Generalization in Representation Models via Random Matrix Theory: Application to Recurrent Networks

• URL: http://arxiv.org/abs/2511.02401v1
• Date: Tue, 04 Nov 2025 09:30:31 GMT
• Title: Generalization in Representation Models via Random Matrix Theory: Application to Recurrent Networks
• Authors: Yessin Moakher, Malik Tiomoko, Cosme Louart, Zhenyu Liao,
• Abstract summary: We first study the generalization error of models that use a fixed feature representation (frozen intermediate layers) followed by a trainable readout layer.<n>We apply Random Matrix Theory to derive a closed-form expression for the generalization error.<n>We then apply this analysis to recurrent representations and obtain concise formula that characterize their performance.
• Score: 7.721672385781673
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We first study the generalization error of models that use a fixed feature representation (frozen intermediate layers) followed by a trainable readout layer. This setting encompasses a range of architectures, from deep random-feature models to echo-state networks (ESNs) with recurrent dynamics. Working in the high-dimensional regime, we apply Random Matrix Theory to derive a closed-form expression for the asymptotic generalization error. We then apply this analysis to recurrent representations and obtain concise formula that characterize their performance. Surprisingly, we show that a linear ESN is equivalent to ridge regression with an exponentially time-weighted (''memory'') input covariance, revealing a clear inductive bias toward recent inputs. Experiments match predictions: ESNs win in low-sample, short-memory regimes, while ridge prevails with more data or long-range dependencies. Our methodology provides a general framework for analyzing overparameterized models and offers insights into the behavior of deep learning networks.

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