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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.25470 |
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| _version_ | 1866914513863835648 |
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| author | Heydenreich, Markus Hirsch, Christian Löwe, Matthias |
| author_facet | Heydenreich, Markus Hirsch, Christian Löwe, Matthias |
| contents | The central question that we address is: How can structured information be stored in a hierarchical Hopfield model involving hidden layers? To this end, we develop a formalism of strokes and concepts that allows us to appropriately structure information: initial features are first classified into strokes, which in a second step are aggregated into concepts. We rigorously derive criteria under which concepts can be retrieved from noisy input data. A remarkable effect is that we do not require a perfect retrieval at the level of strokes, as the second-layer retrieval procedure compensates for first-layer errors. We treat separately the cases of fixed and variable-sized concepts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25470 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A mathematical analysis of hierarchical Hopfield models Heydenreich, Markus Hirsch, Christian Löwe, Matthias Probability 92B20 The central question that we address is: How can structured information be stored in a hierarchical Hopfield model involving hidden layers? To this end, we develop a formalism of strokes and concepts that allows us to appropriately structure information: initial features are first classified into strokes, which in a second step are aggregated into concepts. We rigorously derive criteria under which concepts can be retrieved from noisy input data. A remarkable effect is that we do not require a perfect retrieval at the level of strokes, as the second-layer retrieval procedure compensates for first-layer errors. We treat separately the cases of fixed and variable-sized concepts. |
| title | A mathematical analysis of hierarchical Hopfield models |
| topic | Probability 92B20 |
| url | https://arxiv.org/abs/2604.25470 |