Data-driven discovery of governing differential equations across physical systems

Differential equations play a critical role in scientific discovery because they provide a mathematical framework to describe the behaviour of physical phenomena. As a promising alternative to traditional first principles, data-driven differential equation discovery has attracted increasing attention for its ability to infer governing laws directly from experimental or simulated data, especially when the underlying physics is unclear. However, the field has expanded rapidly along diverse methodological directions, particularly with the emergence of AI-based approaches, and still lacks a clear organizing perspective. In this Review, we propose a problem-oriented perspective on data-driven differential equation discovery. We first introduce a two-dimensional phase diagram of equation discoverability, where discovery problems are organized according to structural complexity and coefficient complexity. This phase diagram shows how the field has moved from the discovery of sparse equations with simple coefficients toward more complex governing laws with richer structures and more flexible parameterizations. It also clarifies why different methodological families succeed or fail in different problem settings. We then present the representation-evaluation-optimization (REO) framework as a fundamental abstraction of the discovery process. By identifying the core problems of equation discovery that persist across algorithmic variations, REO shifts the discussion from individual algorithms to the fundamental principles that determine discoverability. We connect these perspectives to applications across physics and adjacent sciences, and argue that the next challenge is not merely recovering equations, but using them to revise existing theories, distil mechanisms and form new scientific concepts.

Socratic-SWE: Self-Evolving Coding Agents via Trace-Derived Agent Skills

LLM-driven software engineering agents have become a central testbed for real-world language-model capability, yet their training remains limited by the availability of high-quality SWE tasks. Existing synthetic data methods typically create tasks through fixed mutation or bug-injection procedures, making the resulting distributions largely independent of the agent's own weaknesses and training progress. We introduce Socratic-SWE, a closed-loop self-evolution framework that reuses the agent's historical solving traces as a source of training signal. Rather than treating traces only as evidence for reward computation, Socratic-SWE distills them into structured agent skills that summarize recurring failures and effective repair patterns. These skills then guide the generation of targeted repair tasks in real repositories. Candidate tasks are checked through execution-based validation and scored with a solver-gradient alignment reward, so that the retained tasks are both verifiable and useful for improving the Solver. The updated Solver produces new traces, enabling the task curriculum to adapt over successive rounds. Across SWE-bench Verified, SWE-bench Lite, SWE-bench Pro, and Terminal-Bench 2.0, Socratic-SWE consistently improves over self-evolving baselines under the same compute budget, reaching 50.40% on SWE-bench Verified after three iterations. These results suggest that solving traces can serve as a scalable substrate for self-evolving SWE agents.

HLL: Can Agents Cross Humanity's Last Line of Verification?

Multimodal agents are increasingly expected to operate interfaces on behalf of users, raising a central deployment question: can they truly substitute for humans in workflows that services deliberately protect against automation? CAPTCHA verification makes this question concrete. It is not merely a visual puzzle, but a human-verification boundary placed before account creation, content access, form submission, and other protected actions. We introduce \textbf{Humanity's Last Line of Verification (HLL)}, a controlled benchmark that uses interactive CAPTCHA verification to evaluate whether agents can cross this boundary through grounded, human-like interaction rather than recognition alone. HLL covers diverse CAPTCHA interactions and exposes agents to controlled realism stressors, including cluttered webpages, harder task variants, and trace-conditioned validation of the solving process. We evaluate eight frontier multimodal agents in a closed-loop GUI environment. The results show that current agents remain brittle at this human-substitution boundary: performance varies sharply across verification types, degrades under realistic interface conditions, and drops further when correct answers must be supported by valid action traces. By exposing gaps in localization, action calibration, state tracking, and process consistency, HLL provides a concrete testbed for measuring how close multimodal agents are to acting as human substitutes in protected real-world workflows. Our code is available at https://github.com/XinhaoS0101/HLL

STaR-KV: Spatio-Temporal Adaptive Re-weighting for KV Cache Compression in GUI Vision-Language Models

Vision-language-model-based graphical user interface (GUI) agents have shown broad automation capabilities, yet deployment is bottlenecked by a key-value (KV) cache that grows linearly with interaction steps. For instance, UI-TARS-1.5-7B consumes 76 GB of GPU memory on merely five screenshots, approaching the capacity of mainstream 80 GB accelerators. Existing KV compression methods share two structural assumptions: aggregating visual-token importance into a single shared saliency map, and applying a fixed top-B cutoff to the fused score distribution. Pilot measurements refute both: spatial specialization lives at the attention-subspace level and migrates across layers, while the score distribution drifts in shape along a trajectory. We propose STaR-KV (Spatio-Temporal Adaptive Re-weighting), a training-free KV cache compression framework that calibrates token importance along three axes: (i) subspace-aware scoring driven by online spatial mutual information; (ii) a temporal stability discount that suppresses redundant cache entries from persistently attended subspaces; and (iii) an entropy-derived temperature that adaptively reshapes the score distribution. Across four GUI benchmarks, STaR-KV achieves the strongest average accuracy among state-of-the-art KV compression methods (e.g., GUIKV, SnapKV) at matched budgets, with no compression-stage FLOPs overhead (-0.07%) and cutting peak GPU memory by nearly 40% at a 20% KV-cache budget. Code is available at https://github.com/kawhiiiileo/STaR-KV.

Domino: Decoupling Causal Modeling from Autoregressive Drafting in Speculative Decoding

Speculative decoding accelerates LLM inference by drafting multiple tokens and verifying them in parallel with the target model. However, its practical speedup is constrained by the trade-off between draft quality and drafting cost: autoregressive drafters model causal dependencies among draft tokens but incur sequential overhead, while parallel drafters reduce drafting cost but weaken intra-block dependency modeling. In this paper, we propose Domino, a speculative decoding framework that decouples causal dependency modeling from expensive autoregressive draft execution. Domino first uses a parallel draft backbone to produce preliminary draft distributions for the entire block, and then applies a lightweight Domino head to refine them with prefix-dependent causal information. To stabilize teacher-forced causal encoding, we further introduce a base-anchored training curriculum that first strengthens the parallel backbone and then gradually shifts optimization toward the causally corrected final distribution. Experiments on Qwen3 models show that Domino achieves up to \(5.49\times\) end-to-end speedup under the Transformers backend and up to \(5.8\times\) throughput speedup under SGLang serving.

AgentDoG 1.5: A Lightweight and Scalable Alignment Framework for AI Agent Safety and Security

Modern open-world agents such as OpenClaw exhibit powerful cross-environment execution capabilities yet introduce broad new safety risk sources. Meanwhile, advanced frontier AI models drastically lower attack barriers, rendering current agent alignment frameworks inadequate for real-world deployment. To tackle these emerging threats, we propose a lightweight and scalable agent safety alignment framework. Specifically, we update the agent safety taxonomy to accommodate emergent risks from Codex and OpenClaw execution scenarios. We further build a taxonomy-guided data engine with influence-function purification to train lightweight AgentDoG 1.5 variants (0.8B, 2B, 4B, and 8B parameters) using only around 1k samples, achieving comparable performance with leading closed-source models (e.g., GPT-5.4). Based on AgentDoG 1.5, we construct a highly efficient agentic safety SFT and RL training environment, which reduces deployment overhead in Docker-level environments by two orders of magnitude. Finally, we deploy AgentDoG 1.5 as a training-free online guardrail for real-time safety moderation. Extensive experimental results indicate that AgentDoG 1.5 achieves state-of-the-art performance in diverse and complex interactive agentic scenarios. All models and datasets are openly released.

The Missing Piece in Pre-trained Model Evaluation: Reward-Guided Decoding Unlocks Task-Oriented Behavior Without Parameter Updates

With the rapid progress of large language models (LLMs), reliably evaluating the capabilities of pre-trained LLMs has become increasingly important. The challenge is that base pre-trained models are optimized for next-token prediction and often fail to follow instructions or produce well-formed answers under standard prompting and direct decoding. As a result, benchmark performance can conflate model capability with decoding-induced failures to produce task-oriented outputs, while exposing such behavior often relies on costly post-training. Recent decodingonly approaches attempt to reshape output distributions, but such methods can be inefficient and brittle across open-ended tasks. To address these limitations, we propose Energy-Based Decoding (EBD), a training-free, reward-guided framework for activating task-oriented behaviors from frozen pre-trained LLMs across both open-ended and objective tasks. EBD augments decoding with an external lightweight reward model, steering generations toward high-utility responses while anchoring them to the pre-trained model prior through a reward-tilted target distribution. We show that EBD shifts base-model outputs toward more instructionfollowing behavior, increasing behavioral similarity to post-trained counterparts and enabling a fairer inference-time evaluation of accessible pre-trained-model behavior. Empirically, EBD outperforms baselines across five models and six benchmarks, improving Qwen3-8B-Base on AlpacaEval2.0 from 8.8 to 44.5, reducing Mistral-7B Math500 latency by 18.9x relative to prior decoding work, and remaining robust to reward-model size.

Dynamic Video Generation: Shaping Video Generation Across Time and Space

Diffusion models have achieved impressive performance in video generation, but their iterative denoising process remains computationally expensive due to the large number of tokens processed at each timestep. Recently, progressive resolution sampling has emerged as a promising acceleration approach by reducing latent resolution in early stages. However, scaling this idea to video generation remains challenging, as the additional temporal dimension introduces diverse spatio-temporal demands across different videos, and compressing only a single dimension often leads to limited acceleration or degraded quality. Therefore, we propose DVG, a Dynamic Video Generation framework that jointly allocates computation across time and space, automatically selecting content-aware acceleration strategies without manual tuning or retraining. DVG achieves near-lossless acceleration across models and tasks, reaching up to 7 times speedup on HunyuanVideo and HunyuanVideo-1.5, and 18 times when combined with distillation, demonstrating its potential as a key component in today's large-scale efficient video generation systems. Our code is in supplementary material and will be released on Github.

FlexDraft: Flexible Speculative Decoding via Attention Tuning and Bonus-Guided Calibration

Speculative decoding accelerates memory-bound LLM inference without quality degradation by using a fast drafter to propose multiple candidate tokens and the target model to verify them in parallel. However, conventional sequential speculative decoding suffers from mutual waiting between drafting and verification, and repeated exchange of intermediate states further increases memory access overhead. Parallel speculative decoding addresses this limitation by performing drafting and verification within a single target forward pass, allowing future drafts to be prepared while current candidates are being verified. Although effective at small batch sizes, existing parallel speculative decoding methods either require costly continual pretraining with quality degradation or suffer from low acceptance rates. More importantly, this paradigm inherently suffers from uncertainty in both the bonus token and the accepted length, leading to draft verification mismatch and causing throughput gains to collapse at large batch sizes. To address these limitations, we introduce FlexDraft, a lossless speculative decoding framework that flexibly adapts to varying batch sizes through three key designs. (1) Attention Tuning enables block diffusion drafting by tuning only the attention projectors of the final few layers on mask tokens, while keeping the autoregressive path frozen to preserve the target distribution and produce high quality drafts with minimal trainable parameters. (2) Bonus-guided Calibration uses a lightweight MLP conditioned on the resolved bonus token to calibrate draft logits, mitigating draft verification mismatch caused by bonus token uncertainty. (3) Flex Decoding dynamically switches between parallel draft and verify at small batch sizes and sequential draft then verify at large batch sizes, and adjusts verification length based on draft confidence to eliminate redundant computation.

Focused Forcing: Content-Aware Per-Frame KV Selection for Efficient Autoregressive Video Diffusion

Recent advances in autoregressive video diffusion have enabled sequential and streaming video generation. However, long-horizon generation requires increasingly large KV caches, making efficient compression without sacrificing quality challenging. Existing methods mostly select historical frames based on attention scores, but their context decisions remain coarse. When multiple frames are generated in the same chunk, these methods often apply a shared history selection to the whole chunk, score historical frames solely by attention, and assign head-wise budgets either uniformly or by attention-pattern heuristics rather than explicit head-importance estimation. We show that frames within the same generated chunk can depend on distinct historical frames, that the same historical frame can receive different attention scores as its relative temporal distance to the current frames changes, and that masking different heads induces unequal generation degradation. Motivated by these findings, we propose \textbf{Focused Forcing}, a training-free KV selection method that focuses cached history along both generated-frame and head dimensions. For each generated frame, Focused Forcing preserves the most relevant and distinctive historical frames by combining attention scores with diversity scores of historical frames, while assigning larger budgets to heads with higher estimated importance. Across multiple autoregressive generation paradigms, Focused Forcing achieves up to $\textbf{1.48}\times$ end-to-end acceleration without training, while \textbf{improving visual quality and text alignment}. \textit{Our code will be released on GitHub.}