SubNeutralize: The Geometry of Reasoning and the Elimination of the Overthinking Trap

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Large autoregressive reasoning models (e.g., DeepSeek-R1, OpenAI o1, QwQ) scale test-time search through extended chain-of-thought exploration, reflection, and self-verification. However, unconstrained test-time generation introduces an acute, pervasive failure mode: the overthinking crisis. In up to 40% of complex reasoning failures, models successfully derive the algebraically correct conclusion within early decoding tokens, but subsequently enter pathological, repetitive self-doubt loops, drifting away from the true solution and producing catastrophic answer flips. In this work, we uncover the latent geometric mechanism underlying this phenomenon through mechanistic interpretability of transformer residual streams. We prove that prompt tokens establish a persistent, low-rank linear attractor—formalized as the Prompt Bias Subspace (V_bias)—that continuously leaks energy into post-deduction residual states. We formulate SubNeutralize, an O(d) parameter-free runtime inference governor that tracks Riemannian trajectory velocity across a multi-layer cognitive bottleneck band B = {12, 14, 16}, coupled with an information-theoretic threshold dynamically scaled by the instantaneous Shannon Entropy H_t of the token emission distribution. Evaluated across DeepSeek-R1-Distill-Qwen-7B and 14B on dedicated NVIDIA A100 GPUs across GSM8K and Olympiad-level MATH-500 benchmarks, our governor achieves: (1) a +32.0% absolute accuracy surge (28.0% to 60.0%, p = 0.0022 via McNemar’s test) while cutting token compute by 43.7% on GSM8K; (2) an 80.0% vs 60.0% win on Olympiad competition math, reducing Level 5 Intermediate Algebra latency by 55.4%; and (3) under dynamic entropy scaling, an accuracy leap to 50.0% with zero head-to-head regressions (0.0% loss rate) against unconstrained generation. SubNeutralize is training-free, requires zero auxiliary parameters, and executes at 0.04 ms overhead per token, providing an immediate plug-and-play governor for production inference engines.