48 articles mentioning Matrix-Game-4.0
arXiv:2601.05845v2 Announce Type: replace Abstract: Poisson non-negative matrix factorization (NMF) is a widely used method to find interpretable "parts-based" decompositions of count data. While many variants of Poisson NMF exist, existing methods assume that the "parts" in the decomposition combin
arXiv:2603.14360v3 Announce Type: replace-cross Abstract: Transformers are highly parallel but are limited to computations in the TC$^0$ complexity class, excluding tasks such as entity tracking and code execution that provably require greater expressive power. Motivated by this limitation, we revis
arXiv:2610.21273v1 Announce Type: new Abstract: We study the problem of online learning of quantum states with logarithmic loss, which is a quantum generalization of online portfolio selection and has applications to quantum state tomography, the task of estimating an unknown quantum state from meas
arXiv:2610.21312v1 Announce Type: new Abstract: Data-free preconditioning builds the Kronecker factors of KFAC from synthetic probes instead of private data. DP-KFC validates a probe by matching the eigenvalue decay of the private factors; we turn this criterion into a random-matrix account of what
arXiv:2607.24041v3 Announce Type: replace-cross Abstract: Over-parameterized linear regression has been widely studied over the last decade. However, most existing works assume that the covariates are independent and that their covariance matrices are non-degenerate. In this paper, we relax both ass
arXiv:2605.11471v2 Announce Type: replace Abstract: Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, yet their approximation capabilities remain poorly understood in theory. In this paper, we characterize these capabilities from both neg
arXiv:2610.12744v1 Announce Type: new Abstract: Parameter-efficient continual learning updates a restricted subset of adapter parameters to incorporate sequential tasks while limiting catastrophic forgetting. Gradient attribution is a common rule for selecting that subset, but it requires an additio
arXiv:2610.10871v1 Announce Type: new Abstract: Large Language Models (LLMs) achieve strong performance across many domains, but their efficiency is limited by the quadratic cost of attention with respect to prompt length. Sparse attention reduces this cost by retaining only a small fraction of quer
arXiv:2610.09044v1 Announce Type: cross Abstract: Weak-to-strong generalization is the phenomenon where a strong student model trained with labels produced by a weak teacher model is able to generalize better than the teacher. In this paper, we study this phenomenon in two-layer random feature netwo
arXiv:2610.02882v1 Announce Type: cross Abstract: Large-scale foundation models achieve strong performance across diverse tasks, but their size makes inference costly, largely due to dense matrix multiplications. Prior work reduces this cost by replacing dense weight matrices with efficient structur
arXiv:2610.00389v1 Announce Type: new Abstract: Open-ended query generation lacks standard answers, thus necessitating an effective reward mechanism. Pointwise scoring rubrics provide limited information about the relative quality of sample answers under the same prompt; merging multiple rubric judg
arXiv:2610.01361v1 Announce Type: cross Abstract: Multilayer networks allow the modeling of interactions between the same entities across different contexts, such as temporal observations, varying settings, or interactions of different types. The goal of community detection in multilayer networks is
arXiv:2610.00232v1 Announce Type: new Abstract: Fixed-size recurrent memory limits storage growth during inference, but successful recall depends on the task and training. We study a small DeltaNet variant with fixed token-specific key biases, trained to remember 32 new key-value pairings per sequen
arXiv:2609.39816v1 Announce Type: new Abstract: Fast matrix multiplication saves multiplications through exact cancellation, but rounding sums that mix token rows can leave contributions from later tokens in earlier language model outputs. This threatens prefix invariance, which multiple-choice like
arXiv:2609.38835v1 Announce Type: cross Abstract: Optimistic matrix mirror-prox (OMMP) computes $\epsilon$-approximate Nash equilibria in quantum zero-sum games with an $O(1/\varepsilon)$ average-iterate guarantee [arXiv:2311.10859]. We investigate whether this dependence on accuracy is tight and wh
arXiv:2609.39829v1 Announce Type: cross Abstract: Modern machine learning depends heavily on massive datasets, but obtaining high-quality annotations at scale is often expensive. As a result, learning from noisily-labeled data has become common, making accurate estimation of the label-noise transiti
arXiv:2609.38561v1 Announce Type: cross Abstract: Zeroth-order optimization methods are essential for solving black-box problems where gradient information is unavailable or expensive to compute. This paper presents POEM-CMA, a novel parameter-free stochastic zeroth-order algorithm that extends the
arXiv:2606.17531v2 Announce Type: replace Abstract: Non-negative matrix factorisation (NMF) learns additive representations from data, but non-negativity alone does not ensure interpretable basis functions. We introduce Top-NMF, which guides basis learning through general topological preferences wit
arXiv:2601.16294v3 Announce Type: replace-cross Abstract: General Matrix Multiplication (GEMM) is the cornerstone of HPC workloads and Deep Learning. State-of-the-art (SOTA) vendor libraries tune tensor layouts, parallelization schemes and cache blocking to minimize data movement across the memory h
arXiv:2605.09509v2 Announce Type: replace-cross Abstract: The problem of predicting unobserved entries in a binary matrix, known as 1-bit matrix completion, has found diverse applications in fields such as recommendation systems. In this study, we develop an empirical Bayes method for 1-bit matrix c
arXiv:2606.26472v4 Announce Type: replace Abstract: Reasoning models can generate chains of thought tens of thousands of tokens long, making the key--value (KV) cache that holds them a major bottleneck for inference throughput. Existing eviction policies for long reasoning traces typically rank cach
arXiv:2609.21815v2 Announce Type: replace-cross Abstract: Adaptive optimization methods such as AdaGrad and Adam are widely used in modern deep neural network training, but their adaptive scaling is primarily designed for vector-valued parameters and does not explicitly exploit matrix structure. Rec
arXiv:2603.19703v3 Announce Type: replace-cross Abstract: Estimating covariance matrices is fundamental to a wide range of statistical applications. This paper studies minimax and adaptive estimation of high-dimensional covariance matrices under $\rho$-zero-concentrated differential privacy ($\rho$-
arXiv:2605.13312v2 Announce Type: replace Abstract: Multimodal brain network analysis faces a persistent trade-off between predictive accuracy and interpretability. Deep neural networks achieve high accuracy but behave as black boxes that reveal little about the brain modules driving their decisions
arXiv:2609.28562v1 Announce Type: cross Abstract: Aggregation theory has traditionally focused on operators defined over vectors. However, many applications-including Multi-Criteria Decision Making, Group Decision Making, Fuzzy Rule-Based Classification Systems, and overlap/grouping indices-require
arXiv:2609.30078v1 Announce Type: cross Abstract: Matrix completion, the problem of estimating missing entries in a matrix from noisily observed ones, underlies a diverse array of problems such as recommender systems and counterfactual outcome estimation in panel data. Many algorithms address the pr
arXiv:2605.13343v3 Announce Type: replace-cross Abstract: Interactive simulation solves Ax=b for a sparse SPD A that changes every frame, inside an 8-16 ms budget. At a few thousand unknowns, the setup of algebraic multigrid alone exceeds that budget, while Jacobi and other local preconditioners hav
arXiv:2507.22170v2 Announce Type: replace-cross Abstract: Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared singular
arXiv:2609.26978v1 Announce Type: cross Abstract: We study online inverse linear optimization with a fixed unknown linear utility: in each round, an environment presents a compact action set, the learner recommends an action from it, and the environment returns an action that maximizes the utility o
arXiv:2609.22991v2 Announce Type: replace-cross Abstract: Apple Silicon machines with large unified memory make it possible to hold large tensors on a desktop GPU. However, we found that PyTorch's Metal Performance Shaders (MPS) backend silently returns wrong results for batched matrix multiplicatio
arXiv:2607.25967v2 Announce Type: replace-cross Abstract: Singular Value Decomposition (SVD) underlies matrix factorisation tasks across many fields, with imaging applications demanding real-time processing. Yet SVD algorithms are inherently sequential, constraining real-time GPU throughput and limi
arXiv:2609.15643v2 Announce Type: replace Abstract: Flow-matching diffusion models have recently emerged as a strong paradigm for high-fidelity visual generation. However, their prohibitively high fine-tuning cost limits scalability to downstream tasks. While Low-Rank Adaptation (LoRA) combined with
arXiv:2507.02248v2 Announce Type: replace-cross Abstract: In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank target matrix with auxiliary data available. We propose a transfer learning procedure given prior info
arXiv:2609.22991v1 Announce Type: cross Abstract: Apple Silicon machines with 192GB or more of unified memory make it routine to place tensors with more than $2^{32}$ elements on a desktop GPU. We show that PyTorch's Metal Performance Shaders (MPS) backend silently returns wrong results for batched
arXiv:2603.29715v2 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, X, by the product of two nonnegative factors, WH, where W has r columns and H has r rows. In this paper, we consider NMF using the component-wise L1 norm as the error measure
arXiv:2609.21944v1 Announce Type: cross Abstract: In recent years, quantum game theory has gained significant attention as a framework for studying decision-making in multi-agent systems using quantum principles. However, computing equilibrium strategies is challenging because the dimension of the j
arXiv:2609.20068v1 Announce Type: new Abstract: This paper builds a theoretical bridge between the economic notion of marginal utility and two machine-learning constructs, matrix factorization and the Key--Value cache of transformer language models. The singular value spectrum of a rating matrix is
arXiv:2509.11983v3 Announce Type: replace Abstract: Neural network (NN) training is inherently a large-scale matrix optimization problem, yet the matrix structure of NN parameters has long been overlooked. Recently, the optimizer Muon \citep{jordanmuon}, which explicitly exploits this structure, has
arXiv:2609.17594v1 Announce Type: new Abstract: Can gradient-based training learn the rank needed to store and compose associations in a matrix memory? In our earlier study, we used a matrix-augmented reasoner on a task that admits a rank-1 solution, leaving this question open. We train matrix memor
arXiv:2609.17048v1 Announce Type: cross Abstract: We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries. Convex methods achieve sample complexity linear in the matrix dimension and the rank, up to logarithmic factors, whereas globa
arXiv:2512.22282v2 Announce Type: replace-cross Abstract: Across fields such as machine learning, social science, and geology, considerable attention has been given to models that factorize a nonnegative matrix into the product of two or three matrices, subject to nonnegative or row-sum-to-1 constra
arXiv:2609.15838v1 Announce Type: cross Abstract: Per-matrix singular value decomposition (SVD) truncation is Eckart-Young optimal in the whitened Frobenius norm, but errors from independently compressed matrices compound through the block's nonlinear forward pass. Inspired in part by hierarchical v
arXiv:2609.14802v1 Announce Type: cross Abstract: Importance weights are essential in domain adaptation under label shift, yet their utility is often undermined by the finite sample uncertainty associated with their estimation. Existing methods typically analyze this uncertainty through Gaussian eli
arXiv:2609.15044v1 Announce Type: cross Abstract: Data attribution seeks to quantify how individual training examples shape a model's predictions and underpins problems including data valuation, machine unlearning, and model interpretability. Despite having a long line of work, computationally scala
arXiv:2506.04166v3 Announce Type: replace Abstract: Nearest neighbor (NN) methods have re-emerged as competitive tools for matrix completion, offering strong empirical performance and recent theoretical guarantees, including entry-wise error bounds, confidence intervals, and minimax optimality. Desp
arXiv:2512.12767v2 Announce Type: replace-cross Abstract: Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation slows and diversifies inhibitory timescales, leading to improved task performance that is attributed
arXiv:2609.12259v1 Announce Type: new Abstract: Matrix-valued memories make rank the natural budget of a learned representation: the number of independent directions a state spans bounds what it can bind, compose, and track. We report causal evidence, on a group-composition testbed trained under a h
arXiv:2609.11713v1 Announce Type: cross Abstract: Artificial neural networks rely on vector-matrix multiplications (VMMs), whose implementation in von Neumann architectures is dominated by costly data movement between memory and processing units. Spiking neural networks (SNNs) mitigate this bottlene