Neural Information Processing Systems http://nips.cc/

This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and accordingly weighs informative features while discovering biclusters. Moreover, the method is adaptive to the data, and is accompanied by an efficient algorithm based on proximal alternating minimization, complete with detailed guidance on hyperparameter tuning and efficient solutions to optimization subproblems. These contributions are theoretically grounded; we establish finite-sample bounds on the objective function under sub-Gaussian errors, and generalize these guarantees to cases where input affinities need not be uniform. Extensive simulation results reveal our method consistently recovers underlying biclusters while weighing and selecting features appropriately, outperforming peer methods. An application to a gene microarray dataset of lymphoma samples recovers biclusters matching an underlying classification, while giving additional interpretation to the mRNA samples via the column groupings and fitted weights.

The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its exact computation is expensive for large weight matrices. Randomized alternatives such as randomized SVD (RSVD) improve efficiency, yet they can suffer from poor approximation quality when the singular value spectrum decays slowly, a regime commonly observed in modern pretrained models. In this work, we address this limitation from both theoretical and empirical perspectives. First, we establish a connection between low-rank approximation error and predictive performance by analyzing softmax perturbations, showing that deviations in class probabilities are controlled by the spectral error of the compressed weights. Second, we demonstrate that RSVD is inadequate, and we propose randomized subspace iteration (RSI) as a more effective alternative. By incorporating multiple power iterations, RSI improves spectral separation and provides a controllable mechanism for enhancing approximation quality. We evaluate our approach on both convolutional networks and transformer-based architectures. Our results show that RSI achieves near-optimal approximation quality while outperforming RSVD in predictive accuracy under aggressive compression, enabling efficient model compression.

Internet of Things and Deep Learning are synergetically and exponentially growing industrial fields with a massive call for their unification into a common framework called Edge AI. While on-device inference is a well-explored topic in recent research, backpropagation remains an open challenge due to its prohibitive computational and memory costs compared to the extreme resource constraints of embedded devices. Drawing on tensor decomposition research, we tackle the main bottleneck of backpropagation, namely the memory footprint of activation map storage. We investigate and compare the effects of activation compression using Singular Value Decomposition and its tensor variant, High-Order Singular Value Decomposition. The application of low-order decomposition results in considerable memory savings while preserving the features essential for learning, and also offers theoretical guarantees to convergence. Experimental results obtained on main-stream architectures and tasks demonstrate Pareto-superiority over other state-of-the-art solutions, in terms of the trade-off between generalization and memory footprint.

Neural Information Processing Systems http://nips.cc/

In this paper we propose to use an old and surprisingly simple method due to Jacobi to compute these eigenvalue and singular value decompositions, and we demonstrate that it can lead to substantial gains in terms of computation time compared to standard approaches.

The grade of membership model is a flexible latent variable model for analyzing multivariate categorical data through individual-level mixed membership scores. In many modern applications, auxiliary covariates are collected alongside responses and encode information about the same latent structure. Traditional approaches to incorporating such covariates typically rely on fully specified joint likelihoods, which are computationally intensive and sensitive to misspecification. We introduce a covariate-assisted grade of membership model that integrates response and covariate information by exploiting their shared low-rank simplex geometry, rather than modeling their joint distribution. We propose a likelihood-free spectral estimation procedure that combines heterogeneous data sources through a balance parameter controlling their relative contribution. To accommodate high-dimensional and heteroskedastic noise, we employ heteroskedastic principal component analysis before performing simplex-based geometric recovery. Our theoretical analysis establishes weaker identifiability conditions than those required in the covariate-free model, and further derives finite-sample, entrywise error bounds for both mixed membership scores and item parameters. These results demonstrate that auxiliary covariates can provably improve latent structure recovery, yielding faster convergence rates in high-dimensional regimes. Simulation studies and an application to educational assessment data illustrate the computational efficiency, statistical accuracy, and interpretability gains of the proposed method. The code for reproducing these results is open-source and available at \texttt{https://github.com/Toby-X/Covariate-Assisted-GoM}

We consider proximal splitting algorithms for convex optimization problems over matrices. A significant computational bottleneck in many of these algorithms is the need to compute a full eigenvalue or singular value decomposition at each iteration for the evaluation of a proximal operator.In this paper we propose to use an old and surprisingly simple method due to Jacobi to compute these eigenvalue and singular value decompositions, and we demonstrate that it can lead to substantial gains in terms of computation time compared to standard approaches. We rely on three essential properties of this method: (a) its ability to exploit an approximate decomposition as an initial point, which in the case of iterative optimization algorithms can be obtained from the previous iterate; (b) its parallel nature which makes it a great fit for hardware accelerators such as GPUs, now common in machine learning, and (c) its simple termination criterion which allows us to trade-off accuracy with computation time. We demonstrate the efficacy of this approach on a variety of algorithms and problems, and show that, on a GPU, we can obtain 5 to 10x speed-ups in the evaluation of proximal operators compared to standard CPU or GPU linear algebra routines. Our findings are supported by new theoretical results providing guarantees on the approximation quality of proximal operators obtained using approximate eigenvalue or singular value decompositions.

We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to weighting distributions with arbitrary continuous values, thereby providing a unified framework to analyze the impact of various kinds of noise on the training trajectory. We characterize the implicit regularization induced through the random weighting, connect it with weighted linear regression, and derive non-asymptotic bounds for convergence in first and second moments. Leveraging geometric moment contraction, we also investigate the stationary distribution induced by the added noise. Based on these results, we discuss how specific choices of weighting distribution influence both the underlying optimization problem and statistical properties of the resulting estimator, as well as some examples for which weightings that lead to fast convergence cause bad statistical performance.

The Key-Value (KV) cache is central to the efficiency of transformer-based large language models (LLMs), storing previously computed vectors to accelerate inference. Yet, as sequence length and batch size grow, the cache becomes a major memory bottleneck. Prior compression methods typically apply low-rank decomposition to keys alone or attempt to jointly embed queries and keys, but both approaches neglect that attention fundamentally depends on their inner products. In this work, we prove that such strategies are suboptimal for approximating the attention matrix. We introduce KQ-SVD, a simple and computationally efficient method that directly performs an optimal low-rank decomposition of the attention matrix via a closed-form solution. By targeting the true source of redundancy, KQ-SVD preserves attention outputs with higher fidelity under compression. Extensive evaluations on LLaMA and Mistral models demonstrate that our approach consistently delivers superior projection quality.