Attractor basins in transformer hidden states unify conflict and hallucination as basin competition or absence, with geometric margin outperforming entropy for detection and a scaling law governing confident hallucination rates.
The Bayesian Geometry of Transformer Attention
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
abstract
Transformers often appear to perform Bayesian reasoning in context, but verifying this rigorously has been impossible: natural data lack analytic posteriors, and large models conflate reasoning with memorization. We address this by constructing \emph{Bayesian wind tunnels} -- controlled environments where the true posterior is known in closed form and memorization is provably impossible. In these settings, small transformers reproduce Bayesian posteriors with $10^{-3}$-$10^{-4}$ bit accuracy, while capacity-matched MLPs fail by orders of magnitude, establishing a clear architectural separation. Across two tasks -- bijection elimination and Hidden Markov Model (HMM) state tracking -- we find that transformers implement Bayesian inference through a consistent geometric mechanism: residual streams serve as the belief substrate, feed-forward networks perform the posterior update, and attention provides content-addressable routing. Geometric diagnostics reveal orthogonal key bases, progressive query-key alignment, and a low-dimensional value manifold parameterized by posterior entropy. During training this manifold unfurls while attention patterns remain stable, a \emph{frame-precision dissociation} predicted by recent gradient analyses. Taken together, these results demonstrate that hierarchical attention realizes Bayesian inference by geometric design, explaining both the necessity of attention and the failure of flat architectures. Bayesian wind tunnels provide a foundation for mechanistically connecting small, verifiable systems to reasoning phenomena observed in large language models.
representative citing papers
A transformer-based in-context learning model predicts continental-scale subsurface temperatures from sparse borehole observations, outperforming physics and interpolation baselines while adapting to new regions with 20 examples.
TGR performs manifold-informed latent foresight search to boost trajectory coverage in long-context reasoning tasks by up to 13 AUC points with minimal overhead.
Gradient analysis shows cross-entropy induces an EM-like loop in attention that sculpts Bayesian manifolds supporting in-context probabilistic inference.
KNN imputation gives highest photo-z accuracy under ideal random missingness with complete training data, while SAITS is more robust for incomplete training sets and realistic mixed missingness patterns in CSST data.
Agentic AI orchestration should apply Bayesian principles for belief maintenance, updating from interactions, and utility-based action selection.
citing papers explorer
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Attractor Geometry of Transformer Memory: From Conflict Arbitration to Confident Hallucination
Attractor basins in transformer hidden states unify conflict and hallucination as basin competition or absence, with geometric margin outperforming entropy for detection and a scaling law governing confident hallucination rates.
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In-context learning enables continental-scale subsurface temperature prediction from sparse local observations
A transformer-based in-context learning model predicts continental-scale subsurface temperatures from sparse borehole observations, outperforming physics and interpolation baselines while adapting to new regions with 20 examples.
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The Geometric Reasoner: Manifold-Informed Latent Foresight Search for Long-Context Reasoning
TGR performs manifold-informed latent foresight search to boost trajectory coverage in long-context reasoning tasks by up to 13 AUC points with minimal overhead.
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Gradient Dynamics of Attention: How Cross-Entropy Sculpts Bayesian Manifolds
Gradient analysis shows cross-entropy induces an EM-like loop in attention that sculpts Bayesian manifolds supporting in-context probabilistic inference.
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Comparative analysis of missing data imputation methods for CSST survey: Impact on photometric redshift estimation performance
KNN imputation gives highest photo-z accuracy under ideal random missingness with complete training data, while SAITS is more robust for incomplete training sets and realistic mixed missingness patterns in CSST data.
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Position: agentic AI orchestration should be Bayes-consistent
Agentic AI orchestration should apply Bayesian principles for belief maintenance, updating from interactions, and utility-based action selection.