Reasoning models do not stop when they know the answer. On DeepSeek-R1-Distill-Qwen-7B the chain of thought runs about twice as long as the model's own answer probability takes to settle, and how much of that excess is removable varies from problem to problem, so a global length penalty cannot take it out. We take it out by internalizing a causal interpretability finding into the weights. The mechanism is a halt vector: a difference-of-means direction at layer 18 of this model whose steering strength controls how long it thinks, while a replicated value axis does nothing. Installing that intervention in the weights is harder than it looks. Maximizing the scalar projection onto the direction corrupts the off-axis dimensions a frozen downstream reader depends on, and generation gets longer instead of shorter; what works is reconstructing the whole steered activation with those dimensions pinned to their natural values. Fit from 24 problems and no reinforcement learning, the halt removes about a quarter of the thinking at held accuracy across five unseen benchmarks, and the cut tracks each problem's own removable slack at 0.70. It also closes a non-termination pathology that grows with difficulty and that a decoding-time confidence hook makes worse. We do not claim to beat a well-tuned length penalty or decoding-time early exit on the raw trade-off; the contribution is how the halt is obtained.
Steering vectors (SVs) are widely used to influence the expression of concepts (e.g., truthfulness) in large language model outputs. A key assumption underpinning SVs is that they are linearly discriminative with respect to the concept: representations of texts that exhibit the concept are more aligned with the SV than those that do not, motivating shifts along the positive or negative SV direction to respectively promote or suppress the concept. In this work, we identify an inverted detection-control phenomenon in which some highly discriminative SVs that are aligned with positive representations can consistently promote the opposite behavior. We refer to such vectors as inverted-steering vectors (ISVs). We provide a geometric characterization of ISVs' effects, finding that steering along these directions systematically pushes representations in discriminative downstream heads as if the concept were absent, even prior to decoding. Motivated by this analysis, we propose an approach for distinguishing ISVs without requiring generation or associated response scoring. This enables targeted sign flips, which we use to improve a foundational detection-based steering pipeline via Inference Time Intervention (ITI). Our approach improves results in 27/30 experiments, ranging from +0.9% to +138%. We evaluate our findings on Gemma 3 12B, Qwen 2.5 14B, and Olmo 3 7B across 5 concepts.
Tool-augmented large language models extend their capabilities beyond parametric knowledge through external tools, but tend to invoke them unnecessarily. We investigate whether tool-use decisions have any stable internal representation that can be extracted and manipulated, a question that is non-trivial given that tools exist entirely in context at inference time and have no direct encoding in model weights. We show that steering vectors extracted from heading-anchors positions exert bidirectional causal control over tool-invocation behavior across five open-source models and three domains, suppressing unnecessary tool use most effectively in domains where parametric reasoning suffices. However, geometric analysis reveals that this causal effectiveness does not correspond to clean linear structure: tool-invocation steps exhibit diffuse, bimodal alignment with the suppression vector rather than the consistent negative alignment a linear encoding account would predict, and different tool types recruit largely distinct internal signatures with low cross-tool feature overlap. We hypothesize these geometric properties are indicative of the non-parametric nature of tools, and distinguish tool-use steering vectors from those extracted for parametrically grounded concepts. The relationship between this geometric irregularity and the observed causal effectiveness remains an open question.
Modern LLM workflows move coordinate-indexed objects across checkpoints: steering vectors, sparse autoencoders, top-$k$ neuron sets, attribution lists, and merge alignments. This is only well posed after fixing the model's residual-stream gauge, which we show is architecture-dependent: LayerNorm residual charts have permutation gauge $S_d$ (up to a global sign flip), while RMSNorm charts with generic per-channel gain have signed-permutation gauge $B_d = S_d \ltimes \{\pm 1\}^d$. Permutation-only alignment is therefore symmetry-incomplete for RMSNorm models. We introduce sign-marginalized Hungarian matching and prove a sharp failure mode: with decorrelated coordinates, raw signed-correlation matching has a structural permutation-accuracy ceiling at the positive-sign fraction of the true gauge, which sign-marginalization removes. We then make coordinate-preserving transport, not function-level merging, the primary object: composing saved-checkpoint local $B_d$ gauges along same-base fine-tuning trajectories recovers 91.1% of cross-run coordinates at 1500 steps versus 60.3% for endpoint matching, and the gain is not explained by merely routing through the base. The recovered gauge transfers tools that permutation-only alignment breaks: TinyLlama SAE reconstruction has NMSE 0.004 under $B_d$ versus 1.08 under $S_d$; Qwen sentiment steering preserves 95.8% of its effect versus 17.2%; refusal steering reverses sign under $S_d$; coordinate-preserving merges behave the same way. The same covariance governs stateful training: signed transport of AdamW state preserves the resumed trajectory, while permutation-only state follows a different one from a functionally identical checkpoint. Finally, gauge-sweep audits show index-level interpretability claims are reproducible only relative to an explicit gauge.
We investigate whether language models internally track the value of their current trajectory, defined as the likelihood that their ongoing strategy will achieve their goals. Using synthetic, in-context reinforcement learning data, we construct a "value" axis for Qwen3-8B. We find that activations along this axis distinguish between high vs. low verbalized confidence, rollouts without and with backtracking, and correct vs. corrupted code. Steering towards high value causally suppresses self-correction and reduces explanatory verbosity, while steering towards low value induces backtracking and exploration. We demonstrate that direct preference optimization (DPO) can increase the internal value of rewarded behaviors (e.g. use a certain word), causing the model to act more confidently after exhibiting them. Finally, we apply the value axis to study in-the-wild settings. For example, we find that Qwen assigns low value to politically sensitive chat queries after post-training and that supervised fine-tuning increases internal confidence within the training domain. Our results suggest that language models linearly encode an estimate of expected goal success that modulates their confidence in pursuing a direction.