Attention Sinks Are Provably Necessary in Softmax Transformers: Evidence from Trigger-Conditional Tasks

When attention concentrates on a single token, a sink, what is the model actually computing? Attention sinks are ubiquitous in softmax transformers, yet this shared visual signature can hide fundamentally different algorithms. We show that visually similar sink patterns can reflect two distinct mechanisms: (i) adaptive nop, where a head suppresses its update by routing to a null token, and (ii) broadcast, where a sink aggregates and redistributes global information. Each mechanism leaves distinct traces (nop-sinks exhibit negligible value norms; broadcast sinks induce low-rank outputs), which we formalize on synthetic tasks and use to derive practical diagnostics. Applied to pretrained vision transformers, these diagnostics reveal that both mechanisms exist at scale: sinks transition from CLS in early layers to patches in deeper layers and concentrate in specialized heads. Causal interventions further connect these signatures to near-null suppression and shared residual contributions. We then use architectural interventions to show how these computations can be reorganized: gating eliminates detected nop-like sinks but increases broadcast-like sinks, registers relocate rather than remove sink computation, and our position-free global pathway provides an explicit route for shared communication that reduces the broadcast-like sinks induced by gating. On dense probes, combining gating with the global pathway gives the strongest results among the tested variants, despite retaining some broadcast-like sinks. Overall, we find that the same attention pattern can reflect two very different computations, and that effective intervention depends not only on identifying the computation, but also on providing architectural alternatives through which the model can reorganize it.

We study two recurring phenomena in Transformer language models: massive activations, in which a small number of tokens exhibit extreme outliers in a few channels, and attention sinks, in which certain tokens attract disproportionate attention mass regardless of semantic relevance. Prior work observes that these phenomena frequently co-occur and often involve the same tokens, but their functional roles and causal relationship remain unclear. Through systematic experiments, we show that the co-occurrence is largely an architectural artifact of modern Transformer design, and that the two phenomena serve related but distinct functions. Massive activations operate globally: they induce near-constant hidden representations that persist across layers, effectively functioning as implicit parameters of the model. Attention sinks operate locally: they modulate attention outputs across heads and bias individual heads toward short-range dependencies. We identify the pre-norm configuration as the key choice that enables the co-occurrence, and show that ablating it causes the two phenomena to decouple.

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.