Deepak Rajbhar | Search arXiv

arXiv2026

Localization Does Not Imply Steerability: A Mechanistic Study of Sign Errors in LLM Mathematics

When large language models do multi-step mathematics, a characteristic failure recurs: the model writes one wrong sign token mid-computation -- a cofactor sign, the minus of a recursive integration-by-parts step -- then executes the rest of the arithmetic correctly, and the answer comes out wrong. We ask where inside the network that sign is written. Across six open models spanning 14B to 675B parameters, a per-layer readout shows the wrong sign is committed late -- by MLP layers in the last quarter of the network (70-100% per model and task), a pattern present, where tested (Qwen), in the base model before instruction tuning. The mechanism varies: some models carry fixed "minus-stamp" layers that push a minus regardless of the right answer, others carry amplifiers of whichever sign was already chosen, and Qwen adds a downstream rescue layer that opposes the stamp. The circuit is causal: subtracting a single sign direction from the residual stream flips 13 of 14 held-out minus-written integration-by-parts errors on Llama-3.3-70B, with flips replicating on Qwen, Gemma, and Mistral-Small (24-70% per cell), and with representation-level specificity -- the same dose breaks correctly-minus answers while sparing correct-plus answers where the direction is surgical (0/72 on Llama), and matched random-direction and control-layer interventions are null. Core claims were preregistered with pass criteria frozen in git before held-out data was seen: 23 of 29 checks passed, all misses reported. But causality is not uniform: Phi-4 implements an equally well-localized circuit at the same late depth, yet the identical intervention flips almost nothing -- the sign is written redundantly across ~15 layers with margins several times larger (median 17.8 logits). Localization, we conclude, does not imply steerability: two models can share a circuit location yet differ enormously in how overturnable it is.

cs.LG↗

arXiv2026

LinAlg-Bench: A Forensic Benchmark Revealing Structural Failure Modes in LLM Mathematical Reasoning

We introduce LinAlg-Bench, a diagnostic benchmark evaluating 10 frontier large language models on structured linear algebra computation across a strict dimensional gradient of 3x3, 4x4, and 5x5 matrices. Spanning 9 task types and 660 SymPy-certified problems, the benchmark exhaustively evaluates 6,600 model outputs. Beyond binary accuracy, LinAlg-Bench introduces a three-stage automated forensic pipeline classifying 1,156 failures into ten primary error tags with fine-grained subtypes, revealing that LLM mathematical failure is not random but structurally constrained by algorithm type and matrix dimension. Our central finding is a sharp behavioral threshold at 4x4 scale: below it, models fail through execution errors -- sign tracking failures, arithmetic drift, and parity errors; above it, failure transitions to computational abandonment, with models fabricating responses through tool roleplay, constraint-consistent confabulation, and structured hallucination rather than attempting computation. This fabrication-to-abandonment transition is near-universal across all model tiers and architectures, suggesting a working memory limit rather than a knowledge gap, supported by three scale-emergent error types absent at 3x3 but present at 4x4 and 5x5. We further show that solution strategy rigidity is a near-perfect predictor of 5x5 determinant accuracy, document constraint-aware confabulation as a novel structured hallucination failure mode, and release all data, model outputs, error labels, and judge pipeline publicly.

cs.AI↗