We lifted 9 functions out of this paper's own repositories and ran 6 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.
| Repository | Role | Ran |
|---|---|---|
| sophiaas/spectral-universality | canonical | 6 of 9 |
| Function | Status | Where it lives |
|---|---|---|
| complex_array_to_rgb | Ran | sophiaas/spectral-universality/utils.py pointer only (licence: NONE) · get_code("07f4e9b34e80e048") |
| direct_product | Ran | sophiaas/spectral-universality/groups.py pointer only (licence: NONE) · get_code("6b6fd1f38b462a0c") |
| init_weights | Ran | sophiaas/spectral-universality/models_JAX.py pointer only (licence: NONE) · get_code("b084e5a3eb7bc0c1") |
| matmul_complex | Ran | sophiaas/spectral-universality/models_torch.py pointer only (licence: NONE) · get_code("e60f9d31ff4a53fa") |
| pad_eye | Ran | sophiaas/spectral-universality/models_torch.py pointer only (licence: NONE) · get_code("a853a6fa01870647") |
| perm_matrices | Ran | sophiaas/spectral-universality/utils.py pointer only (licence: NONE) · get_code("8ffe99d5ad67b54c") |
| pad_eye | Not yet run | sophiaas/spectral-universality/models_JAX.py pointer only (licence: NONE) · get_code("3de5da36457066c7") |
| perm_frobenius | Not yet run | sophiaas/spectral-universality/utils.py pointer only (licence: NONE) · get_code("d825189f35316425") |
| total_weight | Not yet run | sophiaas/spectral-universality/models_JAX.py pointer only (licence: NONE) · get_code("14cdeef2a19d88e0") |
Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.
In this work, we formally prove that, under certain conditions, if a neural network is invariant to a finite group then its weights recover the Fourier transform on that group. This provides a mathematical explanation for the emergence of Fourier features -- a ubiquitous phenomenon in both biological and artificial learning systems. The results hold even for non-commutative groups, in which case the Fourier transform encodes all the irreducible unitary group representations. Our findings have consequences for the problem of symmetry discovery. Specifically, we demonstrate that the algebraic structure of an unknown group can be recovered from the weights of a network that is at least approximately invariant within certain bounds. Overall, this work contributes to a foundation for an algebraic learning theory of invariant neural network representations.
The same record, over MCP at https://syntology.ai/mcp:
get_harvested_code_for_paper("2312.08550")
get_code_for_paper("2312.08550")
have("2312.08550")
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