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01.
Nature Biotechnology 2026-06-23

Mapping and engineering the human cell–cell interactome

Authors:

Efforts to systematically understand how cell interactions tune tissue-level function have motivated transformative advances in single-cell transcriptomics and spatial profiling. Although these technologies can measure molecular states in individual cells and their spatial mapping within tissues, they also reveal that there exists a fundamental knowledge gap of how cells influence each other in context. In this Perspective, we propose an initiative to map and engineer the human cell–cell interactome: a functional atlas of how all major human cell types communicate. We highlight how recent innovations can make this vision achievable. As a first moonshot, we propose the ‘Billion Cell×Cell Project’, which systematically characterizes the outcomes of defined cell–cell dyads across diverse cell types and conditions. We envision this multistage initiative will produce progressively deeper insights and unlock additional avenues for therapeutic discovery. We call on the scientific community to join us in building the tools, datasets and models that will decode and rewrite the language of life between cells. Di Carlo and colleagues discuss technologies required to map and engineer the human cell–cell interactome and the therapeutic avenues such an atlas could unlock.

02.
arXiv (CS.LG) 2026-06-16

Best Arm Identification with Minimal Regret

arXiv:2409.18909v2 Announce Type: replace Abstract: Motivated by real-world applications that necessitate responsible experimentation, we introduce the problem of best arm identification (BAI) with minimal regret. This variant of the multi-armed bandit problem elegantly amalgamates two of its most ubiquitous objectives: regret minimization and BAI. More precisely, the agent's goal is to identify the best arm with a prescribed confidence level $\delta$, while minimizing the cumulative regret up to the stopping time. Focusing on single-parameter exponential families of distributions, we leverage information-theoretic techniques to establish an instance-dependent lower bound on the expected cumulative regret. Moreover, we present an impossibility result that underscores the tension between cumulative regret and sample complexity in fixed-confidence BAI. Complementarily, we design and analyze the Double KL-UCB algorithm, which achieves asymptotic optimality as the confidence level tends to zero. Notably, this algorithm employs two distinct confidence bounds to guide arm selection in a randomized manner. Our findings elucidate a fresh perspective on the inherent connections between regret minimization and BAI.

03.
arXiv (CS.AI) 2026-06-25

LibEvoBench: Probing Temporal Knowledge Stratification in Code Generation Models

arXiv:2606.25402v1 Announce Type: cross Abstract: Large software projects often depend on older versions of libraries, even as APIs continue to evolve across releases. This creates a challenge for LLMs: they must maintain knowledge of multiple API versions, not merely the latest or most common one. However, current LLMs are trained on temporally mixed corpora and lack explicit mechanisms for such version-specific reasoning, leading to anachronistic errors - calling APIs as they exist in a different library version. To systematically evaluate this phenomenon, we introduce LibEvoBench, a multi-task benchmark spanning multiple versions of widely used Python libraries, along with a new metric, the Software Evolution Understanding Score (SEUS), to measure models' consistency when working with evolving APIs. Our results show that state-of-the-art models are largely version-oblivious: performance degrades for evolving APIs, while for stable APIs it remains the same across versions. Moreover, simply specifying the target version provides no benefit, while relevant documentation significantly boosts models' accuracy. These findings highlight a systematic limitation of current training paradigms and motivate new approaches for temporally grounded knowledge in code generation.

04.
arXiv (CS.CV) 2026-06-16

Planning with Unified Multimodal Models

With the powerful reasoning capabilities of large language models (LLMs) and vision-language models (VLMs), many recent works have explored using them for decision-making. However, most of these approaches rely solely on language-based reasoning, which limits their ability to reason and make informed decisions. Recently, a promising new direction has emerged with unified multimodal models (UMMs), which support both multimodal inputs and outputs. We believe such models have greater potential for decision-making by enabling reasoning through generated visual content. To this end, we propose Uni-Plan, a planning framework built on UMMs. Within this framework, a single model simultaneously serves as the policy, dynamics model, and value function. In addition, to avoid hallucinations in dynamics predictions, we present a novel approach self-discriminated filtering, where the generative model serves as a self-discriminator to filter out invalid dynamics predictions. Experiments on embodied decision-making tasks show that Uni-Plan substantially improves success rates compared to VLM-based methods, while also showing strong data scalability, requiring no expert demonstrations and achieving better performance under the same training-data size. This work lays a foundation for future research in reasoning and decision-making with UMMs.

05.
arXiv (CS.CV) 2026-06-16

Revealing Artifacts via Noise Amplification: A Novel Perspective for AI-Generated Video Detection

With the rapid advancement of video generation models, distinguishing between AI-generated and authentic videos has emerged as a challenging endeavor. The majority of existing research endeavors concentrate on the development of detectors for identifying samples generated by generative adversarial networks. Nevertheless, the detection of AI-generated videos, particularly those produced by text-to-video models, still remains an uncharted territory. Although state-of-the-art text-to-video models can generate realistic visual content similar to real videos, they fall short of generating the details of the images and the changes in details within the videos. Inspired by this, we address AI-generated video detection from a novel perspective of bit-planes, which can effectively describe the details or noises in images or videos. To this end, we propose a simple yet effective approach called Noise Amplification. This approach first extracts noise signals based on bit-planes, then amplifies these noise signals, and finally feeds them into the discriminator networks for video fake classification. Noise amplification is comprehensively constructed by incorporating three aspects: pixel-level intensity enhancement, region-level spatial amplification, and frame-level temporal aggregation. To evaluate methods of AI-generated video detection in challenging scenarios, we also introduce a benchmark named HardGVD. Extensive experiments on both the large-scale dataset GenVidBench and HardGVD show that our simple approach significantly outperforms state-of-the-art methods.

06.
arXiv (CS.CV) 2026-06-17

HRDX: A Large-Scale Vector HD-Map Dataset

Reliable autonomous driving requires vectorized HD maps that are geometrically accurate, semantically rich, and scalable to long-horizon driving. However, existing public HD map datasets are limited in scale, provide sparse semantic attributes, and lack modalities such as aerial imagery that could enable new research directions. We present HRDX, a large-scale dataset for vector HD-map construction, spanning about 40 hours (1,400 km) of minimally overlapping drives, which is several times larger than prior public HD map datasets. Data is captured using six synchronized surround cameras, a 128-beam LiDAR, and centimeter-level RTK GNSS/IMU, and is further complemented by precisely aligned aerial orthoimagery. Annotations cover 10 vector map classes, complemented with over 20 semantic and topological attributes. To evaluate this richer ontology, we introduce the Composite Score (CS) to jointly assess geometric fidelity and attribute correctness. Benchmark experiments show that HRDX's scale improves online vector-map construction, and that aligned aerial imagery provides a useful structural prior: using aerial imagery at training and/or inference improves geometric map quality, while aerial-augmented teachers can transfer part of this benefit to camera-only students without increasing inference-time sensor requirements. HRDX is intended to support reproducible research on large-scale HD-map learning, multimodal BEV fusion, and training-time privileged information. HRDX dataset and benchmarks are available at https://github.com/honda-research-institute/HRDX

07.
arXiv (CS.CV) 2026-06-16

Hierarchical GRU with Input-Conditioned Slot Queries for Ball Action Anticipation

We present a hierarchical model for ball action anticipation in football broadcast video. Given a 30-second observation window, the system predicts actions occurring in the subsequent 5-second window across 10 classes. A shared local Transformer encodes clip-level features within each 5-second sub-window; a GRU then aggregates temporal context across all sub-windows; finally, a Transformer decoder with K input-conditioned event slots decodes the anticipation target via three decoupled heads (objectness, class, temporal offset). We introduce frequency-reweighted Hungarian matching that systematically favours rare action classes, and Gaussian soft targets for temporal bin supervision. On the SoccerNet Ball Action Anticipation benchmark, our method achieves 17.91% mAP on the test server.

08.
arXiv (CS.CV) 2026-06-24

Venice-H1: Failure-Aware Query Re-Ranking with Multi-Scale Grid Signatures for Referring Image Segmentation

Modern Referring Image Segmentation (RIS) systems generate multiple candidate masks per expression but rely on a simple heuristic–typically the argmax detection score–to select the final output. We identify query selection as a failure-case bottleneck: although heuristic selection succeeds on 82-93% of samples, the residual 7-18% of failures dominate the error budget, leaving a best-query selection gap of 3-11% mIoU. We introduce Venice-H1, a lightweight, backbone-decoupled post-hoc re-ranking module that encodes each candidate through multi-scale grid signatures–compact spatial descriptors pooled onto 4x4, 8x8, and 16x16 grids–and feeds them to a Transformer-based re-ranker with a Failure Gate (ROCAUC 0.78-0.82) that intervenes only when the default choice is likely suboptimal. Instantiated on DeRIS-L and DeRIS-B, Venice-H1 achieves delta_fail of +1.40 and +0.89 mIoU with strictly positive 95% CIs on all 16/16 (split, backbone) pairs and harmful-switch rates below 0.53%. Zero-shot transfer to medical referring segmentation (MS-CXR, M3D-RefSeg-2D) yields +1.16 and +0.51 mIoU without RIS-backbone fine-tuning. The module adds approximately 11.3M parameters and under 1 ms latency.

09.
arXiv (CS.LG) 2026-06-17

Tight $L_\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials

arXiv:2606.17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube. To ensure that optimizing the surrogate yields good solutions for the underlying objective, we require uniform $L_\infty$-error guarantees rather than the usual $L_2$-type guarantees. We characterize the minimax sample complexity of uniform estimation under subgaussian noise for two classes of bounded polynomials. First, for polynomials of degree at most $d$ on $n$ variables, the sample complexity scales as $n^{d+1}$. Second, for $s$-sparse Fourier-Walsh polynomials with $s \leq n$, it scales as $ns^2$. These rates differ structurally from the noiseless setting, where uniform exact recovery scales as $n^d$ and $ns$, respectively. Our lower bounds hold even for arbitrary adaptive learners, showing that the additional factors are intrinsic to the noisy cases. Standard Fourier-analysis tools for the $L_2$-norm do not naturally extend to the $L_\infty$-setting in a way that yields uniform guarantees. Our proofs overcome this difficulty by relying on suitably chosen auxiliary norms that serve as proxies for controlling the $L_\infty$-error. Together, our results provide a tight characterization of the sample complexity of learning optimization-safe polynomial surrogates.

10.
arXiv (CS.CV) 2026-06-24

Do Foundation Models See Biology? Evaluating Attention Coherence with Spatial Transcriptomics in Glioblastoma

Whether attention maps from pathology foundation models capture genuine biology remains unknown, yet this question is critical for clinical trust and regulatory approval. We propose a spatial transcriptomics-based framework for orthogonal, hypothesis-free evaluation of attention and apply it to five pathology foundation models (CONCH v1.5, UNI v2, Virchow2, GigaPath, H-Optimus-1) and a ResNet50 baseline. Using attention-based multiple instance learning, we train single-task and multi-task models to predict five molecular alterations in glioblastoma on the CPTAC cohort, validate on an independent TCGA cohort, and evaluate biological coherence of attention maps against 87 transcriptional signatures using co-registered Visium spatial transcriptomics data from 18 samples. Internally, no single encoder dominates across all tasks, and external validation inverts internal performance rankings. Attention maps show a five-fold enrichment gradient from pathways (Cohen's d=0.329) to individual genes (d=0.055), indicating that attention captures emergent multi-gene transcriptional programs rather than individual molecular events. Spatially smooth attention maps do not imply biological coherence, and different encoders attend to distinct biological compartments. Our framework provides objective, quantitative assessment of what foundation models learn from histopathology, moving the field beyond qualitative saliency map review.

11.
arXiv (quant-ph) 2026-06-15

No classical particle limit for massless quanta

arXiv:2606.14632v1 Announce Type: new Abstract: We investigate whether relativistic massless classical particles may emerge as the classical limit of massless quanta. To address this question independently of any specific dynamics, environment, or pointer basis, we develop an axiomatic and purely kinematical framework for the coarse-graining approach. In this formulation, a candidate classical phase space is taken as the outcome space of a POVM subject only to minimal classicality and covariance under the relevant spacetime symmetry group. Applying this framework to the Poincaré group, we prove a no-go theorem for massless particles: the covariance requirement is incompatible with the operational conditions for classicality. The theorem leaves open field-like limits of massless quanta, for example the emergence of electromagnetic or gravitational fields, while ruling out classical massless particles, such as classical photons or gravitons.

12.
arXiv (CS.AI) 2026-06-15

LEPO: Latent Reasoning Policy Optimization for Large Language Models

arXiv:2604.17892v4 Announce Type: replace-cross Abstract: Recently, latent reasoning has been introduced into large language models (LLMs) to leverage rich information within a continuous space. However, without stochastic sampling, these methods inevitably collapse to deterministic inference, failing to discover diverse reasoning paths. To bridge the gap, we inject controllable stochasticity into latent reasoning via Gumbel-Softmax, restoring LLMs' exploratory capacity and enhancing their compatibility with Reinforcement Learning (RL). Building on this, we propose \underline{L}atent R\underline{e}asoning \underline{P}olicy \underline{O}ptimization~(LEPO), a novel framework that applies RL directly to continuous latent representations. Specifically, in rollout stage, LEPO maintains stochasticity to enable diverse trajectory sampling, while in optimization stage, LEPO constructs a unified gradient estimation for both latent representations and discrete tokens. Extensive experiments show that LEPO significantly outperforms existing RL methods for discrete and latent reasoning.

13.
arXiv (quant-ph) 2026-06-16

Adiabatically-induced Kawaguchi geometry and jerk in quantum-classical systems

arXiv:2606.16037v1 Announce Type: new Abstract: Adiabatically eliminating the quantum degrees of freedom in a mixed quantum-classical system produces an effective force in the classical equation of motion. The elimination can be made to any order in the adiabatic parameter, generating a series of higher order forces. By applying a sequence of near-identity unitary transformations to the quantum state, we derive a hierarchy of increasingly accurate effective actions for the classical variables. The third order Euler-Lagrange equation is non-Newtonian as the force depends on the jerk, the third order time derivative of position. We find that the third order terms induce a special kind of Kawaguchi geometry on the space of classical variables. This geometry is characterized by an almost symplectic structure and a differential line element that depends on the acceleration in addition to the velocity. Our results can be used to efficiently capture higher order nonadiabatic effects in molecular dynamics simulations.

14.
arXiv (CS.CL) 2026-06-25

LLM Performance on a Real, Double-Marked GCSE Benchmark

We introduce a dataset of 32,534 double-marked real student responses to GCSE mock exams (GCSEs are the UK's national exams, taken at age ~16), spanning 328 questions across five subjects and including handwritten work. We test whether off-the-shelf large language models agree with examiners as closely as the two examiners agree with each other. We find that models overwhelmingly agree well with the examiner consensus across subjects, with the top performing models agreeing more closely with examiners than examiners agree with each other. Models achieve high scores for subjective tasks like English essay marking, as well as handling complex and messy handwritten Maths paper scripts. Agreement is uniform near the examiner line, and not massively discriminated by model size, providing cost-effective automated marking solutions.

15.
arXiv (CS.AI) 2026-06-16

From Correlation to Causation in Lane Change Prediction for Automated Driving: A Causal Explanation Framework

arXiv:2606.15756v1 Announce Type: cross Abstract: Lane-change prediction is a central task in intelligent vehicles, where early maneuver anticipation can support safer decision-making. However, many existing approaches mainly learn statistical associations between observed driving variables and future maneuvers, while overlooking the causal dependencies among the input variables themselves. This limits interpretability, especially when physically related variables such as longitudinal gap, relative longitudinal velocity, and Time-To-Collision (TTC) are treated as independent flat inputs. This article presents a causal-inference-based framework for lane-change prediction and explanation. The proposed approach combines linguistic feature construction, expert-constrained causal discovery, deep structural causal modeling with Deep End-to-end Causal Inference (DECI), intervention-based effect analysis, refutation testing, and recursive causal-chain explanation. The objective is not only to predict the future maneuver, but also to identify candidate variables that directly contribute to the prediction, the upstream factors influencing them, and the causal chains through which these effects propagate. The framework achieves average F1-scores above 95% during the first three seconds before the lane-marking crossing event. Beyond prediction accuracy, the framework uses intervention-based effect analysis to distinguish influential from weakly influential variables under the learned causal structure. It further distinguishes candidate direct contributors from mediated effects and generates contrastive causal-chain explanations that clarify why the predicted maneuver is favored and why the alternative maneuvers are less supported. The main contribution is therefore a mechanism-aware lane-change prediction pipeline that moves beyond correlation-based classification toward more interpretable causal reasoning for maneuver prediction.

16.
arXiv (quant-ph) 2026-06-24

How rare are Markovian quantum dynamics?

arXiv:2606.24511v1 Announce Type: new Abstract: A profound understanding of decoherence and dissipation in quantum dynamics is crucial for the realistic modeling of the evolution of quantum systems. In open quantum dynamics one distinguishes between a memoryless, so-called Markovian evolution and dynamics incorporating memory effects, termed non-Markovian. In this work we study how prevalent memory effects are in the set of all such dynamics. We thus investigate how often a Markovian description is applicable. This question is approached by investigating randomly generated two-step qubit dynamics with respect to different concepts and witnesses of non-Markovianity. We observe that almost all dynamics are non-Markovian, and only a small (yet finite) fraction is Markovian. Furthermore, we study how this proportion changes when considering certain subclasses such as lower rank or mixed-unitary dynamics. Importantly, our results shed light on the relative ratios of – and interrelations between – the sets of dynamics that are non-Markovian with respect to different criteria. Finally, we investigate the fraction of dynamics in which the memory effects are necessarily of quantum nature and establish a connection between two recently developed concepts that characterize the quantumness of memory in non-Markovian dynamics.

17.
arXiv (CS.AI) 2026-06-16

Training and Evaluating Diffusion Policies with Long Context Lengths

arXiv:2606.16447v1 Announce Type: cross Abstract: Imitation learning has enabled highly-dexterous robotic manipulation from RGB observations. Policies trained with these methods, however, typically condition robot actions on only a short history of observations. These policies cannot solve tasks that require memory and can get stuck repeatedly executing the same failing motions. In this work, we first benchmark policy performance as context length is incrementally increased from short to long, across a spectrum of tasks with varying local stability and memory requirements, and in multiple data regimes. To our knowledge, this is the first study to investigate context length in imitation learning at this level of detail. Our results challenge prior claims: naively scaling context length is not as brittle as advertised in literature. With an appropriate conditioning method and denoising backbone (UNet+Cross-Attention), single-task policies achieve high success rates on many tasks in the usual data regime even with naive scaling. Next, we propose a training algorithm to jointly train policies at multiple context lengths, further reducing the sample complexity of long-context learning. Finally, we apply our findings to re-evaluate some previously proposed solutions to long-context imitation learning.

18.
arXiv (CS.AI) 2026-06-11

A Physics-Inspired Optimizer: Velocity Regularized Adam

arXiv:2505.13196v3 Announce Type: replace-cross Abstract: We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics. Previous algorithms, including the ubiquitous Adam, operate at the so-called adaptive edge of stability regime during training, leading to rapid oscillations and slowed convergence of loss. However, VRAdam adds a higher order penalty on the learning rate based on the velocity such that the algorithm automatically slows down whenever weight updates become large. In practice, we observe that the effective dynamic learning rate shrinks in high-velocity regimes, and damping oscillations. By combining this velocity-based regularizer for global damping with per-parameter scaling of Adam, we create a powerful hybrid optimizer. For this optimizer, we provide rigorous theoretical analysis of operation at the edge of stability from a physical and control perspective for the momentum. Furthermore, we derive convergence bounds with the rate $\mathcal{O}(\ln(N)/\sqrt{N})$ for a stochastic non convex objective under mild assumptions. We demonstrate that VRAdam exceeds the performance against standard optimizers including AdamW. We benchmark various tasks such as image classification, language modeling, and generative modeling using diverse architectures and training methodologies including Convolutional Neural Networks (CNNs), Transformers, and GFlowNets.

19.
arXiv (CS.CL) 2026-06-19

MENTOR: Reinforcement Learning via Flexible Teacher-Optimized Rewards for Tool-Use Distillation

Distilling the tool-use capabilities of large language models (LLMs) into small language models (SLMs) is essential for their practical application. The predominant approach, supervised fine-tuning (SFT), suffers from poor out-of-domain (OOD) generalization due to its rigid alignment with static teacher trajectories. While reinforcement learning (RL) offers an alternative, the capacity limitations of SLMs pose a severe dilemma: sparse outcome rewards provide insufficient guidance, whereas strict trajectory matching imposes overly restrictive constraints. To bridge this capacity-driven gap, we propose MENTOR, which introduces a flexible yet process-aware reward structure. Instead of enforcing rigid replication, MENTOR uses the teacher's reference to guide tool-use behavior, balancing behavioral alignment with downstream performance. Extensive experiments on controlled executable-tool benchmarks demonstrate that MENTOR improves OOD tool-use performance compared to SFT and strict RL baselines. Our findings suggest that within verifiable tool-use environments, flexible tool-use alignment offers a more effective approach than strict trajectory replication for developing adaptable small models.

21.
arXiv (CS.LG) 2026-06-19

Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs

arXiv:2606.20326v1 Announce Type: new Abstract: We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs). Built upon Chebyshev-polynomial KAN layers and parameterized quantum circuits, this hybrid framework embeds physical constraints into the training loss to enforce physical consistency. Our theoretical investigations grounded in approximation theory prove that this design accelerates high-frequency error convergence to an exponential rate and effectively mitigates numerical dispersion. We validate the framework across three typical seepage scenarios in porous media, including single-phase flow, component transport and two-phase flow. Compared with existing quantum-classical physics-informed neural networks, QCPIKAN achieves superior performance in global prediction accuracy, local error control, dynamic evolution tracking and displacement front localization. This work provides a robust and efficient alternative for solving complex PDEs.

22.
arXiv (CS.AI) 2026-06-12

When Smaller Wins: Dual-Stage Distillation and Pareto-Guided Compression of Liquid Neural Networks for Edge Battery Prognostics

arXiv:2601.06227v3 Announce Type: replace-cross Abstract: Battery management systems increasingly require accurate battery health prognostics under strict on-device constraints. This paper presents DLNet, a practical framework with dual-stage distillation of liquid neural networks that turns a high-capacity model into compact and edge-deployable models for battery health prediction. DLNet first applies Euler discretization to reformulate liquid dynamics for embedded compatibility. It then performs dual-stage knowledge distillation to transfer the teacher model's temporal behavior and recover it after further compression. Pareto-guided selection under joint error-cost objectives retains student models that balance accuracy and efficiency. We evaluate DLNet on a widely used dataset and validate real-device feasibility on an Arduino Nano 33 BLE Sense using int8 deployment. The final deployed student achieves a low error of 0.0066 when predicting battery health over the next 100 cycles, which is 15.4% lower than the teacher model. It reduces the model size from 616 kB to 94 kB with 84.7% reduction and takes 21 ms per inference on the device. These results support a practical smaller wins observation that a small model can match or exceed a large teacher for edge-based prognostics with proper supervision and selection. Beyond batteries, the DLNet framework can extend to other industrial analytics tasks with strict hardware constraints.

23.
Nature (Science) 2026-06-08

Fifty years since a simple equation described the chaos of biology

An exploration of chaos theory in population dynamics showed that unpredictable systems can often be modelled using surprisingly simple mathematics. An exploration of chaos theory in population dynamics showed that unpredictable systems can often be modelled using surprisingly simple mathematics.

24.
arXiv (CS.CL) 2026-06-17

Scaling Enterprise Agent Routing: Degradation, Diagnosis, and Recovery

Production LLM assistants route user requests to growing libraries of specialized tools, but how does routing accuracy degrade as the catalog scales? We study single-step routing on a 110-agent, 584-tool catalog from a deployed enterprise productivity assistant, evaluating three frontier models from 10 to 110 agents. Routing F1 on under-specified requests drops 16–23 percentage points across models. An oracle analysis decomposes the degradation into a retrieval gap (the model cannot surface the right tool) and a confusion gap (even with perfect retrieval, the oracle ceiling drops 10pp). Embedding-based shortlisting recovers +10–11pp F1 at full scale across all three models and two providers. A production annotation study (1,435 human-labeled utterances, three annotators) confirms the recovery on real traffic at +10–17pp despite 10–15pp lower absolute performance.

25.
arXiv (CS.AI) 2026-06-15

Formalizing Numerical Analysis: An Agent Pipeline and Quality Audit Beyond Kernel Acceptance

arXiv:2606.14000v1 Announce Type: new Abstract: Recent work has demonstrated that coding agents can formalize entire advanced mathematics textbooks in Lean 4, yet existing efforts concentrate on branches of mathematics already well-represented in mathlib and measure success solely through kernel acceptance. We address both limitations by applying a coding agent to formalize Numerical Methods for Ordinary Differential Equations, a textbook in numerical analysis that is largely absent from mathlib, stressing the agent's capacity to develop new theory from scratch. We further introduce a systematic, reproducible three-dimensional framework for evaluating the quality of agent-produced formalizations beyond compilation: semantic correctness, Mathlib reuse, and cross-file reuse via LLM-as-judge methods. Applying this framework to our own formalization and to the released outputs of RepoProver and M2F, we uncover recurring unfaithful formalization patterns, including incomplete multi-part statements, added weakening hypotheses, and parameter restrictions, that kernel acceptance entirely obscures. Our results suggest that compilation-based metrics substantially overstate formalization quality, and we provide a reproducible audit methodology to support more rigorous evaluation of future autoformalization systems.