Science & Mathematics

Trajectory-based confidence estimation has shown promising performance for large language models (LLMs) by leveraging rich signals from their reasoning processes. However, we find that such confidence estimators can degrade substantially after agentic reinforcement learning (Agentic RL) as it induces substantial shifts in the reasoning trajectories. More importantly, despite these shifts, we uncover a reliability structure that is largely preserved across Base and RL models: $\textbf{more}$ $\textbf{stable}$ $\textbf{trajectories}$ $\textbf{remain}$ $\textbf{more}$ $\textbf{likely}$ $\textbf{to}$ $\textbf{produce}$ $\textbf{correct}$ $\textbf{answers}$. This preserved relationship provides a transferable, label-free reliability signal for post-RL confidence adaptation. Building on this finding, we propose $\textbf{StaR-TTA}$, a stability-guided framework for label-free test-time confidence adaptation. StaR-TTA jointly learns from correctness supervision and stability-derived reliability supervision on labeled Base trajectories, establishing the connection between trajectory stability and answer reliability. At test time, it reuses stability-induced reliability rankings from unlabeled RL trajectories to adapt confidence scores to the shifted trajectory distribution, without requiring target correctness labels. Across four QA benchmarks, StaR-TTA achieves an average AUROC of \(0.721\), with consistent improvements across unseen datasets, model families and scales, and different Agentic RL algorithms.

Learning-based structure-from-motion methods such as ACE-Zero have demonstrated strong performance in estimating cameraposes and scene coordinates from unordered image collections without requiring ground truth supervision. However, the lack of global and multi-view consistency constraints in ACE-Zero can lead to pose drift and misalignment, particularly in complex or ambiguous scenes. In this work, we propose a hybrid framework that integrates pose graph optimization (PGO) into ACE-Zero to refine camera poses and suppress incorrect refinements. We construct pose graphs directly from ACE-Zero outputs by extracting relative pose constraints from predicted scene coordinates. Furthermore, we introduce an uncertainty-aware optimization strategy by estimating confidence scores using geometric priors, including epipolar and optical flow consistencies across views. Our approach improves the robustness and accuracy of pose estimation, demonstrating that global geometric reasoning can effectively complement learning-based inference in structure-from-motion.

Predictions with dynamical systems can be computationally expensive---even with reduced models---because reaching future prediction times can require many sequential time integration steps. We propose Flow-Map First-Order Trajectory Matching (FM-FTM), a nonintrusive model reduction approach that accelerates ensemble predictions of stochastic dynamical systems by learning flow maps that replace multiple time-integration steps. Our method uses first-order trajectory matching (FTM) to learn a deterministic representation of the stochastic probability-current dynamics and then reduces its evolution over time into a flow map whose evaluation directly yields predictions over long time horizons. Numerical experiments on evolution problems with stochastic forcing demonstrate that FM-FTM accelerates ensemble predictions by up to two orders of magnitude while accurately predicting time marginals and ensemble statistics.

Constraint learning is an emerging paradigm of modeling optimization problems with the help of machine learning. In this paradigm, trained machine learning models are embedded into the optimization model. For example, we can learn constraints empirically from available data, or we can avoid using a nonlinear objective function by learning a simpler approximation for it. Neural networks become a compelling option if the machine learning models must capture more elaborate and nuanced relationships. However, optimization models embedding neural networks may become too large or too slow to solve. In this tutorial, we present practical considerations for an effective and efficient use of constraint learning with neural networks and validate it with a case study highlighting the benefit of smaller and sparser networks.

Large organizations consume large language models (LLMs) from several vendors at once, each with its own API dialect, credential model, streaming protocol and pricing. Integrated directly, this heterogeneity yields credential sprawl, format lock-in, unbounded spend and inconsistent governance. We present the design and production operation of the Cosmos LLM Gateway, the governed entry point for enterprise LLM traffic at PayPal. Built on Envoy, it splits work by latency profile: I/O-bound control decisions (authentication, credential brokering, policy and budget evaluation) run in an out-of-process external-processing service, while wire-format translation, token metering and prompt-cache shaping run in-proxy as a Rust WebAssembly filter, so that, by default, streamed response body chunks never wait on an out-of-process call. Models, providers and prices are largely validated data rather than code. Governance is declarative policy evaluated by Open Policy Agent and managed through a control plane with role-scoped authoring, approvals, pilots, shadow-mode rollout, usage notifications and versioned policy bundles. For use cases that require it, a data-loss-prevention layer can block, redact or pseudonymize detected sensitive content before it reaches a provider. Spend scopes are views over per-model usage counters, so a new budget applies to spend already recorded in its window without migration. As of September 2026, the gateway serves more than 12,000 developers and hundreds of business use cases, handling roughly 200 billion tokens per day across more than 100 models at 99.999% availability to business. In a benchmark of the core request path against a synthetic upstream, it adds a median of 4 ms and a p99 of 11 ms of overhead at more than 2,200 requests per second on two 4-vCPU instances. We report the architecture, policy model, evaluation and lessons learned.

Mental health research on social media has been dominated by English-language datasets and DSM-5-centered resources, limiting cross-lingual and cross-cultural understanding of online mental health expression. We introduce MATCHA, the first Chinese multi-disorder mental health dataset that links disorder-specific Weibo Super-Topic communities with users' broader public timelines. MATCHA covers seven DSM-5 disorders and a control group, comprising 46,025 cohort-level users and 1.8 million posts. The dataset distinguishes users with explicit self-disclosure evidence from broader disorder-related participants through an LLM-assisted annotation pipeline, and is released in a rigorously de-identified, controlled-access format. Using MATCHA, we analyze behavioral, linguistic, symptom-related, and life-event-related patterns across disorders, and conduct cross-lingual comparisons with Twitter-STMHD. Our analyses show that Weibo Super-Topics function as concentrated spaces for affective and health-related expression, while cross-platform differences between Weibo and Twitter often exceed cross-disorder variation. MATCHA provides a new resource for community-aware and cross-lingual mental health NLP research.

Neural scaling laws describe the predictable power-law dependence of model performance on training time, dataset size, and model scale, with the exponents quantifying how performance changes with resources. Recent theory has shown how scaling exponents are shaped by the data distribution and the structure of the learning task, but whether network depth can improve training-time scaling has remained unsettled. Through a refined analysis of deep linear networks, we clarify that the task spectrum determines when increasing network depth improves training-time scaling. For spectrally difficult tasks, increasing depth improves the asymptotic training-time scaling exponent, whereas for easy tasks, the exponent remains independent of depth, with depth affecting only a logarithmic correction at the boundary between these regimes. Remarkably, we find that a reparameterization of time governed by the predictor norm provides a unified description of the dynamics across task difficulties. Under this reparameterization, the loss follows a common scaling law whose exponent is independent of depth. Numerical experiments on a task derived from benchmark image data and with nonlinear networks exhibit qualitatively consistent task-dependent effects of depth on training-time scaling. Our findings advance the theoretical understanding of how task structure shapes the effects of network architecture on learning and offer a basis for studying scaling behavior across broader classes of neural networks.

Diffusion-based real-world image super-resolution suffers from limited reconstruction fidelity due to information loss in VAE-based latent representations. Recently, pixel-space diffusion models offer a promising high-faithfulness alternative by avoiding latent compression, but adapting them to Real-ISR remains challenging due to inherent patch boundary artifacts and degraded generative capability. To address the issues and maximize the potential of pretrained pixel-space diffusion models, we propose HiFiPix, a pixel-space Real-ISR framework capable of ultra high-fidelity reconstruction and fine-grained visual generation effects. To suppress patch boundary artifacts, we penalize unrealistic high-frequency periodic components with a Cross-Scale Wavelet Discriminator (CWSD) for image-level supervision, and Mixup Contrastive Self-Distillation (MixCSD) for intermediate representation regularization. Furthermore, we uncover a heterogeneous generation-fidelity trade-off across low-rank adapters (LoRA) and propose Selective LoRA Pruning (LoRA-SP) to adaptively prune LoRA layers, enhancing generative capability with minimal deterioration of reconstruction fidelity. Extensive experiments demonstrate that HiFiPix consistently outperforms existing state-of-the-art latent space methods in terms of both restoration accuracy and perceptual quality by a large margin. Code and models will be released.

Point-supervised temporal action localization (PTAL) aims to recognize and localize action instances in untrimmed videos using only point-level annotations. Existing pseudo-label-based methods have made substantial progress in PTAL. However, confidence-based initialization can overlook well-localized proposals. Meanwhile, existing methods either keep pseudo-labels fixed during detector training or update them without fully exploiting alternative boundary evidence from the original proposal pool. These limitations constrain supervision quality, thereby hindering detection performance. To learn high-quality pseudo-labels, we propose a framework that integrates prior-guided initialization with consensus-guided refinement during detector training. Our framework comprises two modules: Prior-Guided Initialization (PGI) and Consensus-Guided Refinement (CGR). PGI combines proposal confidence with point-derived priors to establish instance-specific reliability for initial pseudo-label selection and candidate retention. CGR continually uses the retained original candidates to construct boundary targets, combining their consensus with evolving detector predictions to refine pseudo-labels throughout training. Experiments on four benchmarks demonstrate that our method achieves competitive detection performance compared with existing methods. In particular, our method achieves 68.5\% average mAP over tIoU thresholds 0.1--0.7 on THUMOS14, surpassing PseR by 3.7 percentage points. Code is available at https://github.com/zhenyingfang/LHQP

Critic-free methods are widely used in reinforcement learning with verifiable rewards (RLVR) for long chain-of-thought (CoT) reasoning, avoiding difficult and costly critic training. Common alternatives lack token-level credit assignment and typically rely on grouped rollouts to estimate prompt-specific baselines. A critic can address both limitations, but long-CoT critic training is hindered by insufficient coverage of trajectories with diverse lengths and early gradients dominated by the newly initialized value head. We introduce S3AC (Stabilized, Selective, and Scalable Actor-Critic) for LLM reasoning, built around a practical critic-training recipe. The trained critic provides token-specific advantages and prompt-specific baselines. Using the prompt-level baseline to estimate difficulty, we propose Difficulty-Aware Prompt Sampling (DAPS). DAPS combines this estimate with outcome history to select prompts before generation, reducing rollout waste without offline difficulty initialization. S3AC improves group-rollout performance across dense and mixture-of-experts models from 1.5B to 397B parameters, outperforming a modern GRPO variant (GRPO-X). At 35B, it sustains single-rollout training while tested critic-free baselines deteriorate after initial gains.

Differentially private synthesis of in-car energy consumption data is challenging because the output is high-dimensional, and known lower bounds show that the privacy-utility trade-off degrades with the square root of the number of output dimensions. However, we observe that the intrinsic dimensionality of in-car energy consumption is much lower than that of the raw trace: given a small set of contextual personal variables-such as start point, end point, the car model, and the driving behavior-the consumption profile can be largely explained by publicly available map data (including elevation) combined with a physical model of vehicle energy use. We exploit this low intrinsic dimensionality in PRISMA, a Privacy-preserving In-car Synthesis and Modelling Algorithm. PRISMA involves three stages: (i) energy consumption traces are encoded into a low-dimensional latent space; (ii) the distribution of latent vectors is synthesized using the differentially private tabular data synthesis algorithm AIM, and (iii) samples drawn from this distribution are decoded back into full energy consumption traces via a differentiable physics-based simulation, a step that consumes no additional privacy budget since it uses only public information. By using a compact, physically-grounded latent representation of the traces, PRISMA significantly reduces the effective output dimension. Our experimental results show that PRISMA achieves for a competitive $\varepsilon = 0.5$ a better data synthesis performance than prior tabular and marginal-based DP synthesis baselines by preserving the diversity of the original power consumption profiles without collapsing to a small set of modes.

Recovering an object's 3D structure and camera motion from a few uncalibrated views is a fundamental problem in computer vision. Classical structure from motion methods recover 3D geometry consistent with the input images but cannot recover unseen regions; native generation methods produce plausible 3D objects which are related but not necessarily faithful to the input images. Methods simply concatenating reconstruction and generation allow error to cascade across the two stages, instead of producing a 3D object consistent with both the distribution and the input. We propose GenSfM, which integrates image-based 3D reconstruction with a native 3D diffusion model. In particular, we use a multi-modal diffusion transformer to jointly denoise the shape latent and per-view pose latents under shared self-attention, grounding generated geometry in the observed views while using object-level priors to infer unobserved regions. A compact 3D-native UV-volume tokenization keeps the joint sequence small as views are added, and a pose-aware stage refines geometry and texture by sampling per-voxel image features at the recovered camera poses. On Toys4k and GSO, for $4$ uncalibrated views, GenSfM improves novel-view PSNR by $3.2$-$4.5$ dB and reduces median Chamfer distance by $2.8$-$3.8\times$ over a strong native-3D generation baseline, while recovering input-view poses over $96\%$ Acc@$5^\circ$ without any external pose-estimation backbone, post-hoc optimization, or known intrinsics. Project page: https://dotb1ue.github.io/GenSfm/.

Ranking functions are a fundamental technique for proving loop termination, but constructing them manually is challenging and requires substantial expertise. We propose RAINFALL, a neuro-symbolic framework which follows the generate-verify-refine paradigm and tightly integrates LLMs with symbolic verification. RAINFALL formulates ranking function synthesis as a code-completion task by inserting placeholders into the input program and constraining the LLM to fill four predefined slots for each loop. The completed program is then checked by a symbolic verifier. If verification succeeds, a valid ranking function is obtained; otherwise, the verifier's diagnostics are translated into natural-language feedback that guides iterative refinement of the LLM's output. We evaluate RAINFALL on two public benchmark suites comprising 358 terminating C programs. Using MiniMax V2.7, RAINFALL synthesizes verifiable ranking functions for 323 programs (90.22%), outperforming all promising baselines. In particular, it solves 12 more programs than PROTON 2.1, the best-performing baseline and winner of the SV-COMP 2026 Termination category. Furthermore, combining RAINFALL with PROTON 2.1 increases the success rate to 96.65% (346/358 programs). We also conduct ablation study confirming individual contributions of placeholder contracts, few-shot examples, symbolic verification, and diagnostic information feedback. Experiments across LLMs further confirm the effectiveness of RAINFALL. Our results suggest a generic, sound framework for ranking-function synthesis and, beyond termination, LLM-assisted synthesis of formally checkable liveness certificates, both of which represent new directions of software engineering research.

Interactive world models keep the KV of past chunks as retrieval memory so that revisited places stay consistent. On a single consumer machine (one RTX 4090, 32 GiB of host memory, one NVMe SSD), long sessions with such memory hit two walls. The first is capacity: the KV of Matrix-Game 2.0 exhausts host memory after 45 seconds of video in bf16 and after 2.8 minutes in int4. The second is the model's positional horizon of 4.3 minutes. We show that this memory is capacity-bound rather than bandwidth-bound and that its access set is known before compute, because the camera pose is an input. An analytical model built on these observations predicts spill points to within one chunk and classifies zero versus non-zero stalls correctly on held-out configurations. Guided by it, WorldPager stores int4 KV in a GPU/DRAM/NVMe hierarchy instead of recomputing it, prefetches each chunk's memory from the extrapolated pose, never waits on a miss, and writes back in the background; to our knowledge, it is the first to place the KV memory of an interactive world model on an NVMe tier with zero-stall prefetching. With training-free position handling, it generates 37.5 minutes of video continuously with zero stalls and constant host memory, at about 9.5 frames per second. On a sealed test set, int4 storage shows no measurable quality loss; on long-gap revisits it lowers image quality by about one MUSIQ point.

Activation steering offers training-free and dynamic control of target behaviors in large language models, but existing methods can impair general capabilities and require domain-specific intervention designs. We introduce Capability-Preserving Neuron Steering (CANS), a unified framework that balances target-behavior control with capability preservation. To make target-behavior improvement and general-capability preservation tractable, we introduce two proxies: log-probabilities of target tokens in model generated responses, and output-distribution KL divergence on general-purpose inputs. Combining the local approximation of the two proxies yields a closed-form solution, enabling lightweight steering without iterative model training or additional inference-time computation. The resulting neuron-wise scaling coefficients achieve effective steering while limiting general-capability loss. A shared data-construction and intervention procedure supports adaptation across domains using sampled responses with target-behavior filtering and target-span annotations. Across safety, toxicity, and hallucination control on Qwen and Llama models, CANS achieves comparable or better steering while better preserving MMLU, BBH, and IFEval performance than SFT, CAA, and neuron-level baselines. On Qwen3-4B, CANS reduces HarmBench attack success from $15.50\%$ to $1.75\%$ with a $1.11$-point decrease in average capability. These results support CANS as a practical approach to behavioral control across domains.