#01Oct 23, 2026
cs.AI
SemantEq: Faithful Bidirectional Equivalence of Formal Statements
Xinrui Li, Pawan Sasanka Ammanamanchi, Siddharth Bhat and 3 more
Statement autoformalization translates mathematics from natural language into a proof assistant such as Lean 4, and models now do it at scale. As provers get stronger, the burden of correctness shifts from the proof to the statement, that is, to whether the formal statement faithfully translates its source. Given a trusted reference formalization, the natural test is logical equivalence, and it proves too much. $P \leftrightarrow Q$ holds trivially for any two statements $P$ and $Q$ that the library proves, because a prover can prove each separately and pass through $P \leftrightarrow \mathrm{True} \leftrightarrow Q$. The stronger the prover, the more unrelated pairs pass. Earlier methods restrict the prover and check that each proof names the other statement. We introduce SemantEq, a more principled relation that instead requires each statement to turn into the other only through a chain of allowed steps, such as logical rearrangement and rewriting with the library's own equations. Our programs judge a proof by the proof term Lean checks, not by its tactic script. SemantEq-Eval, a search without a model, reaches 100% precision and 65.6% recall on the ProofNetVerif test split under our adjudicated labels, against 95.8% and 61.8% for BEq+, and an 8.9-fold increase in its CPU time adds at most three pairs. A language model finds more proofs, but under two of four prompts it proves both directions of about two in five of the non-equivalent pairs. SemantEq-ProofAudit audits each model-written proof under a policy derived from the relation and accepts none of the 104 non-equivalent pairs, and it raises recall on 407 equivalent pairs from 65.4% to 81.1% under the best prompt. Separating the generation of equivalence proofs from their acceptance lets a stronger prover raise recall without changing what an acceptance means. We release code and data at: https://github.com/hlxr89/SemantEq
#02Oct 23, 2026
cs.RO
ViT-H: Generative Video-To-Humanoid Control with Motion Tracking Feedback
Zimo He, Tianyi Bian, Zizhong Yang and 7 more
Learning humanoid control from monocular human videos offers a scalable way to acquire diverse whole-body behaviors. Yet, existing reconstruction-retargeting-tracking pipelines are limited in system-level scalability by separately optimized intermediate stages and cannot directly optimize reference motion executability using downstream tracking feedback. We present ViT-H, a video-to-humanoid control framework following a generation-and-tracking paradigm. ViT-H directly generates humanoid reference motions from videos with a diffusion model, bypassing human motion reconstruction and retargeting, and uses motion-tracking outcomes to post-train the generator with direct preference optimization. We further introduce an autoregressive variant that enables real-time humanoid video teleoperation with sub-400 ms latency. Extensive experiments on the Unitree G1 demonstrate that ViT-H outperforms state-of-the-art reconstruction-retargeting-tracking pipelines in both motion quality and executability. We further show that ViT-H scales favorably with model size and with both pre-training and post-training data scale, while motion-tracking feedback consistently improves executability across different motion trackers.
#03Oct 23, 2026
cs.CV
VTRL-Med: Progressive Visual Refinement with Topology-Guided Regularization for Medical Image Clustering
Guangyu Meng, Pengfei Gu, Peixian Liang and 3 more
Deep clustering offers a promising approach for analyzing large unlabeled medical image datasets, yet prevailing methods still face two limitations: they may neglect class-agnostic structural priors that capture object boundaries and regions, and they do not explicitly encode topological patterns (e.g., connectivity and holes). These sources of information play distinct and complementary roles: visual-structural features provide the primary discriminative representation for clustering, while topological features provide additional global geometric cues for residual visual ambiguities. We introduce VTRL-Med, a progressive visual-structural learning framework with topology-guided regularization for medical image clustering. VTRL-Med first adapts the Segment Anything Model (SAM) to extract image features that retain structural cues inherited from mask-supervised pretraining. It then generates reliable pseudo-labels through a two-step filtering process that combines prototype-based selection with k-nearest neighbor consistency validation. Finally, it progressively refines the visual branch while an auxiliary topology branch, constructed from persistent homology (PH) descriptors, provides additional geometric regularization during training. Across 13 medical image benchmarks, VTRL-Med achieves state-of-the-art clustering performance, improving average accuracy by 4.48% over existing methods. On three representative datasets, topology-guided regularization further improves accuracy by 1.3--4.3% over visual refinement alone.
#04Oct 23, 2026
cs.LG
ZENO: Nonlinear filtering with Zakai Equation Neural Operators
Aaditya Prasad, Steven W. Flavell, Brian DePasquale
State inference and parameter learning for nonlinear filters is a core computation for scientific machine learning with varied applications in engineering and neuroscience. The unnormalized filtering distribution is governed by the Zakai equation, a stochastic partial differential equation (SPDE) that combines the forward Kolmogorov operator (known as the Fokker-Planck equation) with observed likelihood updates. Although solving these high-dimensional SPDEs is often impossible analytically and intractable numerically, advances in operator learning and physics-informed machine learning have made it feasible. Harnessing these advances, we introduce the Zakai Equation Neural Operator (ZENO), a model that optimizes a neural operator against a Zakai Equation based physics-informed loss to approximate the exact unnormalized filtering distribution for latent stochastic dynamical systems. We use this ZENO-inferred posterior distribution in an expectation-maximization (EM) framework to perform parameter learning and state inference. We demonstrate ZENO's ability to accurately infer the posterior distribution and learn its corresponding SDE parameters in three simulated stochastic dynamical systems (Double-Well bistable system, Van Der Pol (VDP) oscillator, and Lorenz system) and compare its performance against established methods for latent SDE inference and learning. We show that ZENO recovers previously observed limit cycles representing forward and backward locomotion from a whole-brain imaging dataset of immobilized \textit{C. elegans} nematodes. ZENO is a novel approach to the problem of nonlinear filtering and dynamical inference through the lens of partial differential equations and operator theory.
#05Oct 23, 2026
cs.LG
Where Rounding Happens Matters: Rounding-Location Alignment Stabilizes LLM Reinforcement Learning
Yijing Ke, Tianle Cai, Ruosong Wang
Reinforcement learning for large language models often uses separate systems for inference and training. Even with identical weights and BF16 tensors, implementation differences can make an intended on-policy update off-policy and destabilize training. Existing remedies align the entire inference and training stacks, change global precision, or modify the learning algorithm. We ask whether aligning selected parts of the execution stack can stabilize BF16 RL while other implementation differences remain. We align training-side rounding locations with inference in three regions---RoPE, SwiGLU, and residual RMSNorm---by retaining selected intermediates in FP32 until their BF16 outputs. Across four Qwen-family models, aligning all three regions prevents the collapse observed under the default BF16 baseline; RoPE-path alignment alone also suffices in the studied runs, despite remaining numerical discrepancies. The interventions keep the inference engine, matrix-multiplication and attention kernels, and learning objective unchanged.