Contribution Weights: A Geometrical Analysis of Self-Attention Transformers

Despite the prevalence of the attention sink phenomenon in Large Language Models (LLMs), where initial tokens disproportionately monopolize attention scores, its structural origins remain elusive. This work provides a \textit{mechanistic explanation} for this phenomenon. First, we trace its root to the value aggregation process inherent in self-attention, which induces a systematic variance discrepancy. We further demonstrate that this discrepancy is drastically amplified by the activation of super neurons within Feed-Forward Network (FFN) layers. Specifically, the channel-sparse down-projections trigger a dimension disparity of the first-token representation, necessitating the formation of attention sinks as a structural anchor. Then, we validate this causal chain through two controlled interventions: (i) isolating the aggregation effect via attention mask modifications and (ii) amplifying the variance of targeted token representations. Both interventions can replicate attention sinks at arbitrary positions. Our mechanistic understanding offers a foundation for the systematic control of sink formation. Finally, as a proof of concept, we propose \textit{head-wise RMSNorm}, an architectural modification that stabilizes value aggregation outputs during pre-training. Our experiments demonstrate that restoring statistical parity across positions significantly accelerates convergence.

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.

Large Language Models (LLMs) often exhibit "Attention Sink" (AS) and the accompanying "Massive Activations" (MAs) at the initial position of a sequence. These phenomena frequently co-occur, and MAs can pose challenges for low-bit quantization. In this study, we analyze the factors underlying AS and MAs that emerge at the initial position regardless of the token occupying it. Our experiments suggest that self-concentration of attention, resulting from the causal mask, and the subsequent Value-non-mixing in attention outputs contribute to AS and MAs. These findings provide new empirical evidence on the internal dynamics of LLMs, offering insights that may inform future quantization strategies and advance our understanding of the internal mechanisms of attention layers.