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AI · Wednesday, 1 July 2026 · Issue 37 · 11 stories

TabFM zero-shot table predictions, Claude Sonnet 5 cost spike

Models & Releases

Research

Closed‑Form Theory Predicts GRPO Training Dynamics and Stability

The paper derives a first‑principles closed‑form model for Group Relative Policy Optimization (GRPO) training dynamics, turning heuristic reward fits into a mechanistic framework. It predicts group‑size invariance, a stability threshold, and an overdamped‑to‑oscillatory transition, offering diagnostics that separate reward hacking from genuine instability. Experiments on multiple models achieve R² ≥ 0.91 and validate the predictions.

arxiv.org ↗2 min read at source

BayesBench Shows LLMs Lag Behind Rational Belief Updating

BayesBench tests whether LLMs reduce epistemic uncertainty in multi-turn dialogs like a Bayesian reasoner. The benchmark shows scaling improves latent inference, but belief updates still fall short of rational posterior tracking, exposing a gap for conversational agents that must adapt to new evidence.

arxiv.org ↗1 min read at source

Geometry, Not Training, Causes Few‑Step Text Generation Collapse

Deterministic few‑step decoders work for image latents but fail on text because a smooth map can’t commit to sharp categorical choices. The paper proves the failure stems from geometric constraints on readout sharpness, not model size or data. It also offers diagnostics (DABI, CCI) and shows how autoregressive or stochastic tricks bypass the limit.

arxiv.org ↗2 min read at source

Agentic LLM System Autoformalizes Research Math into Lean 4

A new agentic autoformalization system uses general-purpose coding LLMs to translate novel research mathematics into Lean 4, extending libraries on the fly and checking proofs mechanically. It succeeded on a random sample of 32 Putnam problems and formalized main theorems from five STOC papers, two of which required only Lean's kernel axioms.

arxiv.org ↗2 min read at source

Tools & Open Source

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That was all 11 stories in the 1 July issue.