How Wrong Can a Good Predictor Be? Diverging Updates with Vanishing Predictive KL
Updated 35 min ago · first seen 11 Sept 2026
paper_01M294FP0ER4N1ZXG9BXY5R5MW
- Published
- 11 Sept 2026
- T1 · 35 min ago
- arXiv
- 2609.11132
- T1 · 35 min ago
- Category
- cs.LG
- T1 · 35 min ago
Abstract
Accurate posterior prediction need not require accurate approximation of Bayesian updates. We prove that an unbounded gap between the update maps can coexist with vanishing predictive KL for every fixed finite $K\ge2$ in a stationary symmetric Gaussian HMM. Exact Bayesian mixing and an explicit deterministic radial filter act on the same $K-1$ belief coordinates. As $q\to0^+$, their separation in centered logits in the worst case grows at least linearly in the natural confidence scale $L_K(q)$, while their categorical $D_{\mathrm{KL}}(\mathrm{exact}\|\mathrm{radial})$ vanishes at the same explicit witness. Along stationary HMM trajectories, the expected terminal KL between filtered posteriors also converges to zero at $H(q)=\lceil-\log(q)/c\rceil+1$. Typical blocks without switches drive both filters into a common confidence cone, where softmax curvature suppresses their disagreement; a single Gaussian maximal event controls adaptive noise. A sweep with equally spaced Gaussians over $K\in\{2,4,8\}$ illustrates the opposing trends, and binary controls at long horizons compare saturating and nonsaturating recurrences. The result isolates two missing links between internal update gaps and predictive cost: the contribution of separating states to expected loss and decoder sensitivity. Thus even an unbounded internal update gap does not by itself certify predictive failure. The construction is fixed in $K$ and does not provide a universal criterion for when compression is harmless or characterize when internal gaps must incur task loss.
Authors 5
Qifu Wen, Shuaijun Liu, Zihan Zhou, Xi Zeng, Ningxin Su
Specification
- Official page
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
- Arxiv announce type
- new
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
- arXiv id
- 2609.11132
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
- Categories
- cs.LG, stat.ML
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
- Primary category
- cs.LG
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
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Provenance
Attributed facts
9
Source tiers
T19
Freshest observation
35 min ago
Conflicts
None
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- Authors
- Qifu Wen, Shuaijun Liu, Zihan Zhou
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Claim history · Abstract
Abstractabstract1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| Accurate posterior prediction need not require accurate approximation of Bayesian updates. We prove that an unbounded gap between the update maps can coexist with vanishing predictive KL for every fixed finite $K\ge2$ in a stationary symmetric Gaussian HMM. Exact Bayesian mixing and an explicit deterministic radial filter act on the same $K-1$ belief coordinates. As $q\to0^+$, their separation in centered logits in the worst case grows at least linearly in the natural confidence scale $L_K(q)$, while their categorical $D_{\mathrm{KL}}(\mathrm{exact}\|\mathrm{radial})$ vanishes at the same explicit witness. Along stationary HMM trajectories, the expected terminal KL between filtered posteriors also converges to zero at $H(q)=\lceil-\log(q)/c\rceil+1$. Typical blocks without switches drive both filters into a common confidence cone, where softmax curvature suppresses their disagreement; a single Gaussian maximal event controls adaptive noise. A sweep with equally spaced Gaussians over $K\in\{2,4,8\}$ illustrates the opposing trends, and binary controls at long horizons compare saturating and nonsaturating recurrences. The result isolates two missing links between internal update gaps and predictive cost: the contribution of separating states to expected loss and decoder sensitivity. Thus even an unbounded internal update gap does not by itself certify predictive failure. The construction is fixed in $K$ and does not provide a universal criterion for when compression is harmless or characterize when internal gaps must incur task loss. | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →
New paper: How Wrong Can a Good Predictor Be? Diverging Updates with Vanishing Predictive KL
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.LG | feed | T1· Official | 35 min ago | 1 |
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