Task-Relevant Null-Space Residuals for Non-Injective Neural Mappings
Non-injective mappings in neural networks map distinct inputs to the same representation, thereby implicitly inducing equivalence relations in the input space. However, the input differences eliminated by these mappings may still be required by downstream tasks, creating a mismatch between operator-induced indistinguishability and task-required distinctions. For non-injective linear operators realized in the current forward pass, their null spaces exactly characterize these invisible input variations. We propose Task-Relevant Null-Space Residuals (NSR), a general residual framework for non-injective linear mappings. NSR combines null-space component extraction from pre-mapping representat...
| Authors | Bizu Feng, Zhimu Yang, Shuming Wang et al. |
|---|---|
| Primary category | cs.AI |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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