Papers

Post-training with verifiable rewards can induce reward hacking, motivating the use of monitors within the training objective rather than solely for offline auditing. We show that a low monitor readout does not identify whether such an intervention controls behavior. In a code-generation environment whose dominant exploit is available at the start of the reasoning trace, we train policies against three monitors that pass the same offline gate: an in-domain activation probe and two penalties conditioned on how early the policy commits to its own final answer. The probe score is at its numerical floor from the first recorded training step, and the trained-score median is zero for every prefix-trained run at the endpoint. These readouts estimate different quantities, and we do not compare their scales; within each monitor family, however, low values do not establish behavioral control. Within one fixed configuration, prefix-trained runs with the same zero-median trained score range, by seed alone, from a mixed regime with a low hacking share to near-pure reward hacking. All probe runs reach the hacking regime, but their floor-level readout reflects a mismatch between the position where the probe was validated and the position where it was read during training, not a second instance of this ambiguity. Text-level analysis identifies a prefix failure mode: generic planning and filler shells postpone the exploit past the cut without eliminating it from the final output. Low measured commitment therefore does not distinguish a low hacking share from delayed commitment to the exploit. Offline discrimination and low monitor-aligned readouts are insufficient evidence of behavioral control; an out-of-band behavioral check is required. We characterize the endpoint readout, not its evolution. Code is available at https://github.com/zhezhou1106/spoof-cost.

Recent progress in multimodal, high-dimensional learning has enabled foundation models to process heterogeneous, large-scale data. However, at test time, acquiring all features or modalities can be prohibitively costly and often redundant. Sequentially selecting informative modalities is therefore critical, yet challenging when the downstream task or prediction target is unknown. To this end, we introduce ECHO-$k$, a task-agnostic and self-supervised learning principle for modality acquisition: we use a deep model's internal pretrained representations (e.g., from a foundation model) as proxy targets that summarize cross-modal information. We provide theoretical guarantees in a stylized linear setting that motivate a reinforcement learning (RL) policy for sequential modality selection. Across task-agnostic and label-free acquisition baselines, ECHO-$k$ consistently improves budgeted downstream performance across diverse foundation-model backends. Our method provides a principled route to cost-aware test-time deployment, with implications for any multimodal system where measurements are expensive or time-constrained, and downstream tasks unknown a priori.

A targeted adversarial perturbation can drive a vision-language model's (VLM's) teacher-forced training loss for a fixed target caption to near zero, yet the same model, allowed to generate freely, produces the original, correct description with no trace of the target. We call this dissociation the train/inference gap, and give it a precise mechanistic account on Qwen2.5-VL-7B-Instruct using a controlled two-stage PGD attack on 200 held-out COCO images. First, we show that image-level pixel statistics, including a correctly re-implemented, texture-based attackability measure from the CNN robustness literature, have essentially no predictive power over which images are corrupted (best predictor r=-0.050, p=0.484; ridge regression R^2=0.069). Second, using the logit lens, we localise the gap to a single autoregressive step: the rank of the target token, conditioned on the correct first token already being generated, is fixed at exactly 3,488 out of 152,064 vocabulary entries for every image and every condition, with zero variance. Third, tracking target-token rank across all 28 LLM decoder layers reveals that the visual encoder corrupts every image's representation by a comparable margin regardless of eventual outcome, but the language model decoder then differentially arbitrates: amplifying the corrupted signal for susceptible images and actively suppressing it, past its clean-image baseline, for resistant ones (p<0.001, rank-biserial r=0.579). A linear probe on the merger hidden state separates these two outcomes with AUC=0.858, though we flag a circularity concern in this estimate. Together these results argue that adversarial robustness in autoregressive VLMs is substantially a property of the language decoder's prior, not the visual encoder, with direct implications for where faithfulness evaluations and defenses for deployed VLM systems should be targeted.

Online data selection has demonstrated substantial efficiency gains for LLM pretraining by training on the most valuable candidates within each batch. Since a candidate's value is realized through its effective model update, principled selection should account for the optimizer step, which reshapes the raw gradient before it updates model parameters. We formalize this optimizer-aware selection paradigm as OptiSelect and present the first systematic study of how the optimizer shapes data selection. Our theory establishes a selection gain principle in which the advantage of online selection is governed by the discriminability of the optimizer-induced utility scores. We prove that sign-based and polar-tangential preconditioners of Lion and Muon would suffer from a discriminability collapse which caps attainable gains from OptiSelect, whereas diagonal-adaptive optimizers such as AdamW and Sophia admit strictly better upper bounds. The proposed principle also yields a quantitative derivation of the optimal candidate oversampling ratio. Pretraining experiments on 124M and 720M models are consistent with our theoretical analysis and show that AdamW's diagonal-adaptive scoring geometry remains the strongest scoring geometry even with Muon as optimizer. We further demonstrate that OptiSelect retains its benefits under data rephrasing, a technique used in modern data processing pipelines. Our findings provide theoretical foundations and practical guidance for co-designing optimizers and data selection in LLM pretraining.

Efficient request scheduling is increasingly important for reducing completion time in large language model (LLM) serving. Size-based policies such as Shortest Job First prioritize shorter requests, but output lengths are unknown before generation, so practical schedulers rely on predicted lengths. We introduce JIL, an attack on prediction-based LLM schedulers that manipulates the scheduling signal to obtain higher priority and reduce completion time. Using TRAIL as a case study, JIL optimizes an adversarial suffix that causes a lightweight output-length probe to underestimate a request's length. We evaluate JIL on two datasets and four LLMs across varied request profiles and deployment configurations. JIL reduces predicted output lengths by up to 83.4 percent, and adversarial requests complete up to 1.53 times faster on average in end-to-end serving experiments. The reduction in predicted length is substantially larger than the change in actual output length, revealing a mismatch between the scheduler's estimate and the request's realized size. Response utility varies across models and tasks, exposing a trade-off between scheduling advantage and response quality. We also evaluate scheduler-side defenses and find that grouping length predictions into coarse intervals reduces JIL's scheduling advantage and mitigates delays to benign requests.

Suspicion is an important, yet elusive concept in anti-money laundering and counter-terrorist financing (AML/CFT), which allows for intervention below the threshold of proof. In its traditional form, suspicion can be understood as a situated legal judgement by human actors within identifiable jurisdictions. It is argued that this understanding is no longer adequate. As artificial intelligence (AI) becomes an integral part of financial surveillance, suspicion is increasingly produced through data-driven processes. This transformation is epistemic, but also spatial. Since AI-driven financial surveillance operates through transnational data infrastructures, regulatory reach is less a matter of where conduct occurs than a question of whether such conduct becomes visible within data systems. This article develops the concept of algorithmic extraterritoriality, understood as a form of regulatory power mediated by data infrastructures rather than formal assertions of jurisdiction. Moreover, since individuals are increasingly constituted as datafied subjects of suspicion, they are rendered governable through dispersed and opaque processes of evaluation. This constitutes a challenge for accountability and contestability because suspicion becomes more difficult to locate, explain or contest.

Epistemic uncertainty should decrease as additional information about the data-generating process (DGP) becomes available to the predictor. Yet, existing graph evidential deep learning (EDL) methods for node classification typically construct epistemic uncertainty from graph-specific properties and evaluate it on downstream tasks such as out-of-distribution detection, which do not test its reducibility as information about the DGP increases. To make reducibility directly testable, we introduce a statistical framework for studying epistemic uncertainty under information growth. Our framework specifies an information-growth experimental protocol and a consistency criterion for epistemic predictors, while using projective graph DGPs to ensure that growing graphs, which in general need not provide increasing information about the same DGP, constitute coherent observations of the same underlying process. We show that EDL methods do not explicitly estimate data uncertainty arising from a single finite graph observation and instead regulate epistemic uncertainty through model hyperparameters, precluding consistency, as corroborated by controlled information-growth experiments. As an alternative, we propose graph bootstrap ensembles, capturing both data and procedural uncertainty through graph resampling and randomized training. Under the same experimental protocol, these ensembles exhibit epistemic uncertainty reduction beyond standard deep ensembles. These findings support bootstrap ensembles as candidate consistent epistemic predictors under information growth.

Forest point cloud segmentation is fundamental for fine-grained 3D forest scene understanding, yet remains challenging due to irregular tree structures, severe occlusions, density variations, and ambiguous instance boundaries. Recent query-based forest segmentation methods have shown promise for unified semantic and instance prediction, but they still insufficiently exploit forest-specific spatial structure and account for boundary uncertainty. In this paper, we propose ForestQuery, a boundary-aware and spatially anchored query learning framework for unified forest point cloud segmentation. ForestQuery enhances instance and semantic query learning through two complementary designs. Specifically, boundary uncertainty is explicitly modeled to guide reliable instance query construction and modulate query optimization through adaptive loss reweighting. Meanwhile, spatially anchored semantic query enhancement (SA-SQE) introduces learnable 3D anchors encoding forest vertical stratification priors to enrich semantic queries with explicit spatial references. We evaluate ForestQuery on multiple public forest point cloud benchmarks and a self-collected annotated real-world dataset. Extensive experiments demonstrate consistent improvements in both individual-tree segmentation and semantic segmentation across diverse forest scenes. Code and data are publicly available at https://zhan994.github.io/ForestQuery

Few-step neural text-to-speech models often rely on short- ened diffusion or flow-matching schedules, or on distillation from pretrained multi-step teachers. To avoid these depen- dencies, we present DriftTTS, a few-step mel-spectrogram generator trained without a generative teacher, distillation, or adversarial discrimination. DriftTTS uses a distribution- matching drift objective in a mel-domain feature space defined by raw mels and a frozen masked-autoencoder encoder pretrained on the same LJSpeech training split. On-policy rollout trains the decoder on its own interme- diate states and supports inference up to the trained roll- out depth. On LJSpeech, DriftTTS at NFE=4 achieves 3.87 dB MCD and 3.7% WER, compared with 3.85 dB and 3.4% for Matcha-TTS. In a fully paired blind listen- ing test, DriftTTS obtains 4.18 MOS, compared with 3.96 for Matcha-TTS and 4.22 for ground truth. These results demonstrate competitive few-step synthesis without a pre- trained generative teacher. Code can be found at https: //github.com/BASHLab/driftTTS.git

Rejection policies must remain useful as candidate sets and tasks change. We compare Laya, Jev and Qwen2.5-7B-Instruct using public reference labels, testing Laya/Jev policy transfer at equal calibration budgets and all three models on artificial omission, natural retrieval misses and public out-of-scope queries. Source calibration often fails to preserve the target operating point. A Jev policy calibrated on DBpedia rejects 69.3% of covered Emotion test inputs, while an Emotion policy loses detection entirely. Retrieval exposes a different tradeoff: with ten intent candidates, Laya detects 99.0% of out-of-scope queries but rejects 48.8% of covered queries. Separating missing-answer sources reveals these costs alongside retrieval coverage. The benchmark provides shared inputs, explicit decision and failure categories, and reproducible scoring to assess rejection policies under the conditions in which they are reused. Code and benchmark artifacts are available at https://github.com/luckykevvv/Decision_Model_Benchmark.

Attack Path (AP) modeling is fundamental to cybersecurity analysis, where the Planning Domain Definition Language (PDDL) has been widely adopted to encode APs into formal and machine-verifiable representations for automated reasoning about vulnerability exploitation, attack progression, and their potential impacts. However, existing AP modeling approaches largely rely on expert-driven manual construction, limiting their scalability and ability to keep pace with rapidly evolving cyber threats. Large language models (LLMs) are promising candidates, as their extensive pre-trained knowledge and reasoning capabilities enable them to interpret and transform threat intelligence into formal representations. In this paper, we propose CVE2AP, an LLM-based approach for automatically generating PDDL-encoded attack paths from natural language CVE (Common Vulnerability Exposure) descriptions. CVE2AP leverages structured prompting and incorporates an error-feedback mechanism that iteratively refines the generated paths using planner-reported syntactic and solvability errors. We conduct a systematic empirical evaluation across multiple LLMs and generation configurations, assessing generation quality across syntactic, solvability and semantic dimensions, together with token consumption and generation time. The results demonstrate that CVE2AP effectively generates high-quality PDDL-encoded attack paths, achieving up to 86.9% syntax correctness, 78.6% solvability, and 93.1% semantic correctness under LLM-as-expert evaluation, while GPT-5.5 offers the best quality-cost trade-off and error feedback yields the most consistent quality improvement.

We understand little about how capabilities acquired in one language carry over to another, or what governs this transfer: evaluations rely on incomparable, saturation-prone datasets and rarely examine its determinants jointly. Identifying what predicts transfer would let us avoid exhaustive evaluation across all language pairs and let developers target the factors that limit performance in low-resource languages. To evaluate cross-lingual capability transfer, we introduce Multilingual GSM-Symbolic, an extensible multilingual mathematical dataset covering 30,000 item-matched question-answer pairs and spanning 15 languages. It utilises symbolic templates to prevent overfitting and ensure generalisation by allowing generation of millions of high-quality variations from a single sample. Using Multilingual GSM-Symbolic, we quantify the largest determinants of capability as model size ($\beta = 1.77$), language resource level ($\beta = 0.77$), reasoning ($\beta = 0.67$) and typological distance ($\beta = -0.25$). This joint estimation allows these determinants to be expressed in terms of one another: a 32B model evaluated in Marathi performs like a 10B model in English. Our findings have important implications for model developers, showing that model size and reasoning narrow the performance gap between low- and high-resource languages ($\beta = -0.27$ and $\beta = -0.20$, respectively), while similar levers have little or no effect on typologically distant languages. Overall, our analysis framework explains 92% of between-language variation, but only 23% of the model-by-language variation, and predicts a model's performance on an unseen language within 6.0pp (r=.96). Incorporating measurements from just 10 templates in the target language reduces this to 4.19pp, enabling reasonable estimates of performance with little or no downstream dataset.

Neural surrogate models for Partial Differential Equations (PDEs) on unstructured 3D geometries are often limited by poor generalization and the high cost of generating large-scale training datasets. Consequently, pre-training on massive datasets of related PDE dynamics has emerged as a critical alternative to enhance the robustness and scalability of these models. However, this strategy is neither compute- nor data-efficient, as it relies on massive pre-computed data that is very costly to generate. In this work, we introduce a disk-data-free pre-training framework tailored to both steady-state and transient regimes. For steady-state problems, we propose a geometry-driven strategy that leverages intrinsic shape descriptors to learn representations of complex 3D domains. For transient problems, we introduce a physics-driven approach based on online generation of synthetic PDE data, enabling scalable pre-training without reliance on expensive datasets. Across multiple experiments, our approach achieves faster convergence, greater data efficiency, and higher accuracy during fine-tuning, particularly under realistic low-data regimes. This methodology provides a practical pathway toward data-efficient neural emulators for large-scale simulations.

Critic-free reinforcement fine-tuning (RFT) for agentic large language models is often done through GRPO-style methods, which compute a group baseline over repeated rollouts to reduce target variance. However, this setup is ill-suited to agents acting in stateful environments such as live services or security sandboxes, where repeated rollouts are impractical to obtain and aggressive updates entrench the noise of long, sparsely verified trajectories. We propose Follow the Winners (FTW), a critic-free policy-learning algorithm that adapts the cross-entropy method to RFT, replacing group rollouts with an ordinal filter on replay-buffer samples that yields polynomial concentration in the order statistic of returns. We derive FTW through a control-as-inference lens, which also recovers GRPO and DPO as specific modelling choices, identifying GRPO as risk-neutral while DPO and FTW share a bounded risk-seeking offset that FTW controls. We identify this offset as an inherent trade-off of variance reduction through ordinal filters on samples, whereas a critic model induces a different trade-off between bias and variance. Scaled to agentic LLM post-training, FTW matches GRPO and PPO on Sokoban and Search-R1 baselines, showing a viable trade-off from a value model or group rollouts to CPU memory.

Large Language Model (LLM) agents are increasingly deployed in high-stakes settings such as industrial maintenance and equipment fault troubleshooting, where workers occupy a variety of roles. A capable agent must therefore act in a way that is calibrated to user's role: taking actions and providing information that respect the role's knowledge and capability boundaries. Unlike coding, where mistakes are usually recoverable, agent responses in these settings are enacted on physical equipment, and can therefore cause irreversible equipment damage, production loss, or personnel harm. Existing benchmarks, however, largely overlook the need for agents to infer what a role intends and acting only through tools that role may legitimately use, a capability which we term Perspective Awareness. To this end, we introduce ReFract, a benchmark of 150 expert-validated entries in which an agent must act differently in response to the same query depending on user's role. Entries of ReFract are grounded in anonymized queries from domain support conversations, against which we construct Text World Models that simulate the agent's operating environments and assemble perspective-aware action trajectories. State-of-the-art LLMs solve at most 69% of the tasks with more than 50% of their trajectories contain attempts of taking perspective-violating actions. ReFract exposes perspective awareness as a distinct, largely unsolved axis of agent evaluation and motivates agents that calibrate not just how to act, but for whom.

Imitation learning for contact-rich manipulation requires high-quality expert data that is expensive to obtain. This makes learning a sample-efficient policy a key issue. To address this, we propose VISTA, a workspace-level equivariant visuotactile diffusion policy for data-efficient contact-rich imitation learning. VISTA projects visual and tactile observations into spherical tokens, injects tactile contact cues into visual spherical directions through permutation-equivariant spherical fusion, and rotates the fused harmonic representation using the end-effector orientation. The resulting representation conditions an equivariant diffusion policy to predict spatially consistent actions. Extensive experiments in both simulation and real-world robotic settings show that VISTA substantially improves data efficiency over strong visuotactile imitation learning baselines. Project website: https://vista-paper.github.io/

We consider a distributed learning task with agents that have correlated data. Specifically, the label of an agent depends on the input of other agents for the same sample, and these inputs are also correlated. Correlated data is the reality when agents share the same environment. Existing decentralized methods, such as federated learning, ignore the structure of the problem and perform poorly on correlated data. On the other hand, centralized approaches are infeasible due to privacy and communication constraints. We introduce cordial (correlated and distributed) learning to address this gap by sharing only low-dimensional outputs between the agents while training local models to extract informative signals from peers. This distributed learning induces a game in which the loss function of each agent depends on the models of others. Assuming a linear model, we prove that cordial learning converges with probability one to a globally optimal solution, despite the nonconvex global objective. Experiments on structured multi-digit MNIST tasks demonstrate that cordial learning remains highly effective even in highly nonlinear settings.

Large language models are increasingly used where small syntactic errors matter, yet character-level reasoning is still evaluated mostly through isolated probes and aggregate accuracy. We introduce SyntaxBench, a diagnostic benchmark and statistical evaluation framework for character-level reasoning. It contains five core tasks, character counting, letter containment, palindrome detection, edit distance, and longest-string selection, plus index_to_span, a harder substring-extraction stress test. The five core tasks use paired English and character-length-matched random-string inputs. index_to_span documents share a 200-500 word band and are not character-length matched. All six tasks use zero-, one-, and four-shot prompts. We evaluate eight open-weight models from 2B to 32B parameters across 11 reasoning-mode configurations. The framework reports exact-match and relaxed accuracy, Cohen's kappa, paired McNemar tests with odds ratios, bootstrap confidence intervals, Kendall's tau, class-conditional metrics, tokenization analysis, and multiple-comparison-corrected tests. Three findings stand out. First, tokenization shapes accuracy: random strings are more character-visible than English strings (1.892 vs. 3.169 characters per token), and character-counting accuracy falls as English words occupy more tokens. Second, reasoning mode is not uniformly helpful: Gemma4-31B is nearly unchanged across modes on the near-saturated tasks, while Qwen3.6-27B is worse with thinking on palindrome detection (0.952 non-thinking vs. 0.886 thinking at four-shot). Third, index_to_span remains largely unsolved; the best four-shot exact-match accuracy is 6.75%. Character-level evaluation needs controlled inputs, paired tests, and analyses of tokenization and reasoning mode rather than aggregate accuracy alone.

Diffusion language model (dLLM) compression faces a known challenge because calibration is typically performed on clean, fully visible activations, whereas inference traverses partially masked intermediate states. For low-rank compression, this raises two questions. First, can low-rank optimality still be characterized when approximation quality is measured over trajectory-distributed states, and second, does the choice of calibration states affect mathematical reasoning preservation under compression? We address these questions by formulating a trajectory-aware low-rank objective over corruption levels and masking realizations. To estimate this objective efficiently, we propose Traj-MC, which estimates the trajectory second moment through Monte Carlo sampling and yields exact sampled-state optimality and population consistency. Under matched compression budgets, trajectory-aware calibration improves reconstruction over the generation trajectory and preserves substantially more mathematical reasoning than clean calibration on mathematical reasoning benchmarks. Our results connect trajectory-aware low-rank optimality to the reasoning capability retained after dLLM compression. Our code is available at: https://github.com/Zishan-Shao/traj-mc.git.

Low-rank approximation can require additional matrix–vector products to verify that its error meets a prescribed tolerance. We characterize this certification cost for both relative matrix error and mean-square output error. For a single approximation matrix candidate, we determine the exact dimension-uniform minimax query constant as the allowed failure probability vanishes. Our main result concerns reusing validation responses as the approximation space expands. For a candidate family constructed independently of validation, one batch supports an entire nested path without increasing the query budget with the number of checks. Across \(W\) paths, a concentration bound exploiting shared residual energy yields a \(\sqrt{\log(W+1)}\) dependence. A matching lower bound establishes its optimality for fixed interior error targets and sufficiently small separation gaps. Finally, we compare two uniformly valid certificates on the same dispersed-spectrum family. Optimizing the validation budget within each rule family yields costs of orders \(N^{1/3}\) and \(N^{2/3}\) for validation and construction beyond the true target. Code is available at https://anonymous.4open.science/r/Low-rank-approximation-1275/

Diffusion language models for text-to-speech combine two forms of computation: model depth (parameters) and refinement steps (inference budget). We ask whether they scale equally across capabilities. We train 15 masked-diffusion codec TTS models varying depth (19-133M parameters, 3 seeds) on 2,000 hours of speech and sweep refinement steps T in [1,16] at inference, measuring zero-shot synthesis via ASR word error rate (intelligibility) and speaker verification (identity) on 174 held-out speakers. Against measured floors, refinement closes 86.2% of the intelligibility range but only 46.4% of the identity range - a 1.86x asymmetry robust across multiple error metrics. Retraining at 3x and 6x schedule attenuates but does not reverse this gap (1.84 to 1.36 to 1.23x), because intelligibility saturates with steps while identity continues improving. Best-of-K search recovers speaker identity where refinement fails, with 64.6-79.0% win rates across four independent encoders. Depth and steps are not interchangeable: separable B(d)B(T) fits significantly better (Delta AICc=+69.3) than substitution models. Analysis shows 62% of remaining identity deficit lies in the codec, not the generator. We conclude that refinement and depth target different bottlenecks and should be optimized separately.

Designing effective heuristics for diverse combinatorial optimization problems requires substantial expertise and repeated search. Large language models (LLMs) automate heuristic generation and refinement, but heuristic search typically depends on evaluation feedback from the problem being optimized. Generalizing to new problem definitions using only source-task feedback therefore remains a central challenge. We introduce MECo, an LLM-driven multi-task evolutionary framework for zero-shot cross-problem generalization. MECo maintains task-conditioned heuristic populations and uses a transfer gap based on cross-task population performance to guide their interactions. These interactions enable the transfer and recombination of heuristics. A complementary selection criterion then constructs a compact heuristic set by rewarding each member's additional coverage of source combinations. The selected set is applied to target problems without further search or adaptation. Experiments on 32 problem variants across vehicle routing (VRP) and flexible job-shop scheduling (FJSP) show that MECo achieves the lowest mean costs compared with eight automated heuristic design (AHD) baselines under the same budgets. On out-of-domain problems, it outperforms the strongest baseline in each family. Moreover, integrating the framework of MECo with different AHD methods improves their ID and OOD performance in both families, supporting its effectiveness across different methods.

Trajectory evaluation is essential for improving the reliability of LLM-based agents, but production use makes it expensive to run repeatedly. Modern agents generate long traces containing tool calls, observations, retries, and external outputs, while not all raw tokens are equally useful for diagnosis. We present LiteTrajEval, a lightweight architecture for budget-bounded trajectory evaluation. LiteTrajEval derives compact domain-specific rule profiles offline, then preprocesses each trajectory online, marks heuristic failure signals, serializes it under a fixed global budget, and invokes a single rubric-guided LLM judge to produce structured diagnostic reports. Evaluated on public Magentic-One-style and $\tau$-bench-style trajectory datasets, LiteTrajEval improves failure-localization alignment with human annotations by roughly 20–35 percentage points on Magentic-One and up to 23 percentage points on $\tau$-retail compared with AgentRx, while reducing cost by about 6$\times$ and evaluation time by more than 8$\times$. This solution has also been deployed in our enterprise agentic platform.

Background: We address the problem of planning when the set of feasible states or actions changes over time. For example, in the problem of path planning among moving obstacles (sometimes known as SIPP), the feasibility of being at a particular location can change as the obstacles move. Or, the action of boarding a particular train is feasible only while it is stopped at the station. This dynamism means that the optimal plan and its duration can change depending on when execution begins. In practice, execution start time is often unknown until planning has completed or another agent gives the go-ahead. However, most prior planning work either ignores dynamism or assumes a known start time. This makes it straightforward to assess state and action feasibility but is impractical for some applications. Objectives: In this paper, we relax the assumption of a known start time. We define the setting of any-start-time planning and provide algorithms for it. Methods: We present a data structure called a compound arrival time function (cATF) that compactly encodes the optimal plan as a function of start time. We provide general-purpose planning algorithms, based on heuristic graph search, that assemble cATFs by propagating functions along edges instead of scalar costs. Results: We prove that the size of a cATF is at most linear in the problem size. An experimental evaluation of an implementation for the specific problem of SIPP shows that, on difficult problems, agents that rely on replanning often fail, while any-start-time algorithms using cATFs can quickly look up the optimal plan once the execution start time is known. Conclusions: By enabling efficient representations and reasoning for time-dependent plans, this work provides a foundation for planning in dynamic worlds.

Existing convergence analyses of Muon either assume exact orthogonalization or analyze classical Newton–Schulz polynomials, and guarantee only stationarity, so it is unresolved what Muon's five tuned Newton–Schulz steps preserve and whether that suffices to reach a prescribed neural-network training loss. We establish a finite-time training guarantee that accounts for both momentum accumulation before orthogonalization and the tuned finite-step update. For full-batch training of a sufficiently wide two-layer ReLU network with fixed random output weights and a positive-definite limiting neural tangent kernel, we prove that Muon reaches any target empirical squared loss $\varepsilon>0$ with high probability over initialization. For every momentum parameter $\mu\in[0,1)$, a target-dependent constant learning rate proportional to $(1-\mu)\sqrt{\varepsilon}$ yields a hitting-time bound of $O((1-\mu)^{-1}\varepsilon^{-1/2})$, with other problem parameters fixed. The sufficient width is independent of both target accuracy and momentum. The analysis shows that the tuned Newton–Schulz map preserves alignment with the momentum buffer while bounding the update's spectral norm. Control of gradient variation near initialization transfers this alignment to the current gradient, ensuring descent until the target is reached without requiring exact orthogonalization. Numerical experiments support these mechanisms at widths below the sufficient theoretical threshold: gradient-update alignment remains above the analytical reference, and all 30 runs across six widths and five student initializations on a fixed teacher-student dataset reach the target loss while maintaining kernel positivity.

Complex reasoning queries can be decomposed into directed acyclic task graphs and distributed across heterogeneous LLMs, reducing latency through parallelism and enabling smaller models to solve complex tasks. In practice, however, the suitability of an LLM for a given subtask may be a priori unknown, and execution alone does not reveal output correctness. We propose JOVE, an online framework that jointly assigns executor LLMs and selects intermediate outputs for paid verification. Verification runs asynchronously and is used to improve future allocations, so the system must balance spending on execution now against learning for later. We study how to optimize this trade-off under a long-term budget and a per-query latency constraint, with stochastic, initially unknown LLM service quality, invocation costs, and execution times. JOVE makes execution and verification decisions by solving a sequence of per-query mixed-integer linear programs. Online learning updates task-dependent estimates of LLM quality based on verification feedback, while an information-gain bonus incorporates the value of learning into allocation decisions. Under a natural set of assumptions, we establish sublinear quality-learning regret for JOVE. Across four reasoning benchmarks, JOVE achieves competitive accuracy against standard inference baselines while reducing average cost and latency by at least 3.17 times.

Reinforcement learning (RL) for learning path recommendation (LPR) faces two coupled obstacles. First, the policy must commit to a sequence of L concepts without intermediate feedback, producing a combinatorial search space that grows super-exponentially with L and provides reward only at the final step. Second, expert learning paths would be the natural cure for sparse-reward RL, but they do not exist in educational data, because student logs record what learners did, not what they should have done. We address both obstacles by importing a recipe from simulator-based demonstration learning in robotics: the knowledge tracing simulator is used both to synthesize per-learner expert demonstrations through evolutionary search and to train a deployment-free policy that distills these demonstrations into a feed-forward learner. Our framework, EVOL, instantiates this pipeline with an asymmetric actor-critic where the actor commits to deployment-realistic blind planning while the critic exploits the privileged simulator state during training. Across three datasets (ASSIST15, Junyi, and EdNet; 39-189 concepts) and path lengths L = 5, 10, and 20, EVOL surpasses 8 baselines spanning heuristic, sequential, RL, graph-enhanced RL, and LLM-enhanced methods. We further compare three imitation strategies (BC, AWR, and DAPG) and show that final performance is governed by the quality of evolutionary experts rather than by the particular imitation objective.

Large-scale pre-training has improved the generalization of neural operators across diverse PDEs. However, existing PDE foundation models still struggle with heterogeneous dynamics, where shared representations may cause knowledge interference, while mixture-of-experts (MoE) architectures suffer from increasing expert redundancy. We propose SPEAR, a spectral-disentangled MoE neural operator with knowledge-guided expert aggregation for large-scale PDE pre-training. SPEAR decouples latent features into low- and high-frequency components, enabling shared modeling of transferable dynamics and specialized learning of PDE-specific patterns. To address expert redundancy, we design a knowledge-guided expert aggregation strategy that measures expert similarity from dataset-specific learned knowledge and routing preferences, enabling the identification and consolidation of similar experts. Experiments on twelve PDE datasets and multiple downstream benchmarks demonstrate superior performance in pre-training, fine-tuning, and transfer learning. Furthermore, our aggregation strategy reduces the number of experts by 50% while maintaining or improving prediction accuracy, achieving a balance between model efficiency and generalization for PDE foundation models.

Solving severely ill-posed imaging inverse problems requires recovering image structures that are unobservable or weakly constrained by the measurements. Diffusion models provide expressive learned priors for inferring such missing information, while posterior sampling incorporates measurement consistency along the reverse process. Standard diffusion posterior samplers, however, rely on instantaneous measurement-aware estimates, without explicitly exploiting information carried by previous posterior corrections. We introduce Consecutive Posterior Fusion Denoising Diffusion Null-Space Models (CPF-DDNM), an inference-time strategy that fuses consecutive measurement-aware estimates to improve the diffusive recovery of unobservable image structures, without requiring retraining or additional denoiser evaluations. We instantiate this principle within DDNM, whose range/null-space decomposition reveals that consecutive fusion preserves the measurement-determined component while acting exclusively on the prior-driven null-space estimate. We thus provide a geometric interpretation of CPF-DDNM and a local error analysis that characterizes the optimal time-dependent fusion coefficient, including the extrapolative regime. Experiments on sparse-view and simulated low-dose computed tomography, as well as medical image super-resolution, show consistent improvements over DDNM and competitive performance against diffusion-based inverse solvers.

Scalable nonlinear causal discovery requires methods that combine flexible mechanism estimators with efficient search over large graph spaces. Several algorithmic families have been proposed to address this challenge, yet their accuracy-runtime trade-offs remain poorly understood. We empirically compare the four major approaches: differentiable structure learning, amortized structure learning, score-matching, and combinatorial search. Our results reveal complementary bottlenecks: differentiable and amortized methods scale well but exhibit an accuracy gap, score-matching methods can be accurate in low dimensions but degrade quickly for increasing feature sizes, and combinatorial methods remain accurate but are slowed by repeated and redundant local scoring. Motivated by this bottleneck, we develop SPADE, a spline-based score-evaluation scheme that compiles sufficient statistics once and reuses them throughout combinatorial search. Under bounded indegree, its Gaussian variant reduces algorithmic complexity from O(nd^3) to O(nd^2+d^3). Empirically, SPADE shifts the observed scalability-accuracy frontier by orders of magnitude: it solves 100-variable problems with 160K samples in seconds and 1600-variable problems with 2.5K samples in minutes, while retaining high structural accuracy across synthetic and real-world benchmarks. These results reveal a substantial shift in the practical scale of combinatorial search and highlight the importance of evaluating scalable causal-discovery methods along the full accuracy-runtime frontier.