RNNs perform task computations by dynamically warping neural representations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917256483569664 |
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| author | Pellegrino, Arthur Chadwick, Angus |
| author_facet | Pellegrino, Arthur Chadwick, Angus |
| contents | Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In parallel, machine learning has seen a surge of interest in understanding how dynamical systems perform computations on time-varying input data. Yet, the link between computation-through-dynamics and representational geometry remains poorly understood. Here, we hypothesise that recurrent neural networks (RNNs) perform computations by dynamically warping their representations of task variables. To test this hypothesis, we develop a Riemannian geometric framework that enables the derivation of the manifold topology and geometry of a dynamical system from the manifold of its inputs. By characterising the time-varying geometry of RNNs, we show that dynamic warping is a fundamental feature of their computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | RNNs perform task computations by dynamically warping neural representations Pellegrino, Arthur Chadwick, Angus Machine Learning Differential Geometry Dynamical Systems Neurons and Cognition Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In parallel, machine learning has seen a surge of interest in understanding how dynamical systems perform computations on time-varying input data. Yet, the link between computation-through-dynamics and representational geometry remains poorly understood. Here, we hypothesise that recurrent neural networks (RNNs) perform computations by dynamically warping their representations of task variables. To test this hypothesis, we develop a Riemannian geometric framework that enables the derivation of the manifold topology and geometry of a dynamical system from the manifold of its inputs. By characterising the time-varying geometry of RNNs, we show that dynamic warping is a fundamental feature of their computations. |
| title | RNNs perform task computations by dynamically warping neural representations |
| topic | Machine Learning Differential Geometry Dynamical Systems Neurons and Cognition |
| url | https://arxiv.org/abs/2512.04310 |