Lihao Sun

How do LLMs do CoT reasoning internally? In our new #ACL2026 paper, we show that reasoning unfolds as a structured trajectory in representation space. Correct and incorrect paths diverge, and we use this to predict correctness before the answer and correct errors mid-flight. 1/

📢 Accepted to #ACL2026 Main Conference! Thanks to all collaborators at Microsoft: Hang Dong, Bo Qiao, Qingwei Lin, Dongmei Zhang, and Saravan Rajmohan. Paper: arxiv.org/pdf/2604.05655 Website: slhleosun.github.io/reasonin… Code: github.com/slhleosun/reasoni… 8/

Reasoning length is also controllable. Steering hidden states toward the termination subspace shortens reasoning; steering away extends it. At moderate strengths this works as a smooth knob with minimal accuracy changes - push too hard and the model enters repetitive loops. 7/

We further introduce trajectory-based steering: when an ongoing trajectory drifts from the ideal path, we apply low-rank corrections to nudge it back. Most effective on harder math problems - +7.6pp on 6- and 7-step questions, with 97%+ preservation of correct solutions. 6/

Unconditionally injecting tokens like "Wait" often hurts accuracy (up to -36%, especially for fewer-step problems). Instead, intervene only when failure is predicted! Using our mid-reasoning correctness signal on just ~12% of examples yields stable gains. 5/

This step-specific organization exists across training regimes and is already present in base models. From this perspective, reasoning training doesn't introduce new representational organization - it accelerates convergence toward a termination-related subspace. 4/

Trajectories for correct and incorrect reasoning start out nearly identical but diverge systematically at late steps. Late-step trajectory features predict final-answer correctness with AUC 0.87 - before the answer is generated. 3/

Each reasoning step occupies a distinct region in representation space, and these regions become increasingly linearly separable with layer depth. This structure generalizes across tasks and answer formats. 2/

Great to see so many convergent findings on affective structure in LLMs lately!

While we find consistent circular VA geometry across Llama and Qwen models, @AnthropicAI concurrently finds similar structure in Claude. Check our work out! arxiv.org/pdf/2604.03147 And thanks to all collaborators: Andrew Lee (@a_jy_l), Lewen Yan, Xiaoya Lu, Jie Zhang, and Jing Shao. 6/

One possible reason why: consider refusal-related token embeddings (“no”) and compliance tokens (“sure”). Take their mean diff and project onto our VA circle, which lands at 256°: negative in both V and A. Steering in -V or -A promotes the likelihood of refusal tokens! Generally, emotion prompting and VA steering change the emission probabilities of these key tokens, thereby affecting downstream behaviors - further supported by logit shifts and neuron analysis. 5/

Somewhat surprisingly, the VA axes also provide monotonic, bidirectional control over multiple downstream behaviors, including refusal and sycophancy. Arousal is a strong lever - increasing arousal leads to lower refusal rates, while decreasing arousal leads to more refusal behavior. 4/

Unlike Anthropic, we steer along the circular manifold at 0°, 30°, 60°, 90°, etc. This controls the valence and/or arousal level of the model’s outputs, validating that the recovered axes correspond to valence and arousal in a human-interpretable sense. 3/

We use mean-diff to extract emotion steering vectors. PCA + ridge regression reveals a circumplex akin to the circumplex model of emotions in human psychology. Projections onto these axes correlate with human-crowdsourced VA ratings across 44k words (valence r=0.71). 2/

💡New paper! Woke up to @AnthropicAI's emotion paper and realized - “wait, that's our finding too.” So we ArXiv'd immediately. We concurrently uncovered a circular geometry of emotions organized by valence and arousal (VA), as well as steering effects on downstream behaviors like refusal and sycophancy. We further provide a mechanistic account for why: refusal and compliance tokens occupy distinct regions in this space. 1/

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7/ 📢 Accepted to #ACL2025 Main Conference! See you in Vienna. Work done by @1e0sun, @ChengzhiM, @vjhofmann, @baixuechunzi . Paper: arxiv.org/abs/2506.00253 Project page: slhleosun.github.io/aligned_… Code & Data: github.com/slhleosun/aligned…