^2 score of 0.98 for runtime prediction (mean error 15.57%) and 0.78 for power prediction (median error 5.42%). The system successfully predicts performance across matrix sizes, demonstrating robust scaling behavior. Our results show that optimal tile size selection can improve performance by up to 3.2x while reducing power consumption by 22% compared to baseline configurations. Analysis of shared memory utilization and SM occupancy reveals that tile sizes of 16x16 achieve the best balance between parallelism and resource usage. The implementation of our framework, including prediction models and analysis tools, is available as an open-source project at GPPerf [https://github.com/pavlyhalim/GPPerf].

In this article, we introduce a neuro-symbolic approach that combines a low-level perception task performed by a neural network with a high-level reasoning task performed by a possibilistic rule-based system. The goal is to be able to derive for each input instance the degree of possibility that it belongs to a target (meta-)concept. This (meta-)concept is connected to intermediate concepts by a possibilistic rule-based system. The probability of each intermediate concept for the input instance is inferred using a neural network. The connection between the low-level perception task and the high-level reasoning task lies in the transformation of neural network outputs modeled by probability distributions (through softmax activation) into possibility distributions. The use of intermediate concepts is valuable for the explanation purpose: using the rule-based system, the classification of an input instance as an element of the (meta-)concept can be justified by the fact that intermediate concepts have been recognized. From the technical side, our contribution consists of the design of efficient methods for defining the matrix relation and the equation system associated with a possibilistic rule-based system. The corresponding matrix and equation are key data structures used to perform inferences from a possibilistic rule-based system and to learn the values of the rule parameters in such a system according to a training data sample. Furthermore, leveraging recent results on the handling of inconsistent systems of fuzzy relational equations, an approach for learning rule parameters according to multiple training data samples is presented. Experiments carried out on the MNIST addition problems and the MNIST Sudoku puzzles problems highlight the effectiveness of our approach compared with state-of-the-art neuro-symbolic ones.

Multi-agent multi-lidar sensor fusion between connected vehicles for cooperative perception has recently been recognized as the best technique for minimizing the blind zone of individual vehicular perception systems and further enhancing the overall safety of autonomous driving systems. This technique relies heavily on the reliability and availability of vehicle-to-everything (V2X) communication. In practical sensor fusion application scenarios, the non-line-of-sight (NLOS) issue causes blind zones for not only the perception system but also V2X direct communication. To counteract underlying communication issues, we introduce an abstract perception matrix matching method for quick sensor fusion matching procedures and mobility-height hybrid relay determination procedures, proactively improving the efficiency and performance of V2X communication to serve the upper layer application fusion requirements. To demonstrate the effectiveness of our solution, we design a new simulation framework to consider autonomous driving, sensor fusion and V2X communication in general, paving the way for end-to-end performance evaluation and further solution derivation.

Simulating large, strongly interacting fermionic systems remains a major challenge for existing numerical methods. In this work, we present, for the first time, the application of neural quantum states - specifically, hidden fermion determinant states (HFDS) - to simulate the strongly interacting limit of the Fermi-Hubbard model, namely the t-J model, across the entire doping regime. We demonstrate that HFDS achieve energies competitive with matrix product states (MPS) on lattices as large as 8 times 8 sites while using several orders of magnitude fewer parameters, suggesting the potential for efficient application to even larger system sizes. This remarkable efficiency enables us to probe low-energy physics across the full doping range, providing new insights into the competition between kinetic and magnetic interactions and the nature of emergent quasiparticles. Starting from the low-doping regime, where magnetic polarons dominate the low energy physics, we track their evolution with increasing doping through analyses of spin and polaron correlation functions. Our findings demonstrate the potential of determinant-based neural quantum states with inherent fermionic sign structure, opening the way for simulating large-scale fermionic systems at any particle filling.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

As a typical and practical application of Large Language Models (LLMs), Retrieval-Augmented Generation (RAG) techniques have gained extensive attention, particularly in vertical domains where LLMs may lack domain-specific knowledge. In this paper, we introduce an omnidirectional and automatic RAG benchmark, OmniEval, in the financial domain. Our benchmark is characterized by its multi-dimensional evaluation framework, including (1) a matrix-based RAG scenario evaluation system that categorizes queries into five task classes and 16 financial topics, leading to a structured assessment of diverse query scenarios; (2) a multi-dimensional evaluation data generation approach, which combines GPT-4-based automatic generation and human annotation, achieving an 87.47\% acceptance ratio in human evaluations on generated instances; (3) a multi-stage evaluation system that evaluates both retrieval and generation performance, result in a comprehensive evaluation on the RAG pipeline; and (4) robust evaluation metrics derived from rule-based and LLM-based ones, enhancing the reliability of assessments through manual annotations and supervised fine-tuning of an LLM evaluator. Our experiments demonstrate the comprehensiveness of OmniEval, which includes extensive test datasets and highlights the performance variations of RAG systems across diverse topics and tasks, revealing significant opportunities for RAG models to improve their capabilities in vertical domains. We open source the code of our benchmark in https://github.com/RUC-NLPIR/OmniEval{https://github.com/RUC-NLPIR/OmniEval}.

When sound waves hit an object, they induce vibrations that produce high-frequency and subtle visual changes, which can be used for recovering the sound. Early studies always encounter trade-offs related to sampling rate, bandwidth, field of view, and the simplicity of the optical path. Recent advances in event camera hardware show good potential for its application in visual sound recovery, because of its superior ability in capturing high-frequency signals. However, existing event-based vibration recovery methods are still sub-optimal for sound recovery. In this work, we propose a novel pipeline for non-contact sound recovery, fully utilizing spatial-temporal information from the event stream. We first generate a large training set using a novel simulation pipeline. Then we designed a network that leverages the sparsity of events to capture spatial information and uses Mamba to model long-term temporal information. Lastly, we train a spatial aggregation block to aggregate information from different locations to further improve signal quality. To capture event signals caused by sound waves, we also designed an imaging system using a laser matrix to enhance the gradient and collected multiple data sequences for testing. Experimental results on synthetic and real-world data demonstrate the effectiveness of our method.

Previously, methods for learning marginally stable linear dynamical systems either required the transition matrix to be symmetric or incurred regret bounds that scale polynomially with the system's hidden dimension. In this work, we introduce a novel method that overcomes this trade-off, achieving dimension-free regret despite the presence of asymmetric matrices and marginal stability. Our method combines spectral filtering with linear predictors and employs Chebyshev polynomials in the complex plane to construct a novel spectral filtering basis. This construction guarantees sublinear regret in an online learning framework, without relying on any statistical or generative assumptions. Specifically, we prove that as long as the transition matrix has eigenvalues with complex component bounded by 1/poly log T, then our method achieves regret O(T^{9/10}) when compared to the best linear dynamical predictor in hindsight.

Video generation technologies are developing rapidly and have broad potential applications. Among these technologies, camera control is crucial for generating professional-quality videos that accurately meet user expectations. However, existing camera control methods still suffer from several limitations, including control precision and the neglect of the control for subject motion dynamics. In this work, we propose I2VControl-Camera, a novel camera control method that significantly enhances controllability while providing adjustability over the strength of subject motion. To improve control precision, we employ point trajectory in the camera coordinate system instead of only extrinsic matrix information as our control signal. To accurately control and adjust the strength of subject motion, we explicitly model the higher-order components of the video trajectory expansion, not merely the linear terms, and design an operator that effectively represents the motion strength. We use an adapter architecture that is independent of the base model structure. Experiments on static and dynamic scenes show that our framework outperformances previous methods both quantitatively and qualitatively. The project page is: https://wanquanf.github.io/I2VControlCamera .

The Poisson equation has wide applications in many areas of science and engineering. Although there are some quantum algorithms that can efficiently solve the Poisson equation, they generally require a fault-tolerant quantum computer which is beyond the current technology. In this paper, we propose a Variational Quantum Algorithm (VQA) to solve the Poisson equation, which can be executed on Noise Intermediate-Scale Quantum (NISQ) devices. In detail, we first adopt the finite difference method to transform the Poisson equation into a linear system. Then, according to the special structure of the linear system, we find an explicit tensor product decomposition, with only 2log n+1 items, of its coefficient matrix under a specific set of simple operators, where n is the dimension of the coefficient matrix. This implies that the proposed VQA only needs O(log n) measurements, which dramatically reduce quantum resources. Additionally, we perform quantum Bell measurements to efficiently evaluate the expectation values of simple operators. Numerical experiments demonstrate that our algorithm can effectively solve the Poisson equation.

A central goal of sequence modeling is designing a single principled model that can address sequence data across a range of modalities and tasks, particularly on long-range dependencies. Although conventional models including RNNs, CNNs, and Transformers have specialized variants for capturing long dependencies, they still struggle to scale to very long sequences of 10000 or more steps. A promising recent approach proposed modeling sequences by simulating the fundamental state space model (SSM) \( x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) \), and showed that for appropriate choices of the state matrix \( A \), this system could handle long-range dependencies mathematically and empirically. However, this method has prohibitive computation and memory requirements, rendering it infeasible as a general sequence modeling solution. We propose the Structured State Space sequence model (S4) based on a new parameterization for the SSM, and show that it can be computed much more efficiently than prior approaches while preserving their theoretical strengths. Our technique involves conditioning \( A \) with a low-rank correction, allowing it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. S4 achieves strong empirical results across a diverse range of established benchmarks, including (i) 91\% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet, (ii) substantially closing the gap to Transformers on image and language modeling tasks, while performing generation 60times faster (iii) SoTA on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors.

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

The weight matrix (WM) of a neural network (NN) is its program. The programs of many traditional NNs are learned through gradient descent in some error function, then remain fixed. The WM of a self-referential NN, however, can keep rapidly modifying all of itself during runtime. In principle, such NNs can meta-learn to learn, and meta-meta-learn to meta-learn to learn, and so on, in the sense of recursive self-improvement. While NN architectures potentially capable of implementing such behaviour have been proposed since the '90s, there have been few if any practical studies. Here we revisit such NNs, building upon recent successes of fast weight programmers and closely related linear Transformers. We propose a scalable self-referential WM (SRWM) that learns to use outer products and the delta update rule to modify itself. We evaluate our SRWM in supervised few-shot learning and in multi-task reinforcement learning with procedurally generated game environments. Our experiments demonstrate both practical applicability and competitive performance of the proposed SRWM. Our code is public.

Large Language Models (LLMs) have become instrumental across various applications, with the customization of these models to specific scenarios becoming increasingly critical. System message, a fundamental component of LLMs, is consist of carefully crafted instructions that guide the behavior of model to meet intended goals. Despite the recognized potential of system messages to optimize AI-driven solutions, there is a notable absence of a comprehensive benchmark for evaluating how well different LLMs follow these system messages. To fill this gap, we introduce SysBench, a benchmark that systematically analyzes system message following ability in terms of three challenging aspects: constraint complexity, instruction misalignment and multi-turn stability. In order to enable effective evaluation, SysBench constructs multi-turn user conversations covering various interaction relationships, based on six common types of constraints from system messages in real-world scenarios. Our dataset contains 500 system messages from various domains, each paired with 5 turns of user conversations, which have been manually formulated and checked to guarantee high quality. SysBench provides extensive evaluation across various LLMs, measuring their ability to follow specified constraints given in system messages. The results highlight both the strengths and weaknesses of existing models, offering key insights and directions for future research. The open source library SysBench is available at https://github.com/PKU-Baichuan-MLSystemLab/SysBench.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

Post-training is essential for enabling large language models (LLMs) to follow human instructions. However, its effectiveness depends on high-quality instruction data, which is challenging to obtain in the real world due to privacy concerns, data scarcity, and high annotation costs. To fill this gap, inspired by the recent success of using LLMs to simulate human society, we propose MATRIX, a multi-agent simulator that automatically generates diverse text-based scenarios, capturing a wide range of real-world human needs in a realistic and scalable manner. Leveraging these outputs, we introduce a novel scenario-driven instruction generator MATRIX-Gen for controllable and highly realistic data synthesis. Extensive experiments demonstrate that our framework effectively generates both general and domain-specific data. On AlpacaEval 2 and Arena-Hard benchmarks, Llama-3-8B-Base, post-trained on datasets synthesized by MATRIX-Gen with just 20K instruction-response pairs, outperforms Meta's Llama-3-8B-Instruct model, which was trained on over 10M pairs.

System messages play a crucial role in interactions with large language models (LLMs), often serving as prompts to initiate conversations. Through system messages, users can assign specific roles, perform intended tasks, incorporate background information, specify various output formats and communication styles. Despite such versatility, publicly available data are often lack system messages and subject to strict license constraints in the industry field. Manual labeling of publicly available data with system messages that align with user instructions demands significant resources. In view of such challenges, our work introduces SysGen, a pipeline for generating system messages with better aligned assistant responses from the supervised fine-tuning dataset without system messages. Training on SysGen data has demonstrated substantial improvements in the alignment of model responses with system messages and user instructions, as demonstrated across various open-source models on the Multifacet benchmark, while maintaining minimal impact on other unseen benchmarks such as Open LLM Leaderboard 2. Our qualitative analysis highlights the importance of diverse system messages to ensure better adaptability across different contexts.

We study the complexity of sampling from a distribution over all index subsets of the set {1,...,n} with the probability of a subset S proportional to the determinant of the submatrix L_S of some ntimes n p.s.d. matrix L, where L_S corresponds to the entries of L indexed by S. Known as a determinantal point process, this distribution is used in machine learning to induce diversity in subset selection. In practice, we often wish to sample multiple subsets S with small expected size k = E[|S|] ll n from a very large matrix L, so it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). For this purpose, we propose a new algorithm which, given access to L, samples exactly from a determinantal point process while satisfying the following two properties: (1) its preprocessing cost is n cdot poly(k), i.e., sublinear in the size of L, and (2) its sampling cost is poly(k), i.e., independent of the size of L. Prior to our results, state-of-the-art exact samplers required O(n^3) preprocessing time and sampling time linear in n or dependent on the spectral properties of L. We also give a reduction which allows using our algorithm for exact sampling from cardinality constrained determinantal point processes with ncdotpoly(k) time preprocessing.

A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.

Large neural networks excel in many domains, but they are expensive to train and fine-tune. A popular approach to reduce their compute or memory requirements is to replace dense weight matrices with structured ones (e.g., sparse, low-rank, Fourier transform). These methods have not seen widespread adoption (1) in end-to-end training due to unfavorable efficiency--quality tradeoffs, and (2) in dense-to-sparse fine-tuning due to lack of tractable algorithms to approximate a given dense weight matrix. To address these issues, we propose a class of matrices (Monarch) that is hardware-efficient (they are parameterized as products of two block-diagonal matrices for better hardware utilization) and expressive (they can represent many commonly used transforms). Surprisingly, the problem of approximating a dense weight matrix with a Monarch matrix, though nonconvex, has an analytical optimal solution. These properties of Monarch matrices unlock new ways to train and fine-tune sparse and dense models. We empirically validate that Monarch can achieve favorable accuracy-efficiency tradeoffs in several end-to-end sparse training applications: speeding up ViT and GPT-2 training on ImageNet classification and Wikitext-103 language modeling by 2x with comparable model quality, and reducing the error on PDE solving and MRI reconstruction tasks by 40%. In sparse-to-dense training, with a simple technique called "reverse sparsification," Monarch matrices serve as a useful intermediate representation to speed up GPT-2 pretraining on OpenWebText by 2x without quality drop. The same technique brings 23% faster BERT pretraining than even the very optimized implementation from Nvidia that set the MLPerf 1.1 record. In dense-to-sparse fine-tuning, as a proof-of-concept, our Monarch approximation algorithm speeds up BERT fine-tuning on GLUE by 1.7x with comparable accuracy.

This paper explores the relationship between matrix factorizations and linear matrix equations. It shows that every matrix factorization defines two hidden projectors, one for the column space and one for the row space of a matrix, and how to calculate them. The projectors can be applied to solve linear matrix equations, generate low-rank approximations, or design randomized matrix algorithms. But also, as demonstrated, they can be applied in cryptography to encrypt and decrypt messages. The paper discusses some of the security implications of this application and leaves some questions open for further investigation. The basic concepts are illustrated with source code listings. Finally, this work shares some personal reflections on the meaning and importance of understanding in the time of the artificial intelligence revolution.