Protoreasoning in Tiny Transformers

We show that tiny transformers can profitably employ a simple form of Chain of Thought, which we call protoreasoning, allowing us to study step-by-step reasoning on ~1M-parameter models and opening up opportunities for much more detailed experimentation and analysis than is feasible for larger models. Current Large Language Models exhibit impressive step-by-step reasoning, but we have yet to understand its generality, i.e., when and how LLMs learn genuinely general algorithms rather than "bags of heuristics." Such questions are hard to settle on compute-intensive frontier models trained on opaque data. To work at model scales far below the threshold for natural-language competence, we define reasoning-friendly tasks on Dyck languages (sentences of correctly nested brackets). We find that protoreasoning traces substantially close the out-of-distribution generalization gap, and ablations confirm that the trace's content, not merely its extra tokens, drives the gain.

A Reference-Free Score for Detecting Silent Reasoning Failures in Large Language Models

Mathematical chain of thought (CoT) evaluation is commonly reduced to whether the final answer matches a reference. This conflates producing a correct conclusion with producing a valid derivation an invalid chain can accidentally reach the right answer, while a valid calculation can be followed by a transcription error. We call this mismatch the reasoning answer consistency gap. This framework paper introduces the Reasoning Answer Faithfulness Score (RAFS), a reference free, instance level diagnostic of whether an emitted mathematical trace is locally credible, supports its answer, and is stable under resampling and targeted counterfactual interventions. RAFS combines step validity, reasoning to answer entailment and counterfactual sensitivity, answer consensus, and conditional reasoning stability. It evaluates transcript level agreement, not a models private computation and not factual correctness outside the tested mathematical setting. We retain a preregistered, results blind confirmatory study on GSM8K and MATH, with hypotheses, admissibility rules, calibration, and tests fixed before confirmatory outcomes are inspected. A separate feasibility pilot is specified to verify end to end execution and estimate interven tion coverage before that freeze numerical pilot claims are re ported only when trace level artifacts are available. We formalize four reasoning answer outcomes, justify the non compensatory aggregator, instantiate semantic trace distance, quantify compute and abstention tradeoffs, and define verifier independence and power analyses. RAFS is intended to complement mathematical answer accuracy with an auditable warning signal for silent reasoning failures and answer extraction errors

Inference-Time Mitigation of Adversarial Political Bias in Large Language Models

As Large Language Models (LLMs) become the mainstay for information retrieval and summarization tasks, ensuring that they are always non-partisan and invulnerable to political bias is a critical step towards safer and more trustworthy Artificial Intelligence (AI). Current model alignment paradigms, such as reinforcement learning from human feedback (RLHF), make LLMs follow overarching safety instructions. However, this instruction tuning can be exploited via adversarial prompt injection and be used to generate unsafe content. In particular, political bias has not been specifically targeted by modern alignment techniques as harmful and biased content. To address this vulnerability of LLMs, we propose mitigation strategies using Chain of Thought (CoT) prompting and Direct Preference Optimization (DPO). Using a public dataset of legislative videos, we generate summaries using LLMs, inject bias via adversarial prompting and evaluate their performance on a four axis scale designed for political summarization. In this paper, we present different methods to shield LLMs against the injection of political bias. Our results demonstrate that the proposed Recursive Self-Correction approach raises model performance from a Political Neutrality Likert scale baseline of 2.14 to 4.56, averaged across all models, demonstrating effective inference-time mitigation of political bias in LLM-generated summaries.

Verifiable Rewards for Calibrated Probabilistic Forecasting

Reinforcement learning with verifiable rewards can in principle train calibrated probabilistic forecasters, since a proper scoring rule such as the Brier score is computed from outcomes alone and is minimized in expectation by the true probability. In practice it degrades calibration, and existing remedies address epistemic uncertainty, where a model's confidence accompanies a verifiably correct or incorrect answer. We study aleatoric forecasting, where the forecast itself is the output and the label is one stochastic outcome, taking NFL in-game win probability as a testbed with the betting market as a reference. Rewarding the realized per-play outcome fails, because the single outcome is a noisy target and the policy gradient corrupts the chain of thought. We introduce a verifiable, label-free reward, a state-conditioned empirical win rate estimated from past outcomes, that removes the label noise, and we keep the gradient off the reasoning, by direct prediction or a gradient mask, so it cannot be corrupted. Trained with this reward alone, without human labels or supervised fine-tuning, a 7B model reaches the calibration of the betting market by direct prediction and is better calibrated than a zero-shot frontier model. That frontier model and a tabular estimator reach the same Brier score as this model, identifying the market's small remaining edge as live in-game information beyond their shared inputs. Masking the gradient, rather than dropping the chain of thought, preserves reasoning from which the forecast follows, which ordinary chain-of-thought training corrupts.

Self-Commitment Latency: A Reward-Free Probe for Prompted Implicit Hacking

Implicit reward hacking is hard to audit when a language model's chain of thought appears benign: a final answer may be anchored by a prompt shortcut while the written reasoning still resembles ordinary problem solving. Verifier-based probes expose such behavior by measuring how early truncated reasoning contexts obtain high reward, but require a task-specific reward signal. This paper proposes a weaker-input alternative, self-commitment latency, which measures how early a prompted reasoning context commits to the model's own final answer. We evaluate the probe in a controlled paired GSM8K setting using Qwen2.5-3B-Instruct-4bit, comparing ordinary prompts with prompts that include an answer hint. Hinted contexts commit substantially earlier and with lower uncertainty than honest contexts. The primary latency metric, first-commitment latency at threshold 0.8, reaches AUROC 0.878; supporting whole-curve summaries reach AUROC 0.926 for commitment range and 0.904 for mean uncommitted mass. The signal is stronger when both prompt conditions answer correctly and remains stable across thresholds. These results show that shortcut-available reasoning contexts can leave an early behavioral commitment signature detectable without a reward model, external judge, or trained classifier.

On the Cost and Benefit of Chain of Thought: A Learning-Theoretic Perspective

We develop a learning-theoretic framework for understanding Chain of Thought (CoT). We model CoT as the interaction between an answer map and a chain rule that generates intermediate questions autoregressively, and define the reasoning risk of a hypothesis under this interaction. Our first result is a tight canonical decomposition of this risk into two terms with opposing roles: an oracle-trajectory risk (OTR), which captures the benefit of CoT and reduces to a target-domain risk in a domain adaptation problem, and a trajectory-mismatch risk (TMR), which captures the cost of CoT through error accumulation along mismatched reasoning trajectories. We then show that this cost is unavoidable without structure: if any one of the loss, the hypothesis answer map, or the chain rule lacks stability, the TMR can be arbitrarily large even when the OTR is zero and the hypothesis is uniformly close to the ground truth. Conversely, under stability, we prove a tight upper bound on the TMR governed by an exact amplification factor that identifies bounded, linear, and exponential error-growth regimes. Together, these results give a precise theory of when CoT helps, when it hurts, and what controls the transition between the two.