A Symmetry-Matching Approach to Blind-Spot Reduction in Sparse Autoencoders

arXiv:2610.24908v1 Announce Type: new Abstract: Language models can treat semantically distinct inputs as interchangeable at the representation level, creating blind spots that standard sparse autoencoder (SAE) objectives do not target. In safety-critical settings such as clinical dosage extraction, legal clause interpretation, or financial amount verification, such failures can propagate silently into downstream decisions. We study this problem as one of feature-basis orientation. Building on a symmetry-matching view from algebraic error-detection theory, we add a differentiable $V_{\mathrm{Gini}}$ regularisation term to SAE training that penalises uneven perturbation response within a specified family. Across GPT-2, Gemma 2, and Qwen 2.5, a frozen multi-seed evaluation shows that $V$-regularisation raises both relative and absolute lower-tail responses while reducing response-profile imbalance, with no material general-text reconstruction degradation. JumpReLU and minimum description length (MDL) objectives remain close to the Standard SAE profile under the same protocol. Family-geometry controls show that the effect is not explained by template duplication or a single dominant perturbation family, and held-out probes plus null-calibrated separation tests evaluate how far the representation-level change carries to downstream discriminability. A zero-shot audit on out-of-distribution clinical radiology minimal pairs finds the relative weak-tail lift in all evaluated model-by-family cells, not perfectly rank-aligned with the trained statistic, and a held-out family audit finds it on family kinds never used in training. Together, the results show that perturbation-aware SAE training can reorient feature bases toward safety-relevant input changes while leaving downstream validation as a separate empirical step.