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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.11768 |
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| _version_ | 1866915810369339392 |
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| author | Chlon, Leon Khamis, Zein Chlon, Maggie Zein, Mahdi El Awada, MarcAntonio M. |
| author_facet | Chlon, Leon Khamis, Zein Chlon, Maggie Zein, Mahdi El Awada, MarcAntonio M. |
| contents | Exchangeability-based martingale diagnostics have been used to question Bayesian explanations of transformer in-context learning. We show that these violations are compatible with Bayesian/MDL behavior once we account for a basic architectural fact: positional encodings break exchangeability. Accordingly, the relevant baseline is performance in expectation over orderings of an exchangeable multiset, not performance under every fixed ordering.
In a Bernoulli microscope (under explicit regularity assumptions), we bound the permutation-induced dispersion detected by martingale diagnostics (Theorem~3.4) while proving near-optimal expected MDL/compression over permutations (Theorem~3.6). Empirically, black-box next-token log-probabilities from an Azure OpenAI deployment exhibit nonzero expectation--realization gaps that decay with context length (mean 0.74 at $n = 10$ to 0.26 at $n = 50$; 95\% confidence intervals), and permutation averaging reduces order-induced standard deviation with a $k^{-1/2}$ trend (Figure~2).
Controlled from-scratch training ablations varying only the positional encoding show within-prefix order variance collapsing to $\approx 10^{-16}$ with no positional encoding, but remaining $10^{-8}$--$10^{-6}$ under standard positional encoding schemes (Table~2). Robustness checks extend beyond Bernoulli to categorical sequences, synthetic in-context learning tasks, and evidence-grounded QA with permuted exchangeable evidence chunks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | LLMs are Bayesian, In Expectation, Not in Realization Chlon, Leon Khamis, Zein Chlon, Maggie Zein, Mahdi El Awada, MarcAntonio M. Machine Learning Exchangeability-based martingale diagnostics have been used to question Bayesian explanations of transformer in-context learning. We show that these violations are compatible with Bayesian/MDL behavior once we account for a basic architectural fact: positional encodings break exchangeability. Accordingly, the relevant baseline is performance in expectation over orderings of an exchangeable multiset, not performance under every fixed ordering. In a Bernoulli microscope (under explicit regularity assumptions), we bound the permutation-induced dispersion detected by martingale diagnostics (Theorem~3.4) while proving near-optimal expected MDL/compression over permutations (Theorem~3.6). Empirically, black-box next-token log-probabilities from an Azure OpenAI deployment exhibit nonzero expectation--realization gaps that decay with context length (mean 0.74 at $n = 10$ to 0.26 at $n = 50$; 95\% confidence intervals), and permutation averaging reduces order-induced standard deviation with a $k^{-1/2}$ trend (Figure~2). Controlled from-scratch training ablations varying only the positional encoding show within-prefix order variance collapsing to $\approx 10^{-16}$ with no positional encoding, but remaining $10^{-8}$--$10^{-6}$ under standard positional encoding schemes (Table~2). Robustness checks extend beyond Bernoulli to categorical sequences, synthetic in-context learning tasks, and evidence-grounded QA with permuted exchangeable evidence chunks. |
| title | LLMs are Bayesian, In Expectation, Not in Realization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2507.11768 |