For normalized self-attention in the d ~ N limit, the overlap gap controls a manifold of clustered fixed points and a finite-sharpness dynamical attention-condensation transition.
Robust Probabilistic Bisimilarity for Labelled Markov Chains
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abstract
Despite its prevalence, probabilistic bisimilarity suffers from a lack of robustness under minuscule perturbations of the transition probabilities. This can lead to discontinuities in the probabilistic bisimilarity distance function, undermining its reliability in practical applications where transition probabilities are often approximations derived from experimental data. Motivated by this limitation, we introduce the notion of robust probabilistic bisimilarity for labelled Markov chains, which ensures the continuity of the probabilistic bisimilarity distance function. We also propose an efficient algorithm for computing robust probabilistic bisimilarity and show that it performs well in practice, as evidenced by our experimental results.
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cond-mat.dis-nn 1years
2026 1verdicts
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Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention
For normalized self-attention in the d ~ N limit, the overlap gap controls a manifold of clustered fixed points and a finite-sharpness dynamical attention-condensation transition.