Thinking with Looped Flows

Humans and machines often solve harder problems by spending more time on computation. In deep learning, looped models implement this idea during inference by recurrently updating a hidden state. In practice, however, their training backpropagates through only one or a few updates, making it hard to train early updates to support future ones. We propose looped flows, an approach that sidesteps this issue by training the recurrence with local denoising objectives. By imposing temporal association across denoising objectives through progressively decreasing noise levels and shared noise, the model is incentivized to learn recurrent states that transfer useful computation over time, even when gradients cover only a few updates. We then formulate inference as integrating the velocity of a probability flow parameterized by the learned denoiser, coupled with recurrent states. This allows solving harder problems by spending more computation through a finer temporal grid and enables multiple valid predictions from different initial noise samples. Across six reasoning benchmarks including two multi-solution benchmarks, looped flows outperform prior state-of-the-art looped models overall, achieving 58.8% test accuracy on ARC-AGI-1 and 12.2% on ARC-AGI-2.

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arXiv AI Papers·anteontem☆

TCSP3.0: Template-Based Crystal Structure Prediction with Coefficient-Preserving Element Substitution and Structural Diversity↗

Template-based crystal structure prediction (CSP) transfers a known crystal structure to a new composition by element substitution, so its accuracy depends on retrieving suitable templates, mapping elements and ranking the resulting candidates correctly. Auditing the original TCSP2.0 implementation on the T180 benchmark, we found that 469 of its 2,347 selected structures (20%) have the wrong composition, caused by element mappings that ignore stoichiometric coefficients and by sequential text substitution that cascades or corrupts element symbols. We propose TCSP3.0, which enforces coefficient-preserving mappings, substitutes species simultaneously on parsed structures and validates every candidate's composition and cell. It further adds periodic-number retrieval, soft oxidation-state evidence, radius-compatibility scoring, structural deduplication, and ORB-v3 machine-learning-potential relaxation and energy ranking of its candidates, as used by deep generative CSP baselines. TCSP3.0 achieves Top-1 and Top-20 match rates of 72.2% and 90.6% on T180, compared with 28.3% and 45.6% for TCSP2.0, and a Top-20 match rate of 74.0% on a new 800-target benchmark (T800). On T180 it also outperforms PNcsp+ and deep generative models CrystalFlow and MaskGXT (Top-1 72.2% versus at most 63.9%). Even without relaxation, TCSP3.0 reaches 67.8% at Top-1 and 90.6% at Top-20 in a median of 28 s per target on two CPU cores, about ten times faster than CrystalFlow. Paired ten-arm ablations on T180 and T800 show that most of the improvement comes from the correctness fixes; structural deduplication significantly improves the Top-5 match rate, embedding-based retrieval is required for coverage, and the remaining scoring features have small or null effects.

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arXiv AI Papers·anteontem☆

When Does GEPA Merge Help? A Mechanism-Level Diagnostic↗

GEPA is among the strongest reflective prompt optimizers for language-model programs, but its system-aware merge operator is unstable across models: merge improves gpt-4.1-mini on average while degrading Qwen3-8B, an asymmetry noted but left unexplained by the GEPA paper. We investigate this instability across five datasets and two models. Our nine-configuration sweep over merge timing and merge operator shows that merge can improve both models when configured appropriately. This suggests that merge instability is better explained by configuration sensitivity than by an inherent flaw in the merge operator. We then test whether prompt-level features predict GEPA's merge-accept decisions and find that they do not, ruling out static-feature gating. As a proof of concept, a behavior-based probe built from these diagnostics avoids large merge failures in our multi-seed runs by abstaining on high-risk tasks, although it does not consistently outperform NoMerge. Code is available as GEPA-MergeProbe at https://github.com/ChongZZZZ/GEPA_MERGE .

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arXiv AI Papers·anteontem☆

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The differential neural tangent kernel (DNTK) is a tool for analyzing the training dynamics of overparameterized physics informed neural networks. In this work, we investigate the symmetry of the infinite DNTK under an orthogonal group, for two layer and deep neural networks separately, based on the explicit expression of the DNTK and recursive formula, respectively. The results are for all activations with or without a bias term, and shed insight into the structure of the infinite width DNTK. Then we prove that the integral operators over the unit sphere induced by operators from the same group orbit share the spectrum, and their reproducing kernel Hilbert spaces differ only by an orthogonal transformation, and that the operator fixed DNTK exhibits zonal symmetry on the unit sphere for symmetric operators. Thus the eigenvalue decay rate of the associated integral operator can be derived for shallow networks with RePU activation and zero bias initialization.

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arXiv AI Papers·anteontem☆

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