Abstract
Compositional inference - the decomposition of observations into an unknown number of latent components - is central to perception and scientific data analysis. Attention-based models perform well when components are approximately separable, as in object-centric vision. Under additive superposition, however - where multiple components contribute to every observation - we identify a structural failure mode we term slot collapse: multiple slots converge to the same dominant component while weaker ones remain unrepresented. We trace this to a general limitation: attention is memoryless with respect to explained evidence. All slots repeatedly operate on the same input without accounting for what has already been explained, so gradients are dominated by the strongest component, inducing shared fixed points across slots. As a result, attention fails to enforce non-redundant allocation under additive superposition. We address this by introducing residual evidence modeling, instantiated via evidence depletion - a minimal modification combining multiplicative depletion with an attention bias. Controlled ablations show that parallel attention, sequential processing alone, and loss-based regularization fail to resolve collapse; evidence depletion, which adds residual state to sequential attention, consistently succeeds. Across synthetic benchmarks and real-world audio mixtures (FUSS), evidence depletion reduces slot collapse by up to an order of magnitude, generalizing beyond synthetic settings. On gravitational-wave source inference for the ESA/NASA LISA mission, under identical architectures, data, and losses, standard attention fails while evidence depletion prevents collapse and enables multi-source posterior estimation. These results show that under additive superposition, residual evidence tracking is the operative ingredient for preventing collapse and enabling compositional inference.
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Post-training is routinely evaluated through aggregate benchmark scores that treat multi-hop reasoning as a single capability -- as if a model that answers more questions correctly must be better at assembling facts. We show that this assumption can be misleading: recipes with statistically indistinguishable atomic knowledge produce composition behaviour separated by over 40 percentage points, a phenomenon we call composition collapse: the systematic failure to assemble stably-known facts into chains, invisible to aggregate metrics. We introduce a double-gate protocol that changes the estimand from an aggregate compositionality gap to residual composition failure conditioned on stable atomic access, decomposing post-training gains into three independent channels: atomic stability, residual composition, and critical depth. On a benchmark of temporal factual chains spanning depths 2--11 across four post-training recipes, this decomposition reveals that post-training objectives shift composition capability in directions that aggregate metrics mask, and suggests that claims about multi-hop reasoning improvement should be accompanied by atomic-gate-controlled composition metrics. Diagnostic probes further show that a substantial share of measured composition failure reflects generation-time computation constraints rather than permanent inability to compose.
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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. In that case, sinks serve an analogous role: a safe destination when there is nothing useful to compute. Proposed interventions like gating or registers work because they implicitly target one or the other, revealing a duality between method and assumed mechanism: gating implicitly assumes nop; registers implicitly assume broadcast. 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. Strikingly, register tokens, designed for broadcast, are repurposed to also serve nop, confirming that neither intervention alone suffices. Combining gating with registers yields complementary gains in stability and performance. Overall, we find that the same attention pattern can reflect two very different computations and effective intervention requires first asking what the model is actually computing.
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