{"ID":2846143,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.02401","arxiv_id":"2511.02401","title":"Generalization in Representation Models via Random Matrix Theory: Application to Recurrent Networks","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.","short_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-dime...","url_abs":"https://arxiv.org/abs/2511.02401","url_pdf":"https://arxiv.org/pdf/2511.02401v1","authors":"[\"Yessin Moakher\",\"Malik Tiomoko\",\"Cosme Louart\",\"Zhenyu Liao\"]","published":"2025-11-04T09:30:31Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}