A Mechanistic Account of Attention Sinks in GPT-2: One Circuit, Broader Implications for Mitigation

Transformers commonly exhibit an attention sink: disproportionately high attention to the first position. We study this behavior in GPT-2-style models with learned query biases and absolute positional embeddings. Combining structural analysis with causal interventions, validated across natural-language, mathematical, and code inputs, we find that the sink arises from the interaction among (i) a learned query bias, (ii) the first-layer MLP transformation of the positional encoding, and (iii) structure in the key projection. Crucially, each component we identify is individually dispensable: architectures omitting each of them robustly exhibit sinks. This indicates that attention sinks may arise through distinct circuits across architectures. These findings inform mitigation of sinks, and motivate broader investigation into why sinks emerge.

Outcome-Based RL Provably Leads Transformers to Reason, but Only With the Right Data

Transformers trained via Reinforcement Learning (RL) with outcome-based supervision can spontaneously develop the ability to generate intermediate reasoning steps (Chain-of-Thought). Yet the mechanism by which sparse rewards drive gradient descent to discover such systematic reasoning remains poorly understood. We address this by analyzing the gradient flow dynamics of single-layer Transformers on a synthetic graph traversal task that cannot be solved without Chain-of-Thought (CoT) but admits a simple iterative solution. We prove that despite training solely on final-answer correctness, gradient flow drives the model to converge to a structured, interpretable algorithm that iteratively traverses the graph vertex-by-vertex. We characterize the distributional properties required for this emergence, identifying the critical role of "simple examples": instances requiring fewer reasoning steps. When the training distribution places sufficient mass on these simpler instances, the model learns a generalizable traversal strategy that extrapolates to longer chains; when this mass vanishes, gradient-based learning becomes infeasible. We corroborate our theoretical results through experiments on synthetic data and with real-world language models on mathematical reasoning tasks, validating that our theoretical findings carry over to practical settings.