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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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48 results for Low-rank activations

LASER compresses recursive model activations by exploiting their low-dimensional structure.

problem Understanding and optimizing the geometric structure of recursive reasoning trajectories.
method Dynamic low-rank basis tracking via matrix-free subspace tracking with a fidelity-triggered reset mechanism.
result Recursive activations occupy a linear, low-dimensional subspace that can be compressed efficiently.

IMPACT optimizes LLM compression by focusing on activation importance, reducing model size up to 55.4%.

problem Resource constraints in deploying large language models (LLMs).
method IMPACT integrates activation importance into low-rank compression, optimizing for both size and accuracy.
result IMPACT achieves up to 55.4% greater model size reduction while maintaining comparable or better accuracy.

Active learning method for neural population dynamics using optogenetics.

problem Efficiently selecting neurons to stimulate for identifying neural population dynamics.
method Developed active learning procedure for low-rank regression to determine informative photostimulation patterns.
result Demonstrated a two-fold reduction in data required for predictive power using low-rank linear dynamical systems model.

New method recovers matrix column space with active sampling for better results.

problem Recovering column space of partially observed matrices with limited data.
method Alternating minimization with active sampling strategy.
result Active sampling improves convergence to true column space with higher probability.

New CSC model extracts EEG signals with low noise sensitivity.

problem Analyzing noisy EEG signals during anesthesia.
method Kruskal CSC model using Kruskal decomposition for low-rank tensor activations.
result TC-FISTA efficiently extracts robust, sparse, and interpretable EEG encodings.

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of methods have been developed for this recovery problem. However, a principled meth…

2011-02-25abs ↗pdf ↗

Active sampling selects few points for accurate model reduction of high-fidelity systems.

problem Efficiently identify dominant subspaces for model reduction of large training sets.
method Proposes an active sampling strategy to select a few points from the training set to estimate dominant subspaces accurately.
result Active sampling can provide 17x speed-up without sacrificing accuracy.

The paper reveals low-rank structure in neural network gradients, influenced by data and model parameters.

problem Investigating low-rank structure in gradients of neural networks under relaxed assumptions.
method Spiked data model, relaxation of isotropy assumptions, analysis of mean-field and neural-tangent-kernel scalings.
result Gradient of input weights is approximately low rank, dominated by two rank-one terms.

Sharp asymptotics reveal how network width controls learnability in quadratic neural networks.

problem Understanding learnability in overparameterized quadratic neural networks.
method Mapping ERM to convex matrix sensing with nuclear norm penalization.
result Characterization of global minima and precise generalization thresholds.

Kolmogorov-Arnold Networks offer improved interpretability and parsimony in science tasks.

problem Improving interpretability and parsimony in science-oriented tasks.
method Theoretical analysis of Kolmogorov-Arnold Networks (KAN) with generalization bounds and model complexity.
result Generalization bounds for KAN with various activation functions, scaling with the l1l_1 norm of coefficient matrices and Lipschitz constants.

Flat minima lead to better generalization in low-rank matrix recovery models.

problem Understanding why flat minima generalize well in overparameterized models.
method Analysis of overparameterized matrix and bilinear sensing, robust PCA, covariance matrix estimation, and neural networks with quadratic activation functions.
result Flat minima, measured by the trace of the Hessian, exactly recover the ground truth in low-rank matrix recovery models under standard statistical assumptions.

The paper establishes theoretical foundations for low-rank knowledge distillation in LLMs.

problem Understanding the theoretical underpinnings of low-rank knowledge distillation in LLMs.
method Theoretical framework for low-rank knowledge distillation, including convergence rates and generalization bounds.
result Theoretical analysis reveals optimal rank r=O(n)r^* = O(\sqrt{n}) for minimizing generalization error.

EVA adapts LoRA for faster, more efficient fine-tuning.

problem Fast and efficient fine-tuning of large models for specific tasks.
method EVA uses directions capturing most activation variance for initialization, maximizing gradient signal and reducing parameters.
result EVA achieves faster convergence and higher average scores across tasks, reducing parameters.

This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model achieves a significantly more efficient encoding of the multivariate signal-partic…

2019-08-09abs ↗pdf ↗

New method for robust PCA with exponential family distributions.

problem Recovering low-rank structure from data matrices with outliers.
method Alternating Direction Method of Multipliers for eextRPCAe^{ ext{RPCA}}.
result Demonstrated effectiveness in steel sheet defect detection and crime activity monitoring.

New method estimates neuronal connectivity from partially observed data.

problem Estimating neuronal connectivity from partially observed data.
method Two-step approach: low-rank covariance completion followed by graph structure estimation.
result Graph selection consistency demonstrated for one approach.

New method accelerates CNNs for mobile devices by approximating tensors and quantizing weights.

problem Efficiently compress and accelerate CNNs for mobile devices.
method Low-rank tensor approximation in Tucker format combined with quantization of weights and activations.
result Our method significantly improves CNN performance on various classification tasks.

LoRA fine-tuning explained with gradient dynamics for low-rank perturbations.

problem Understanding why gradient descent converges to useful low-rank perturbations in LoRA fine-tuning.
method Generalized student-teacher setting with i.i.d. samples and online gradient descent.
result Gradient descent converges to the teacher model in dkO(1)dk^{O(1)} iterations under certain conditions.

Active learning aims to obtain a classifier of high accuracy by using fewer label requests in comparison to passive learning by selecting effective queries. Many active learning methods have been developed in the past two decades, which sample queries based on informativeness or representativeness of unlabeled data poi…

2015-07-15abs ↗pdf ↗

ZDP detects drift in large language models without labels, proving key theorems and metrics.

problem Detecting drift in large language models without task labels or output evaluations.
method Zero-Direction Probing (ZDP) framework based on null directions of transformer activations, proving theoretical guarantees.
result Proves the Variance--Leak Theorem, Fisher Null-Conservation, Rank--Leak bound, and logarithmic-regret guarantee.

Study on identifiability of deep polynomial neural networks.

problem Understanding when polynomial neural networks can be uniquely identified.
method Comprehensive analysis including various architectures, using tensor decompositions and Kruskal-type theorems.
result Identifiability conditions for deep PNNs, including layer width and activation degree constraints.

This paper proposes a new method to compress CNNs for medical image analysis, improving efficiency and accuracy.

problem Large memory and computational requirements of CNNs in resource-constrained environments.
method Hierarchical spatio-channel low-rank compression framework that partitions feature maps into spatial regions and groups channels according to co-activation patterns within each region.
result The proposed method achieves significant FLOP reduction, inference speed-up, and improved classification accuracy compared to existing methods.

This paper extends the Gaussian process interpretation of deep networks to more varied weight distributions.

problem Understanding the impact of different weight initialization schemes on deep learning dynamics.
method Extending the Gaussian process interpretation to PSEUDO-IID weight distributions, including sparse and low-rank networks.
result PSEUDO-IID initialized networks are effectively equivalent up to variance, enabling tractable posterior distributions.

Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning, the current methods of choice are arguably K-SVD and its variants, which learn a …

2017-03-22abs ↗pdf ↗

How can we correlate neural activity in the human brain as it responds to words, with behavioral data expressed as answers to questions about these same words? In short, we want to find latent variables, that explain both the brain activity, as well as the behavioral responses. We show that this is an instance of the C…

2013-02-28abs ↗pdf ↗

FMMNN combines sine activations with multi-component, multi-layer structure for high-frequency function approximation.

problem Effective representation and learning of high-frequency features in neural networks.
method Introduces FMMNN with sine-type activations and multi-component, multi-layer structure.
result FMMNN achieves strong accuracy and favorable convergence on oscillatory function-approximation benchmarks.

This paper addresses anisotropy in Transformer models, providing geometric insights and empirical support.

problem Anisotropy phenomenon in Transformer models, challenging their geometric interpretation.
method Derive geometric arguments and use concept-based mechanistic interpretability during training.
result Activation-derived directions capture large gradient energy and a larger share of gradient anisotropy than normal controls.

Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix factorization approximates the entries of the matrix by a simple, fixed function-…

2015-11-19abs ↗pdf ↗

Residential homes constitute roughly one-fourth of the total energy usage worldwide. Providing appliance-level energy breakdown has been shown to induce positive behavioral changes that can reduce energy consumption by 15%. Existing approaches for energy breakdown either require hardware installation in every target ho…

2019-09-02abs ↗pdf ↗

Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal processing and bioinformatics. Recently, much progress has been made in theories, algori…

2014-01-15abs ↗pdf ↗

SGD with mini-batches can solve convex low-rank matrix problems efficiently.

problem Solving large-scale convex low-rank matrix problems efficiently.
method Stochastic Gradient Descent with mini-batches and low-rank projections.
result SGD with mini-batches produces low-rank iterates with high probability.

Novel method for efficient low-rank matrix estimation and bandit algorithms.

problem Low-rank matrix estimation and bandit problems.
method LowPopArt method for low-rank matrix estimation and novel experimental design criterion.
result Improved recovery guarantees and regret bounds for low-rank bandit algorithms.

In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to …

2018-11-05abs ↗pdf ↗

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy becau…

2019-05-24abs ↗pdf ↗

The paper proposes using low rank assumption to improve causal structure learning in DAGs.

problem Challenges in learning causal structures in high-dimensional, non-sparse DAGs.
method Exploits low rank assumption of DAG adjacency matrix to adapt causal structure learning methods.
result Maximum rank is highly related to hubs, suggesting low rank for scale-free networks.