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Bayesian Optimality of In-Context Learning with Selective State Spaces

Di Zhang, Jiaqi Xing · Feb 19, 2026 · Citations: 0

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Feb 19, 2026, 12:41 PM

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Apr 13, 2026, 6:43 AM

Fresh

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Confidence 0.15

Abstract

We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL). Unlike interpretations framing Transformers as performing implicit gradient descent, we formalize ICL as meta-learning over latent sequence tasks. For tasks governed by Linear Gaussian State Space Models (LG-SSMs), we prove a meta-trained selective SSM asymptotically implements the Bayes-optimal predictor, converging to the posterior predictive mean. We further establish a statistical separation from gradient descent, constructing tasks with temporally correlated noise where the optimal Bayesian predictor strictly outperforms any empirical risk minimization (ERM) estimator. Since Transformers can be seen as performing implicit ERM, this demonstrates selective SSMs achieve lower asymptotic risk due to superior statistical efficiency. Experiments on synthetic LG-SSM tasks and a character-level Markov benchmark confirm selective SSMs converge faster to Bayes-optimal risk, show superior sample efficiency with longer contexts in structured-noise settings, and track latent states more robustly than linear Transformers. This reframes ICL from "implicit optimization" to "optimal inference," explaining the efficiency of selective SSMs and offering a principled basis for architecture design.

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HFEPX Relevance Assessment

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Eval-Fit Score

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Human Feedback Signal

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Field Provenance & Confidence

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Evidence snippet: We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL).

Evaluation Modes

missing

None explicit

Confidence: Low Source: Persisted extraction missing

Validate eval design from full paper text.

Evidence snippet: We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL).

Quality Controls

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Evidence snippet: We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL).

Benchmarks / Datasets

missing

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Confidence: Low Source: Persisted extraction missing

No benchmark anchors detected.

Evidence snippet: We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL).

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Evidence snippet: We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL).

Rater Population

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Unknown

Confidence: Low Source: Persisted extraction missing

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Evidence snippet: We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL).

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
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  • Expertise required: General
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes:
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  • Confidence: 0.15
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

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Research Brief

Deterministic synthesis

We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL). HFEPX protocol signal is limited in abstract-level metadata, so treat it as adjacent context. Updated from current HFEPX corpus.

Generated Apr 13, 2026, 6:43 AM · Grounded in abstract + metadata only

Key Takeaways

  • We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL).
  • Experiments on synthetic LG-SSM tasks and a character-level Markov benchmark confirm selective SSMs converge faster to Bayes-optimal risk, show superior sample efficiency with…

Researcher Actions

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Caveats

  • Generated from title, abstract, and extracted metadata only; full-paper implementation details are not parsed.
  • Low-signal flag detected: protocol relevance may be indirect.

Research Summary

Contribution Summary

  • We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL).
  • Experiments on synthetic LG-SSM tasks and a character-level Markov benchmark confirm selective SSMs converge faster to Bayes-optimal risk, show superior sample efficiency with longer contexts in structured-noise settings, and track latent…

Why It Matters For Eval

  • Experiments on synthetic LG-SSM tasks and a character-level Markov benchmark confirm selective SSMs converge faster to Bayes-optimal risk, show superior sample efficiency with longer contexts in structured-noise settings, and track latent…

Researcher Checklist

  • Gap: Human feedback protocol is explicit

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  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Gap: Metric reporting is present

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