The Matching Principle: A Geometric Theory of Loss Functions for Nuisance-Robust Representation Learning

Robustness, domain adaptation, photometric and occlusion invariance, compositional generalisation, temporal robustness, alignment safety, and classical anisotropic regularisation are usually treated as separate problems with separate method families. This paper argues that much of their shared structure is one statistical problem: estimate the covariance of label-preserving deployment nuisance, then regularise the encoder Jacobian along a matrix whose range covers that covariance (the matching principle). CORAL, adversarial training, IRM, augmentation, metric learning, Jacobian penalties, and alignment-style constraints are different estimators of that object, not independent robustness tricks. In the linear-Gaussian model we prove closed-form optimality (Theorem A), including cube-root water-filling within the matched range; necessity of range coverage for quadratic Jacobian penalties (Theorem G); the same range dichotomy at deep global minima; and two falsification controls (Lemma C; Corollaries E), with seven conditional consistency lemmas (D1-D7) for estimation under standard identifiability assumptions. We introduce the Trajectory Deviation Index (TDI), a label-free probe of embedding sensitivity when task accuracy or Jacobian Frobenius norm is insufficient. Thirteen pre-registered blocks from classical ML through Qwen2.5-7B test the predicted matched, then isotropic, then wrong-W ordering on geometry and deployment drift; twelve pass, and the sole exception (Office-31) is an eigengap failure named before the run. At 7B scale, matched style-PMH improves selective honesty and preserves Style TDI where standard DPO degrades it. The contribution is naming the deployment nuisance covariance, stating what the regulariser must do, and supplying a closed-form falsifiable theory once that object is identified, not universality on every leaderboard.

From Snapshots to Trajectories: Learning Single-Cell Gene Expression Dynamics via Conditional Flow Matching

Single-cell RNA sequencing (scRNA-seq) provides high-dimensional profiles of cellular states, enabling data-driven modeling of cellular dynamics over time. In practice, time-resolved scRNA-seq is collected at only a few discrete time points as unpaired snapshot populations, leaving substantial temporal gaps. This motivates trajectory inference at unmeasured time points. Existing methods mainly follow two directions, optimal-transport (OT) alignment provides distribution-level matching between observed snapshots, while continuous-time generative models support forecasting via learned dynamics. However, two challenges remain: (i) unpaired snapshots render local transitions between adjacent time points ambiguous, leading to unstable supervision; and (ii) long-horizon prediction relies on repeated integration, where small modeling errors compound and cause distribution drift. To address these challenges, we propose single-cell Flow Matching (scFM), a latent generative framework based on coupling-conditioned flow matching. First, we compute entropically regularized OT couplings between adjacent snapshots and use them to construct soft, weighted flow-matching targets for learning time-dependent velocity fields. Second, we learn bidirectional velocity fields and leverage their consistency to refine couplings and improve temporal coherence under sparse supervision. Third, we introduce distribution-level alignment and latent dynamic regularization to anchor long rollouts and mitigate drift. Experiments on real-world time-series scRNA-seq datasets show that scFM consistently improves distributional prediction performance for both temporal interpolation and extrapolation. Moreover, scFM yields more accurate trajectory reconstruction and temporally coherent visualizations where intermediate time points are absent, indicating a more faithful recovery of underlying temporal gene expression dynamics.

Benchmarking Autonomous Agents against Temporal, Spatial, and Semantic Evasions

As autonomous agents (e.g., OpenClaw) increasingly operate with deep system-level privileges to execute complex tasks, they introduce severe, unmitigated security risks. Current vulnerability analyses overwhelmingly focus on single-turn, stateless behaviors, overlooking the expanded attack surface inherent in stateful, multi-turn interactions and dynamic tool invocations. In this paper, we propose a novel, multi-dimensional evasion framework targeting LLM-based agent systems. We introduce three stealthy attack vectors: (1) Temporal evasion, which fragments malicious payloads across sequential interaction turns; (2) Spatial evasion, which conceals payloads within complex external artifacts that evade standard LLM parsing mechanisms; and (3) Semantic evasion, which obscures malicious intents beneath benign contextual noise. To systematically quantify these threats, we construct A3S-Bench, a comprehensive benchmark comprising 2,254 real-world agent execution trajectories. Evaluating a standard agent framework separately integrated with 10 mainstream LLM backbones against 20 practical threat scenarios, we demonstrate that our evasion framework elevates the average risk trigger rate from a 28.3\% baseline to 52.6\%. These findings reveal systemic, architecture-level vulnerabilities in current autonomous agent systems that existing defenses fail to address, highlighting an urgent need for defense mechanisms tailored to the unique threats.

From Patches to Trajectories: Privileged Process Supervision for Software-Engineering Agents

Supervised fine-tuning (SFT) on long teacher trajectories is the dominant way to instill investigation and reasoning in open software-engineering (SWE) agents. Since every retained response becomes an imitation target, the student inherits the final outcome and intermediate flaws, including ungrounded leaps and redundant loops. High-quality training data must be effective(each step is grounded and narrows the agent's epistemic gap to the correct fix) and efficient(each step is information-bearing rather than redundant or looping). Existing recipes filter or relabel teacher rollouts using only a binary terminal verifier, which does not directly target these axes and provides no supervision on instances where the teacher fails. Most real issue includes a developer-authored reference patch, $p^\star$, revealing the file paths, runtime behaviors, and coding conventions presupposed by the correct fix, yet standard pipelines discard it. We propose Patches-to-Trajectories (P2T), which uses $p^\star$ as privileged information during curation and formulates trajectory construction as bi-objective optimization over per-step effectiveness and trajectory length. A reverse phase distills $p^\star$ into a latent process graph, $G^\star$, of contextual facts and solution milestones. A forward phase curates trajectories from blinded teacher continuations by scoring per-step progress against $G^\star$ under a leakage-blocking groundedness check and retaining the shortest effective segments. Using only 1.8k curated SWE-Gym instances, P2T improves effectiveness and efficiency over outcome-filtered SFT and its tool-error-masking variant. On SWE-bench Verified, it raises Pass@1 by up to 10.8 points while reducing per-instance inference cost by ~15%, with consistent gains on SWE-bench Lite. Size-matched ablations and qualitative analysis further isolate trajectory quality from data scale.

ChronoMedicalWorld: A Medical World Model for Learning Patient Trajectories from Longitudinal Care Data

Long-horizon clinical simulation -- predicting how a patient's physiology evolves over years under specified interventions -- is central to chronic-disease care, yet existing electronic health record (EHR) models are predominantly discriminative, and general-purpose large language models drift under repeated interventions. We propose the \textbf{ChronoMedicalWorld Model (CMWM)}, an action-conditioned latent world-model framework for learning patient trajectories from longitudinal care data. CMWM couples a joint-embedding state encoder with a wide action encoder that admits both structured intervention indicators and free-text communication embeddings, and trains a recurrent latent transition module under a six-term objective: next-observation supervision, next-latent prediction, SIGReg latent regularisation, and three physiology-aware shape priors (slope, continuity, large-jump penalty). A closed-loop rollout-prefix protocol matches training to deployment, so the model is optimised against the same multi-step error it exhibits at inference. As a concrete case study, we instantiate CMWM for annual estimated glomerular filtration rate (eGFR) trajectory forecasting in chronic kidney disease (CKD). On a 2{,}232-patient nephrology cohort, the CKD instantiation achieves a dynamic-50\% history rollout test mean absolute error (MAE) of 7.384 and root-mean-square error (RMSE) of 10.256, against 7.964 and 11.069 for a tuned GPT-5.5 structured-prompting baseline ($-7.28\%$ MAE, $-7.35\%$ RMSE), with the gain dominated by the dialogue portion of patient--health-coach communication. The framework is not CKD-specific: its architecture, loss design, and training protocol apply to any chronic condition that can be cast as periodic clinical state interleaved with structured and conversational interventions.

MotiMotion: Motion-Controlled Video Generation with Visual Reasoning

Current motion-controlled image-to-video generation models rigidly follow user-provided trajectories that are often sparse, imprecise, and causally incomplete. Such reliance often yields unnatural or implausible outcomes, especially by missing secondary causal consequences. To address this, we introduce MotiMotion, a novel framework that reformulates motion control as a reasoning-then-generation problem. To encourage causally grounded and commonsense-consistent interactions, we leverage a training-free vision-language reasoner to refine image-space coordinates of primary trajectories and to hallucinate plausible secondary motions. To further improve motion naturalness, we propose a confidence-aware control scheme that modulates guidance strength, enabling the model to closely follow high-confidence plans while correcting artifacts under low-confidence inputs with its internal generative priors. To support systematic evaluation, we curate a new image-to-video benchmark, MotiBench, consisting of interaction-centric scenes where new events are triggered by motion. Both VLM-based evaluation and a human study on MotiBench demonstrate that MotiMotion produces videos with more plausible object behaviors and interaction, and is preferred over existing approaches.

Remember to be Curious: Episodic Context and Persistent Worlds for 3D Exploration

Exploration is a prerequisite for learning useful behaviors in sparse-reward, long-horizon tasks, particularly within 3D environments. Curiosity-driven reinforcement learning addresses this via intrinsic rewards derived from the mismatch between the agent's predictive model of the world and reality. However, translating this intrinsic motivation to complex, photorealistic environments remains difficult, as agents can become trapped in local loops and receive fresh rewards for revisiting forgotten states. In this work, we demonstrate that this failure stems from a lack of spatial persistence and episodic context. We show that effective curiosity requires a model of the world that is persistent and continuously updated, paired with an agent that maintains an episodic trajectory history to navigate toward novel regions. We achieve this using an online 3D reconstruction as a persistent model of the world, while the agent policy is parameterized as a sequence model over RGB observations to maintain episodic context. This design enables effective exploration during training while allowing the agent to navigate using solely RGB frames at deployment. Trained purely via curiosity on HM3D, our agent outperforms RL-based active mapping baselines and generalizes zero-shot to Gibson and AI-generated worlds. Our end-to-end policy enables efficient adaptation to downstream tasks, such as apple picking and image-goal navigation, outperforming from-scratch baselines. Please see video results at https://recuriosity.github.io/.

The Value of Covariance Matching in Gaussian DDPMs and the Lanczos Sampler

A central error measure in Gaussian DDPMs is the path-space KL divergence between the exact reverse chain and the learned Gaussian reverse process. This quantity is especially relevant for procedures such as classifier guidance, which perturb the entire reverse trajectory rather than only the terminal sample. Prior analyses show that standard isotropic reverse covariances suffer an unavoidable $Ω(1/T)$ path-KL error as the number of denoising steps $T$ grows. We show that matching the full posterior covariance breaks this barrier, yielding an order-wise improvement that reduces the path KL to $O(1/T^2)$. To make full covariance matching practical, we introduce the Lanczos Gaussian sampler (LGS), a training-free, matrix-free method for sampling from the optimal reverse covariance using only covariance-vector products, which are available through Jacobian-vector products of the posterior mean. LGS avoids dense covariance storage and auxiliary covariance models. We prove that LGS approximation error decays exponentially in the number of Lanczos steps, where each Lanczos step requires a single Jacobian-vector product. Empirically, using only just three such steps improves sample quality over strong diagonal-covariance baselines, including OCM-DDPM, across standard image benchmarks. This identifies full covariance matching as both theoretically valuable and practically accessible for fast DDPM sampling.

N3P: Accelerated Automated Parking via a Learning-Based Naturalistic Three-Stage Scheme

Autonomous parking requires efficient path planning that ensures kinematic feasibility and collision avoidance in constrained environments. Hybrid A* is widely used but computationally expensive, while reinforcement learning (RL) methods lack reliability and often struggle with long-horizon geometric constraints, leading to suboptimal trajectories. We present N3P, a fast learning-based three-stage framework for automated parking. By introducing an intermediate preparatory pose and using a learning module to predict it, N3P decomposes the maneuver into simpler subproblems, thereby reducing computational complexity and accelerating path generation. We validate the framework by integrating it with Hybrid A* algorithms. Experiments in perpendicular and parallel parking scenarios show that N3P-enhanced Hybrid A* speeds up planning by more than 80%. It also outperforms RL baselines in success rate and trajectory quality, producing shorter trajectories with fewer gear changes, while achieving comparable or lower planning time in most cases.

Swift Sampling: Selecting Temporal Surprises via Taylor Series

While most frames in long-form video are redundant, the critical information resides in temporal surprises: moments where the actual visual features deviate from their predicted evolution. Inspired by the human brain's predictive coding, we introduce Swift Sampling, an elegant, training-free frame selection algorithm that automatically identifies high-information moments in a video. Specifically, we model a video as a differentiable trajectory in the visual latent space and compute the velocity and acceleration of its features. Then, we apply Taylor expansion to project the expected path of subsequent frames. Frames that diverge sharply from this predicted manifold are identified as temporally surprising frames and selected for sampling. Unlike prior training-free methods that rely on auxiliary networks or video-specific hyperparameter tuning, Swift Sampling is incredibly lightweight, adding only 0.02x additional computational cost over baseline making it 30x cheaper overhead than leading baselines. Across three long-video question answering benchmarks and 10 different downstream tasks, Swift Sampling outperforms uniform sampling and prior query-agnostic baselines. It is especially powerful for long videos with limited frame budgets improving accuracy by up to +12.5 points.