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arXiv AI

Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks

The paper discusses tensorizing neural networks by reshaping dense weight matrices into higher-order tensors and approximating them with low-rank tensor network decompositions. This approach offers promising model compression and introduces bond indices that create new latent spaces, potentially enhancing interpretability. Despite encouraging empirical results, tensorized neural networks remain underused, and the authors call for more research to address practical scaling and adoption challenges.

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On the Architectural Complexity of Neural Networks

The paper presents a unified theoretical framework for analyzing and constructing deep neural networks by explicitly modeling tensor operations, which are often abstracted in existing theories. This framework allows researchers to study how architectural complexity has evolved over the past 40 years and to automatically generate new architectures using novel tensor operations. The authors also release a dataset of over 3,000 higher‑complexity architectures that have not yet been explored, providing a resource for future research.

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Sublinearly Structured Deep Neural Networks Achieve Feature Learning Consistency for Compositional Functions

Over the past decade, deep neural networks (DNNs) have achieved remarkable success on complex machine-learning tasks, yet the theoretical foundations of their performance remain incomplete. From a statistical viewpoint, a natural question is: can DNNs attain feature-learning and prediction consistency comparable to that of classical models?

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arXiv AI
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Tensor Methods for Language Models: From Token Representation to Training, Adaptation, Inference, Compression, and Interpretability

This survey reviews tensor methods applied to large language models, framing them through a seven‑stage lifecycle (tokenization, embeddings, pre‑training, adaptation, compression, inference, interpretability) and a component view (embeddings, attention, feed‑forward networks). It offers unified notation, theoretical foundations, and comparative analyses of tensorization strategies for Transformer components, while highlighting evaluation protocol differences and model scale effects. The paper also introduces a new metric, ρ_gap, to quantify the gap between theoretical memory savings and actual system‑level speedup, and connects tensor techniques to related efficiency and probabilistic methods.

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arXiv AI
Sep 2

A Mathematical Theory of Reusable Neural Bases for Network Compression

The paper introduces the Linear Reusable Neural Bases Architecture (LRNBA), a framework that represents each network block as a linear combination of shared neural bases to improve parameter efficiency and reduce memory cost. Inspired by recurrent neural network designs, LRNBA enables the construction of wider and deeper networks within the same parameter budget. Experiments show that models using LRNBA converge as fast or faster than classical architectures, achieve lower loss, and maintain stable training dynamics.

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