# Bayesian Filtering

The work proposes SAUCE, a training-free uncertainty estimator that casts uncertainty in parallel multi-agent reasoning as sequential inference over a latent system-level belief: each round's cross-agent agreement serves as evidence and its generation uncertainty sets the evidence weight, updated through a filtering-style recursion, improving misclassification detection, selective prediction, and calibration across five backbones, five benchmarks, and the Debate and DyLAN protocols.

The work proposes SAUCE, a training-free uncertainty estimator that casts uncertainty in parallel multi-agent reasoning as sequential inference over a latent system-level belief: each round's cross-agent agreement serves as evidence and its generation uncertainty sets the evidence weight, updated through a filtering-style recursion, improving misclassification detection, selective prediction, and calibration across five backbones, five benchmarks, and the Debate and DyLAN protocols.

The work proposes an "infinite-parameter LLM" architecture in which a compact hypernetwork encodes run-time data (facts, instructions, demonstrations) into a low-dimensional latent code, that code generates a low-rank additive modulation of a shared base feed-forward network so each token's "expert" is generated rather than drawn from a stored bank, and a Bayesian belief over the latent code is carried and updated online so the effective weight keeps evolving within a session; the authors also specify an evaluation protocol that pits carrying knowledge in the weights against carrying it in the prompt at matched budget.

The work proposes an "infinite-parameter LLM" architecture in which a compact hypernetwork encodes run-time data (facts, instructions, demonstrations) into a low-dimensional latent code, that code generates a low-rank additive modulation of a shared base feed-forward network so each token's "expert" is generated rather than drawn from a stored bank, and a Bayesian belief over the latent code is carried and updated online so the effective weight keeps evolving within a session; the authors also specify an evaluation protocol that pits carrying knowledge in the weights against carrying it in the prompt at matched budget.