Task-Restricted Symmetries in Recurrent Weight Space
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Computer Science > Machine Learning
Title:Task-Restricted Symmetries in Recurrent Weight Space
Abstract:Recurrent networks can contain substantial functional redundancy in
weight space: changing a recurrent matrix may leave the input-output
rollout nearly unchanged on a task distribution, while similar-scale
changes can destroy the same behavior. We study this redundancy in
one-layer tanh RNNs using ordered real Schur coordinates. The Schur
form separates spectral blocks from directed nonnormal couplings,
giving a diagnostic basis for structured ablations that keep the input
and readout maps fixed. In a fixed-length copy task, selected
nonnormal Schur couplings can be removed with little loss in some
trained solutions, whereas other couplings are necessary for accurate
autonomous replay. Across flip-flop, sine generation, and
context-dependent integration, the loss-preserving ablation profile
varies across tasks and trained solutions. These results identify
candidate approximate functional invariances, not universal symmetries
of recurrent weight space. Schur-coordinate ablations provide a
practical diagnostic for which structured perturbations preserve a
trained recurrent solution and which ones disrupt its computation.
| Comments: | 6 pages, 2 figures. Accepted at the ICML 2026 Workshop on Weight-Space Symmetries |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2606.18457 [cs.LG] |
| (or arXiv:2606.18457v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.18457
arXiv-issued DOI via DataCite (pending registration)
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