Nils Lukas
Publications
Entropy-Gated Latent Recursion
Inference-time scaling has become the dominant lever for improving language-model reasoning, but existing methods derive rollout diversity from a single source: stochastic token-level sampling. We argue that this single-axis sampling space is fundamentally limiting, and identify a second, fully deterministic and complementary axis: the layer span $L$ at which a frozen model's top decoder layers are recursively re-applied at high-uncertainty tokens. Different choices of $L$ produce distinct rollouts that solve different subsets of problems, with no stochasticity. We instantiate this axis through Entropy-Gated Latent Recursion (EGLR), a training-free decoding procedure that re-applies the top-$L$ layers for at most $K_{\max}$ iterations until the next-token distribution converges. Combined with $T$ temperature samples, EGLR turns a single-axis stochastic rollout pool into an $L\times T$ Cartesian sampling space at almost the same per-rollout cost. We characterize this space across $8$ instruction-tuned models and $6$ math reasoning benchmarks, and show that the $L$-axis is genuinely complementary to temperature: on MATH-500 with Qwen2.5-3B-Instruct, the joint $L\times T$ oracle reaches $91.6\%$, $+8.2$ percentage points beyond the temperature-only oracle ($83.4\%$) and $+10.4$ points beyond the layer-only oracle ($81.2\%$), confirming that the two axes capture genuinely complementary problems. The expanded rollout pool provides richer per-prompt candidates for any downstream procedure that consumes rollouts, including self-consistency, best-of-$N$ with verifiers, and group-relative RL training (GRPO), opening a new direction for inference-time scaling that does not rely on stochastic noise.
When the Chain of Thought Knows Better: Failure Modes in Multi-Turn Reasoning Models
Failures in multi-turn reasoning models are largely invisible to terminal-score evaluation. A model can lock onto an unsafe stance early in a long dialogue, yet its final-turn refusal rate may appear indistinguishable from a robustly aligned baseline. To expose these hidden temporal dynamics, we propose a trace-level diagnostic - the CoT-Output 2x2 safety matrix. This framework labels every turn along two independent axes (internal reasoning and visible output), yielding four operationally defined failure cells: robust alignment, alignment faking, overt jailbreak, and a distinct failure mode we term context-injection failure (where the CoT maintains safe reasoning, but the visible output produces harm, highlighting a multi-turn manifestation of reasoning unfaithfulness). We evaluate three distilled reasoning targets against a fixed attacker across five oversight conditions, collecting 6750 turn-level observations on the Information-Hazard scenario. Our analysis reveals two reproducible vulnerabilities: an oversight paradox where explicit monitoring cues paradoxically increase alignment-faking rates rather than suppress them, and a context-injection failure where models lock onto unsafe external outputs despite safe internal states. We release the full dataset of multi-turn dialogues and CoT traces to support follow-up trace-diagnostic research.
Robust Safety Monitoring of Language Models via Activation Watermarking
Large language models (LLMs) can be misused to reveal sensitive information, such as weapon-making instructions or writing malware. LLM providers rely on $\emph{monitoring}$ to detect and flag unsafe behavior during inference. An open security challenge is $\emph{adaptive}$ adversaries who craft attacks that simultaneously (i) evade detection while (ii) eliciting unsafe behavior. Adaptive attackers are a major concern as LLM providers cannot patch their security mechanisms, since they are unaware of how their models are being misused. We cast $\emph{robust}$ LLM monitoring as a security game, where adversaries who know about the monitor try to extract sensitive information, while a provider must accurately detect these adversarial queries at low false positive rates. Our work (i) shows that existing LLM monitors are vulnerable to adaptive attackers and (ii) designs improved defenses through $\emph{activation watermarking}$ by carefully introducing uncertainty for the attacker during inference. We find that $\emph{activation watermarking}$ outperforms guard baselines by up to $52\%$ under adaptive attackers who know the monitoring algorithm but not the secret key.
CORE: Collaborative Reasoning via Cross Teaching
Large language models exhibit complementary reasoning errors: on the same instance, one model may succeed with a particular decomposition while another fails. We propose Collaborative Reasoning (CORE), a training-time collaboration framework that converts peer success into a learning signal via a cross-teaching protocol. Each problem is solved in two stages: a cold round of independent sampling, followed by a contexted rescue round in which models that failed receive hint extracted from a successful peer. CORE optimizes a combined reward that balances (i) correctness, (ii) a lightweight DPP-inspired diversity term to reduce error overlap, and (iii) an explicit rescue bonus for successful recovery. We evaluate CORE across four standard reasoning datasets GSM8K, MATH, AIME, and GPQA. With only 1,000 training examples, a pair of small open source models (3B+4B) reaches Pass@2 of 99.54% on GSM8K and 92.08% on MATH, compared to 82.50% and 74.82% for single-model training. On harder datasets, the 3B+4B pair reaches Pass@2 of 77.34% on GPQA (trained on 348 examples) and 79.65% on AIME (trained on 792 examples), using a training-time budget of at most 1536 context tokens and 3072 generated tokens. Overall, these results show that training-time collaboration can reliably convert model complementarity into large gains without scaling model size.
SD-E$^2$: Semantic Exploration for Reasoning Under Token Budgets
Small language models (SLMs) struggle with complex reasoning because exploration is expensive under tight compute budgets. We introduce Semantic Diversity-Exploration-Exploitation (SD-E$^2$), a reinforcement learning framework that makes exploration explicit by optimizing semantic diversity in generated reasoning trajectories. Using a frozen sentence-embedding model, SD-E$^2$ assigns a diversity reward that captures (i) the coverage of semantically distinct solution strategies and (ii) their average pairwise dissimilarity in embedding space, rather than surface-form novelty. This diversity reward is combined with outcome correctness and solution efficiency in a z-score-normalized multi-objective objective that stabilizes training. On GSM8K, SD-E$^2$ surpasses the base Qwen2.5-3B-Instruct and strong GRPO baselines (GRPO-CFL and GRPO-CFEE) by +27.4, +5.2, and +1.5 percentage points, respectively, while discovering on average 9.8 semantically distinct strategies per question. We further improve MedMCQA to 49.64% versus 38.37% for the base model and show gains on the harder AIME benchmark (1983-2025), reaching 13.28% versus 6.74% for the base. These results indicate that rewarding semantic novelty yields a more compute-efficient exploration-exploitation signal for training reasoning-capable SLMs. By introducing cognitive adaptation-adjusting the reasoning process structure rather than per-token computation-SD-E$^2$ offers a complementary path to efficiency gains in resource-constrained models.