Papers

Reinforcement learning with human feedback (RLHF) learns from human comparisons, which can be corrupted or deliberately manipulated. This paper studies online risk-sensitive RLHF with static conditional value-at-risk (CVaR) under adversarial preference-label flips. We consider additive linear rewards and a fixed-reference protocol with one comparison per episode and at most $C$ flipped labels over $K$ episodes. We propose weighted streamed-preference CVaR RLHF (WSP-CVaR-RLHF), which combines uncertainty-weighted reward estimation with optimistic augmented-state CVaR planning. For known transitions and normalized rewards, we establish the regret bound $\widetilde{O}\left(\frac{d}{\kappa}\sqrt{\frac{K}{\alpha}}+\frac{dC}{\kappa\alpha}\right)$ up to lower-order terms, where $d$ is the reward-feature dimension, $\alpha$ is the CVaR level, and $\kappa$ characterizes the preference link. The bound separates the clean statistical cost from the penalty caused by corrupted feedback. We further extend the analysis to unknown tabular transitions, where the trajectory distribution entering the CVaR objective must be learned together with the reward. We address the resulting coupled uncertainty using rectangular transition confidence sets, joint optimistic planning, and a history-level CVaR simulation argument. Experiments under four adversarial attacks demonstrate that WSP-CVaR-RLHF consistently reduces cumulative regret relative to its unweighted robust counterpart while preserving confidence-set coverage.

Turbulence regulates star formation by influencing the density structure and fragmentation of molecular clouds, and therefore it is expected to play a key role in setting the initial mass function (IMF). We study how the strength of the turbulent shocks affects star formation and the IMF by comparing a series of magnetohydrodynamical (MHD) simulations of star cluster formation in clouds with three different rms Mach number values, $M=2.5, 5$, and $10$, but otherwise the same Alfvén Mach number ($M_\mathrm{A}\sim3$) and virial parameter ($\alpha_\mathrm{vir}\sim0.5$). All three simulations include stellar feedback in the form of protostellar jets/outflows and accretion heating. We find that the star formation rate per freefall time ($\mathrm{SFR_{ff}}$) for the $M=10$ model is higher by a factor of $\sim3$ compared to the $M=2.5$ and $5$ cases, which have similar $\mathrm{SFR_{ff}}$. In terms of the IMF, the $M=5$ and $10$ models produce almost similar distributions, resembling typical observed IMFs. The $M=2.5$ model, on the other hand, produces a bimodal IMF with a primary peak at supersolar masses ($\sim 2\, \mathrm{M_\odot}$) and a secondary peak in the substellar regime ($< 0.1\, \mathrm{M_\odot}$). The $M=2.5$ and $5$ simulations producing significantly different IMFs while having similar $\mathrm{SFR_{ff}}$, suggest that a distinct set of physical processes governs the SFR and IMF. Through a resolution study for the $M=2.5$ case, we find our base models have reached near numerical convergence, potentially only slightly underestimating close-binary formation. We also see signatures of bimodality in the $M=2.5$ model for the multiplicity fraction and stellar angular momentum distribution.

When a classifier is recalibrated from only a few thousand held-out examples, the capacity of the calibration map becomes a statistical design choice rather than a purely architectural one: a scalar map can underfit structured residual miscalibration, while a highly adaptive map can be hard to estimate reliably from so small a split. We disentangle the calibration objective from adaptive capacity and propose signal-routed temperature scaling (SRTS-BCE), a 10-parameter, argmax-preserving calibrator that cross-fits a correctness-risk score over six logit statistics and fits one top-label-BCE temperature per $K=3$ risk groups, recovering TvA-TS as its $K=1$ limit. On fine-tuned CIFAR-100 / ViT-B/16, SRTS-BCE reduces $\mathrm{ECE}_{15}$ from 1.65 (scalar TvA-TS) to 0.96, matching the higher-capacity SMART+BCE head (0.95) at the full calibration budget. The two regimes separate as the budget shrinks: at $n=250$ SRTS-BCE beats SMART+BCE on all three CIFAR-100 backbones (the seed-to-draw hierarchical interval excludes zero), whereas the flagship comparison against the scalar remains directional. A protocol-frozen Tiny-ImageNet follow-up reproduces the small-budget separation and exhibits a budget-dependent ranking reversal on Swin-T; matched routing and map controls show that the effect is tied neither to the learned router nor to discrete grouping. Together the results identify post-hoc calibrator capacity as a finite-sample design choice whose preferred level shifts with the amount of available calibration data.

Two non-geostationary orbit (NGSO) mega-constellations over shared spectrum leads to inter-constellation interference. Existing mitigation mainly relies on frequency/time partitioning, spatial isolation and satellite selection. However, these approaches may sacrifice resource reuse or be constrained by spatial geometry. To enable interference mitigation without centralized coordination, this letter investigates distributed power control for independent, equal-priority NGSO operators. We formulate the interaction as a non-cooperative game and propose a distributed water-filling best response using local serving-channel estimates and aggregate interference measurements. Pure-strategy Nash equilibrium existence and a weighted spectral-norm sufficient condition for uniqueness and convergence are established. Simulation results demonstrate utility gains of 3.91% over uncoordinated transmission with 20 active beams.

Differentially private (DP) text generation can protect individual records, but privacy alone does not specify what evidence a released statement carries about the underlying data. We identify this as an evidence gap: a private report may contain plausible claims without indicating whether they are strongly supported by the private dataset. We introduce PrivCert, a framework for privacy-preserving reporting that makes statement support explicit through privacy-preserving certificates and emit-or-abstain decisions. As a canonical instantiation, PrivCert-PF (Proposal-and-Filter) separates data-independent candidate discovery from private support certification, emitting only statements whose support passes a private evidence test. We provide theoretical grounding for this framework by characterizing the limits of implicit evidence under DP, deriving a sharp privacy–honesty frontier for single-statement certification, and establishing a worst-case cost for fine-grained multi-statement certification. Experiments on synthetic tasks and TAB, WildChat, and Yelp show that explicit certification maintains low unsupported emission, while free-text DP baselines frequently produce low-support claims under the same declared support semantics. We further show that the PrivCert contract can be realized with histogram, sparse-vector, and Gaussian mechanisms, and use DP synthetic data to illustrate an important boundary: support in a private proxy does not automatically certify support in the original data. Together, these results position privacy-preserving reporting as an evidence-design problem: not only how to generate private text, but what a private report can substantiate about its underlying data.

Number-conserving cooling can fail to prepare an interacting flat-band target when Pauli exclusion blocks its transfer destinations. We study this failure on vertex-edge decorated graphs at one particle per flat orbital. The rank of a cut block of the flat-orbital Gram matrix bounds the number of residual source directions that can remain flat. For sublinear-range cooling with no Hamiltonian term, separated spin domains on periodic decorated hypercubic lattices support exponentially many stationary states with a nonzero bright-particle density. For a chain with fixed finite cooling range, we construct a physical Fock initial state whose overlap with a wrong dark state is independent of system size. This gives fidelity and bright-density bounds valid at every time. In higher dimensions, the bare overlap decays with boundary area, while local boundary rotations prepare states with a finite failure weight in constant circuit depth. Dephasing the occupations of all compact bright modes restores global attraction to the ferromagnetic target when the graph and cooling destinations satisfy the stated conditions. The result allows Hamiltonians that preserve the target. The compressed dynamics in the strong-dephasing limit also remains attractive and has a positive gap at each fixed size. Gram calculations, finite-system dynamics, and Liouvillian spectra test the analytic results. Weak-dephasing and particle-transport bounds constrain the preparation time despite eventual convergence.

Surface electromyography (sEMG) provides a wearable, camera-free signal for continuous hand-motion inference. Mapping muscle activity to joint kinematics remains challenging because the recorded waveforms are indirect measurements, their relationship with motion changes over time, and individual anatomy and sensor placement alter the signal distribution. This paper presents EFormer, a residual feature-correction network built on a frozen tracking backbone. EFormer combines a high-rate event branch, temporally aligned local cross-attention, two causal rotary position embedding (RoPE) temporal layers, and a bounded, dynamically gated residual. EFormer receives 16-channel sEMG sampled at 2 kHz and fuses a 64-channel tracking representation at 25 Hz with a 128-channel event representation at 200 Hz. Cross-attention uses a nominal delay of 100 ms, a 300 ms history parameter, and a 50 ms tolerance; its causal mask restricts each query to events occurring 50-400 ms earlier. The correction scale is 0.15. The evaluated continuation-training configuration contains 585,376 trainable parameters and 5,974,508 frozen parameters. On the test set, EFormer achieves an MAE of 0.1546634 rad, an RMSE of 0.24063 rad, and an R^2 of 0.74801, compared with 0.1745326 rad, 0.2715448 rad, and 0.6791103 for the official tracking baseline. EFormer reduces MAE by 11.38% relative to the baseline. The results show that temporally aligned event-feature correction can reduce continuous hand-pose tracking error.

Self-consistency samples many reasoning trajectories and aggregates their final answers, treating the LLM as a black box that returns one answer per trajectory. Yet the final answer of each trajectory is sampled from a softmax vector that is available from the model's log-probabilities. We refer to this as the grey-box setting in which each trajectory reveals this answer distribution rather than a single draw from it. We formulate efficient inference in this setting as sequential mode identification with distribution-valued observations: sample trajectories one at a time and stop as soon as the LLM's modal answer is identified at a prescribed confidence level. We characterize the asymptotic stopping rate of mode identification with distribution-valued observations exactly and show that it is never worse than the black-box rate. We then propose the ASC-D algorithm, a betting stopping rule that attains this asymptotic stopping rate. On MMLU-Redux, ASC-D uses $46.4$–$95.6\%$ fewer trajectories than answer-only adaptive self-consistency baselines and achieves the highest fixed-budget correct-certification rate across three open-source models.

In semantic segmentation, a recent line of RankSEG methods directly optimizes Dice/IoU scores at inference time, improving alignment with evaluation metrics without modifying model training. Despite its theoretical and empirical success, RankSEG relies on the restrictive Conditional Independence Assumption (CIA), which ignores crucial label correlations and therefore degrades performance in ambiguous or low-contrast scenarios. However, accounting for full label dependence is computationally prohibitive, requiring $\mathcal{O}(d^3)$ time. To address this, we replace the CIA with a Spatially Localized Dependence (SLD) structure that captures local label correlations while keeping the dependence model tractable. We further overcome the remaining computational bottleneck via a Reciprocal Moment Approximation coupled with a novel fixed-point optimization strategy that eliminates exhaustive search. The proposed algorithm achieves a highly practical $\mathcal{O}(d \log d)$ complexity and consistently outperforms conventional argmax and CIA-based RankSEG across diverse segmentation benchmarks. Improvements are significant in low-contrast or small-object scenarios, where label dependence offers valuable signals complementary to image information for accurate segmentation. The code of experiments is available at https://github.com/ZixunWang/RankSEG-DEP.

Machine learning systems increasingly face the need to remove the influence of entire data domains, such as toxic language, harmful behavior, or topical content, rather than isolated records. Recent work formalizes this problem as distributional unlearning: selecting a subset of a forget domain whose removal moves the training distribution away from an unwanted population while preserving proximity to the desired one. However, existing analyses often impose parametric assumptions to obtain tractable selection rules. These assumptions may be poorly suited to high-dimensional language-model representations. We introduce Mamushi, a framework for non-parametric distributional unlearning that ranks forget examples using a probabilistic classifier whose Bayes-optimal logit equals the forget-to-retain log-density ratio (up to an additive class-prior constant). We show that thresholding the population log-density ratio yields the optimal fixed-budget selection rule for our removal–preservation objective and establish a non-asymptotic transfer guarantee relating score-estimation and threshold-calibration errors to degradation from the population-optimal selection rule. Our empirical evaluation spans real-world datasets on toxic-language removal and topical-domain removal regimes using different representations, with Mamushi achieving a more favorable removal–preservation trade-off than other baselines. Our work shows that Mamushi can serve as an efficient selection approach for downstream machine unlearning procedures, reducing the number of forget examples required to reach a fixed forgetting target.

Mapless navigation in unknown and partially observable environments remains challenging for mobile robots, particularly when local minima prevent the robot from making progress toward its goal. Existing local navigation methods often lack an explicit mechanism for escaping such situations, while deep reinforcement learning (DRL) approaches typically learn recovery behaviors implicitly through reward design and policy optimization. In this work, we propose LME (Local-Minimum Escaper), a programmatic hierarchical framework that explicitly generates and reasons subgoals to guide robots out of local-minimum regions. LME operates solely on local observations and selects candidate subgoals using interpretable heuristic criteria that account for both surrounding obstacle geometry and candidate-location safety. A local planner then generates low-level motion commands toward the selected subgoal. This design enables LME to handle environments both with and without local minima within a unified framework, while remaining independent of the underlying local planner and requiring no additional training. Extensive experiments in simulated and real-world environments demonstrate that LME provides robust navigation performance and generalizes to challenging unseen scenarios. Furthermore, the generated subgoals can be used to guide different local planners, substantially improving their ability to escape local minima. Successful deployments on both differential-drive and quadruped robots further demonstrate the practical applicability and generality of the proposed framework.

World models aim to learn representations of real-world environments and predict their future evolution. Recent object-centric world models have made expressive progress by representing visual scenes as sets of object-level latent states, but object-object relations are often captured only implicitly, which limits explicit relational and temporal structure modeling and object-centric dynamic memory modeling. To address such challenges, we propose World-As-Graph (WAG), a graph-based object-centric world model that introduces relational inductive bias into JEPA-style predictive representation learning. The proposed WAG contains two main modules: (1) Relation-aware structure induction, which constructs time-varying latent graphs from object-centric slots and designs relation-aware object masking policies to guide relational object representation learning in latent space; (2) Object-centric memory transition, which maintains and updates object-level dynamic states by combining relational information from neighboring objects with historical memory, enabling effective autoregressive future prediction. Extensive experiments on both visual reasoning and robotic manipulation tasks could demonstrate the superior performance of our proposed WAG.

Long-term precipitation nowcasting requires modeling radar-echo evolution while preserving localized high-intensity structures. Recent radar-specific studies motivate location-aware prediction and separating echo displacement from intensity change. However existing encoders learn historical representations mainly from final forecast errors. We propose PrecipJEPA, which couples a structured forecasting path with an auxiliary path that enriches its encoder from observed radar history. In the forecasting path, an online encoder first converts the observations into spatiotemporal tokens. The Task-Driven Future-State Predictor (TFP) combines these tokens with a recent-dynamics summary and spatiotemporal queries to construct future radar states. The Parallel Motion-Source Renderer (PMSR) decodes these states into motion and source-sink fields that transform the latest observation into future frames. During joint training, the History-Masked JEPA (H-JEPA) operates on the auxiliary path to predict masked historical features from visible context, directly supervising the same online encoder from the observed sequence. Experiments on SEVIR and MeteoNet show that PrecipJEPA improves highest-threshold CSI by 118.6% and 35.1%, respectively, over the strongest baselines, while maintaining the highest mean CSI throughout the 3-hour forecast.

Multimodal federated learning (MFL) has emerged as a pivotal paradigm for leveraging distributed data to enhance model performance. However, existing methods predominantly rely on idealized assumptions of model homogeneity and balanced modality distributions, rendering them ill-suited for practical scenarios characterized by heterogeneous client architectures and severe modality imbalance. To address these challenges, we propose a Multimodal Federated learning Prototype-guided Bilateral Alignment (MFedPBA) framework. MFedPBA facilitates robust knowledge synergy through a dual alignment mechanism: (i) at the feature level, it aligns heterogeneous feature spaces via a projection encoder optimized by contrastive learning and the Gromov-Wasserstein distance; (ii) at the decision level, it employs an entropy-weighted aggregation of naturally aligned logit prototypes. This novel design achieves robust MFL by jointly tackling heterogeneous feature spaces and collectively aggregating decisions. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art baselines under conditions of model heterogeneity and modality imbalance.

Major adverse cardiovascular events (MACE) remain the leading cause of mortality worldwide. Opportunistic screening using routinely acquired clinical data offers a scalable approach for identifying high-risk individuals before acute events occur. Although chest X-rays (CXRs) capture latent cardiovascular biomarkers and clinical histories provide complementary patient context, existing medical vision-language models are primarily optimized for radiology interpretation rather than prognostic reasoning. We propose a causal reinforcement learning framework for multimodal clinical reasoning that integrates CXRs and physician-authored clinical histories for opportunistic MACE prediction. The framework introduces (1) a role-decoupled dual-LLM architecture that separates reasoning from risk prediction, (2) a dual-action causal reinforcement learning policy for evidence selection and reasoning optimization, and (3) causal token pruning to learn compact multimodal representations. Evaluated on an internal cohort, an emergency department cohort, and the external MIMIC dataset, the proposed framework consistently outperformed unimodal baselines and state-of-the-art medical vision-language models, achieving AUROCs of 0.720, 0.760, and 0.845, respectively. It also substantially improved reasoning quality, achieving higher GREEN scores and higher expert preference while maintaining robust predictive performance across diverse patient populations.

Working agents need to read diverse files, coordinate tools, and produce deliverables. Training such agents requires tasks built on many real files with verifiable results, but few pipelines exist to synthesize this kind of data. Existing pipelines either generate files with models, which lack realism and diversity, or build tasks on real files without task-specific verifiers, leaving result quality unchecked. We introduce GraphForge, an evidence-graph based framework that grounds both the task and its verification in real files. Starting from occupation-grounded seeds for controlled diversity, GraphForge assembles a workspace of real files for each seed and builds an evidence graph over their relations. Since the task statement and rubrics are both derived from this graph, task requirements are backed by the workspace files and each criterion is anchored to the files needed to verify it. An initial rollout further tests executability, and a revision agent repairs the task and rubrics against the original files before trajectories are collected. Fine-tuning Qwen3.6-27B on 2,169 GraphForge trajectories brings GDPVal to 1445.7 (+65.7) under OpenHands, and Workspace-Bench-Lite and SpreadsheetBench II to 63.7 (+7.7) and 24.0 (+13.7) under Claude Code. Rejection fine-tuning on the SFT model's own rollouts, with candidates selected by the evidence-anchored rubrics, yields further improvements on all three benchmarks, suggesting that the rubrics provide a useful selection signal.

Diffusion-weighted MRI can probe tissue microstructure non-invasively, however interpreting microstructural parameter estimates remains challenging due to the intrinsic ambiguity of the inverse problem. While simulation-based approaches can incorporate increasingly realistic tissue models, they still lack voxel-wise characterisation of the reliability and degeneracy of the inferred parameters. Here, we introduce a reliability framework for simulation-based microstructure estimation based on three complementary scores that identify distinct sources of unreliability in the estimation process: out-of-distribution signals, local signal mismatch, and parameter degeneracy. The framework was implemented using a Monte Carlo dictionary of 1,050 synthetic voxels generated from geometrically realistic substrates, with parameter ranges grounded in electron microscopy measurements of rat corpus callosum. The dictionary spans biologically plausible axon radii (0.25-0.85 $\mu$m), microscopic angular spread (0-10$^\circ$), packing densities (60-92%), and intrinsic diffusivities (1.75-3.0 $\mu$m$^2$/ms). On synthetic data, the resulting Reliability Index correlated with actual estimation error (Spearman $\rho = -0.742$) and distinguished between extrapolation, poor local interpolation, and parameter degeneracy. Applied to in vivo corpus callosum DW-MRI in rat (256 voxels, four animals) and human (MGH-USC HCP, 18,765 voxels, nine subjects), 91% and 73% of voxels respectively exceeded $R > 0.5$. These results demonstrate how reliability-aware analysis can support the interpretation and future development of simulation-based diffusion MRI microstructure models.

Planetesimals are a key intermediate stage of planet formation and originate from dust concentration in protoplanetary disks, which is strongly regulated by gas dynamics. In this study, we use the multifluid dust module of Athena++ to investigate dust concentration in 2D axisymmetric global non-ideal MHD (ambipolar diffusion, AD) simulations of outer disks. Our simulations simultaneously launch large-scale MHD disk winds and resolve both streaming instability (SI) and vertical shear instability (VSI). We systematically explore the effects of magnetic field strength, cooling timescale, ambipolar Elsasser number, and dust size on dust concentration. We find that strong dust clumping persists across a broad range of magnetized and wind-launching disk conditions. MHD winds also enhance dust clumping by modifying background conditions in the following ways: (1) secular gas depletion by MHD wind mass loss, and (2) dust trapping in zonal flows as a result of magnetic flux concentration (which occurs in more strongly magnetized cases). Overall, our results demonstrate that strong dust clumping can persist in global magnetized disks with AD and large-scale MHD winds, leading to conditions favorable for planetesimal formation.

Offline multi-objective optimization (MOO) seeks solutions with better objective trade-offs using only a fixed dataset, without querying the objectives. Diffusion models trained on such data have emerged as a promising approach, but their samples are not inherently better than the data and must be steered toward the Pareto front. Existing methods guide or condition every sampling step. We instead act on the initial noise and leave the sampling process unchanged. Across Off-MOO-Bench, we observe that the objectives, as functions of the noise, are sensitive to only a few directions. We estimate these directions once per task via a Recursive Feature Machine using function values alone, and a small cache serves every trade-off, so each candidate costs one noise displacement and one ODE solve. We prove that this displacement increases the learned scalarized objective in expectation, and that sweeping trade-offs recovers the flow's attainable front up to proxy and steering errors. With additional guidance, for which we introduce novel data-adaptive and Pareto-aware operators, our method attains the best average hypervolume rank among generative methods on 47 tasks, at comparable or lower sampling cost. Steering alone outranks the best prior generative method at a fraction of its sampling cost.

We encode the vertices of every finite complete bipartite graph as binary strings at each scale. The information distances between these strings approximate the scaled graph distances with an additive error bounded by a constant independent of the scale. We also assign one fixed infinite binary sequence to each vertex; suitable prefixes satisfy the same distance estimate with logarithmic error. This extends Hutter's construction for $K_{3,3}$ and resolves his open problem on scale-embeddings of finite complete bipartite graphs. Combined with his complete bipartite obstruction, these embeddings show that no positive power of information distance can be represented exactly by distances in a real Hilbert space, resolving his question about such representations. For conditional prefix complexity, we further prove that at most $2^{\delta+C}$ strings lie between any two strings with total distance exceeding their mutual distance by at most $\delta$, where $C$ is independent of the endpoints. This bound rules out scale-embeddings of the integer line and every positive-dimensional integer lattice, resolving Hutter's lattice embedding problem for both string and sequence embeddings. Restriction to the integer lattice gives the same conclusion for $(\mathbb R^m,\|\cdot\|_1)$ for every $m\ge1$.

Flow Matching (FM) learns a velocity field whose ODE transports a simple source distribution to a target law. Existing finite-sample theory largely treats ambient-space regularity or data supported exactly on low-dimensional sets. We study linear FM under a noisy latent-generator model, where a low-dimensional Hölder map is perturbed by nondegenerate ambient Gaussian noise, so the target law is full-dimensional despite its latent structure. We construct a spatially regular ReLU velocity class and establish non-asymptotic high-probability approximation and estimation bounds whose leading sample-size exponent is governed by the latent dimension rather than the ambient dimension, with ambient and noise dependence kept explicit. Fixed positive target noise keeps the interpolation nondegenerate over the full time interval. The same spatial regularity propagates the learned velocity error through the transport ODE, yielding a corresponding Wasserstein convergence guarantee. These results show that exact low-dimensional support is not necessary for Flow Matching to retain latent-dimensional statistical behavior.

A classifier's conditional accuracy can change while its confidence distribution stays exactly the same. We study the worst-case movement of the reliability relation under covariate shifts that preserve the distribution of the confidence score, constraining the reweighting within each confidence level by a $\chi^2$ budget; the resulting worst case, as a function of the budget, is a fragility profile. On an interval of budgets that can be computed from the source distribution, the profile equals exactly the square root of the budget times the within-level variance of the correctness propensity – the grouping-loss term of calibration-refinement decompositions. Beyond this interval the profile is governed by the tails of the propensity law, and the entire upward profile determines the centred within-level law; consequently, calibration residual and grouping variance do not determine fragility in general, though they do when labels and predictions are deterministic. Since the propensity is not observed, we restrict reweightings to a learned finite readout within confidence bins, bound the part the restriction misses by the grouping variance remaining inside readout cells, estimate the restricted profile with role-separated labels, and provide a separate split-sample lower confidence bound. On ImageNet this bound is positive in both splits for four of six primary classifiers and nine of twelve additional ones as released, and for three of eighteen after temperature scaling. Held-out drift under optimised reweightings fitted without evaluation labels tracks the estimated profile; an exploratory label-permutation diagnostic yields near-zero agreement for this statistic while largely reproducing the correlation observed for unsigned random reweightings.

Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and dimensions. Inspired by the GNN transferability literature, we show mathematical conditions under which a partial differential equation (PDE) learning-based solver can be trained in small dimensions and directly applied to solve a higher dimensional PDE in a zero-shot fashion. These conditions are based on symmetries in both the partial differential equation and the initial data. When the equations satisfy the symmetries but the data does not, which is the case for many PDEs arising from physics, we show that our theory gives a principled way of warm-starting low-dimensional PDE solvers for higher dimensional PDEs. We apply this method on the heat equation, Burgers' equation, and the compressible Navier–Stokes equations, improving the performance in both zero-shot and typical training regimes on high dimensional data. For example, we train a surrogate model on 2D Navier–Stokes data and achieve better results on 3D test data than a baseline surrogate model trained on 3D data, while only using 12$\%$ of the flops and 20$\%$ of the total data size.

Certified deletion allows a client to upload encrypted data to a server as a quantum state, then later request that the server delete their data and detect whether the server complies. If verification passes, then the data on the server will remain hidden even if the decryption key is later leaked. In publicly verifiable certified deletion, the verification key is published so that anyone may check for deletion compliance. In this work, we give a general compiler to publicly verifiable certified deletion that allows the client to initially upload the *quantum* ciphertext using purely *classical* communication, assuming the post-quantum hardness of LWE in the plain model. Our approach can be applied to a wide variety of primitives, including commitments and public-key, attribute-based, identity-based, and fully-homomorphic encryption. Moreover, our constructions allow the client to classically manage the encrypted data beyond just verifying its deletion. The classical client may non-destructively audit the ciphertext via a Proof of No Intrusion to check whether it has been leaked to a third party. The classical client may also retrieve the data while simultaneously verifying its deletion from the server. Thus, they do not have to choose between retrieving the data and protecting it against future key leakage. As our core technical contribution, we give a classical-communication protocol and simulation technique that allows adapting purification-based security arguments for BB84-style states which are prepared through classical interaction. It makes the required purification available in a hybrid experiment, despite the classical transcript uniquely determining the prepared state in a real execution.

Evaluating interactive agents is expensive. Agent behavior is stochastic, so reliability must be measured over repeated trials, but failures are rare and differ widely in how much they matter. Standard benchmarks spend this budget uniformly: a read-only lookup is sampled as often as an irreversible payment action. We instead formulate evaluation as a sequential allocation problem. Given a fixed trial budget and a set of scenarios whose failure behavior is unknown, which scenarios should be run, and run again? We propose a risk-aware contextual Thompson Sampling policy that combines a pre-execution scenario context vector and a fixed impact score with the failure outcomes observed during evaluation, and we test it by offline replay over 70 $\tau$-bench airline scenarios and 824 recorded trials. Our main result is at the smallest budget: with only 50 trials ($6\%$ of the corpus), the policy recovers $86\%$ of the impact-weighted failures an oracle could find, compared to $25\%$ for uniform allocation. It discovers $3.5\times$ more impact-weighted failures (215.4 vs. 62.2) with the same number of trials, delivers $5\times$ the discovery per dollar, and cuts the budget wasted on scenarios that never fail from $34\%$ to $2.8\%$. The rest of our analysis demonstrates and qualifies this result: a budget sweep shows the advantage shrinks as the budget approaches the corpus size, and paired significance tests show that scenario context helps mainly at small budgets while posterior-based exploration helps at moderate ones. Risk-aware adaptive allocation therefore helps most exactly where evaluation budget is scarcest.

Remote photoplethysmography (rPPG) enables non-contact physiological measurement but remains vulnerable to domain shifts from illumination, motion, and sensors. We propose FLOW (Feature-Level Optimal Warping), an optimal transport–driven framework for domain-generalized rPPG. FLOW integrates a Temporal Refinement Module (TRM) to stabilize temporal dynamics and a Prototype-based Cross-Temporal Optimal Transport (PCOT) module to achieve domain-invariant alignment via learnable prototypes.Beyond feature alignment, FLOW employs soft cross-temporal correspondence modeling that aligns temporal features in a flexible manner, allowing the model to respect and preserve the intrinsic rhythmic patterns of physiological signals. Moreover, the lightweight design of our modules allows seamless integration into existing end-to-end rPPG architectures without additional preprocessing. Two regularization terms further enforce source consistency and identity preservation. Theoretically, we derive a generalization bound under conditional optimal transport. Extensive experiments across four rPPG benchmarks show that FLOW achieves state-of-the-art cross-domain performance with lightweight design and strong physiological fidelity.

Agent harnesses govern how large language models (LLMs) gather context, invoke tools, verify results, preserve state, and terminate, largely affecting agent performance. However, the value of each harness mechanism can differ across heterogeneous tasks: a mechanism that improves one task may impose overhead or context distraction on another, leading to the suboptimality of a global harness. We characterize this suboptimality as a mismatch induced by fixed mechanism choices, motivating task-specific harness construction. Nonetheless, generating harness code for each task introduces generation and debugging costs, with execution risks that can compound as more mechanisms are generated. To address those challenges, we introduce Harness Primitives, reusable harness mechanisms with clear application scope and composition contract mined from failed task trajectories. Based on Harness Primitives, we propose STITCH, a framework that Selects suitable primitives given Task Information and compiles them into Task-speCific Harnesses at test time. This separation enables task-specific harnesses without generating or repairing mechanism code at test time. Extensive experiments demonstrate that STITCH not only improves harness adaptability and robustness, but also scales with the primitive library size, boosting task success rates by up to 12 points over fixed harness baselines, surpassing human-designed harnesses like Codex CLI while maintaining a minimal test-time harness composition overhead of only 2.7%, 638 times more efficient than generating task-specific harnesses from scratch. Ultimately, our work demonstrates that building task-adaptive harnesses can be beneficial for completing diverse tasks and that building reusable primitives can be a promising path towards this goal.

Learning must acquire new capabilities while preserving both prior responsibilities and the capacity to learn again. We introduce Generalized Residual Closure (GRC), a framework for learning as recursive closure of future-relevant discrepancies: closing a residual establishes the conditions for subsequent prediction, interaction, and learning. Under a complete representation-relation description at a fixed learner-world boundary, persistent internal learning has two primitive modes: Transformation within a representation and revision of the Representation itself. We establish a local tangent decomposition under regularity assumptions and a criterion for when representation revision is necessary. In an affine model, we derive a necessary-and-sufficient condition for stability-plasticity compatibility and the unique solution of a constrained quadratic update problem, which preserves registered old responsibilities while reducing residuals with an effective safe response. We prove that reconstructive semantic protection weakly enlarges the safe-response operator relative to preserving an exact historical realization. Dynamic sufficiency and future-closure viability extend representation adequacy from current prediction to lawful future updating and continued learning. Growth Learning expands the lawful closure domain or lowers optimal closure cost without regression of the registered capability-cost frontier; a conditional commit rule maintains this order. Restricted-sector recoveries and a conditional representation theorem connect the framework to optimization, machine learning, and control. Together, these results organize adaptation, representation revision, and reusable capability within a common account of continued learning.

We continue the study of the Stoquastic Local Hamiltonian problem, a physically motivated restriction of the QMA-complete Local Hamiltonian problem (Kitaev, Shen, and Vyalyi, 2002). For the $\beta$-gapped, frustration-free case, Bravyi, Bessen, and Terhal (2006) showed that the problem is MA-complete when $\beta = 1/\mathrm{poly}(n)$. Aharonov and Grilo (2019) derandomized this algorithm and proved membership in NP for constant gap $\beta = \Omega(1)$. We present an improved algorithm and analysis, establishing membership in NP even when $\beta = \Omega(1/(\log\log n))$. We complement our result with an explicit example demonstrating why the analysis does not extend directly to $\beta = o(1/\log\log n)$.

Large language models often know the truth and say otherwise: a model that answers correctly when asked neutrally will affirm a user's mistaken belief, or misstate a fact its system prompt wants hidden, once the context rewards it. Such deception is a behavior conditioned on context, not knowledge, yet machine unlearning, the natural tool for removing a behavior from the weights, is built to forget facts that a deceptive model still needs. We propose to unlearn when a model deceives rather than what it knows, with a contrastive forget unit built from the model's own realized deceptions: the same question under a deception-triggering and a neutral context, admitted only where belief holds and behavior flips. Standard objectives on this unit face a dilemma. Suppression objectives such as NPO leave much of the deception in place. Target-based objectives, which distill the model's neutral behavior into the pressured context, remove it but induce context blindness: a target generated without the context teaches the model to stop reading it, eroding benign system-prompt instructions, secret-keeping and the reasoning a monitor inspects, a failure invisible to deception rates and capability benchmarks. We introduce PACT, which trains toward pressure-aware counterfactual targets (the model's own honest response, with a trace that registers the pressure and resists it) while retaining the benign uses of the triggering context. On two 32B reasoning models, PACT reduces held-out deception from over 50% to under 3% while system-prompt adherence, secret-keeping and the reasoning trace stay at the base model's level. On a tug-of-war score of removal against retention, PACT reaches 0.94 and 0.86, against at most 0.77 and 0.60 for any baseline. Like removed knowledge, removed deception is shallow under relearning, and terms that simulate the attacker hold it only at a cost in context use.