Papers

Mathematical problem solving often requires deterministic computational steps that agents delegate to tools and implicitly trust. Yet tools can fail silently, returning plausible but incorrect results. How well can agents detect and correct corrupted tool call outputs? We study this through a controlled corruption framework where a hidden interceptor replaces tool call results with plausible incorrect information on targeted problems. We evaluate agents across 31 problems under four verification designs including no verification (baseline), mandatory same-context reflection, optional fresh-context verification, and optional structural verification. Without verification, corruption causes dramatic accuracy loss, from 100% down to 72.4%. Mandatory reflection fully recovers this performance to 100%. Optional verification improves accuracy only when models actively invoke it. Our results show that checking frequency is strongly associated with robustness differences, while unequal invocation prevents a controlled comparison of verifier quality. A supporting recovery experiment shows that full problem restart succeeds in 100% of cases after explicit detection. These findings demonstrate that verifier availability and verification policy are separate components of mathematical-agent reliability. Mandatory policies enforce verification while optional policies depend on the model's own choice to invoke it.

We study object reallocation problems with single-peaked preferences. On the unrestricted domain of strict preferences, top trading cycles (TTC) is the unique rule that satisfies efficiency, individual rationality, and strategy-proofness. On the single-peaked preference domain, the crawler introduced by Bade (2019) satisfies the same properties. We show that the Nash equilibrium allocations of the crawler's direct revelation game form a complete lattice under weak Pareto dominance. The truthful allocation is the greatest element of this lattice, while the initial endowment allocation is its least element.

Natural-language access to RDF knowledge graphs is a core Semantic Web ambition. Large language models (LLMs) have advanced Text-to-SPARQL, yet on unfamiliar graphs they often generate valid queries that misrepresent the populated data model. QRAKEN is a training-free, ontology-agnostic neurosymbolic pipeline grounding generation in empirical graph evidence rather than schema expectations. An offline distiller produces TTQL, a compact description of populated multi-hop patterns, conditional frequencies and path-conditioned literal examples, plus a class-property co-occurrence matrix. Online, TTQL guides the LLM, while deterministic syntax, vocabulary and data-model checks provide diagnostics for iterative refinement. On CK25 (First International Text2SPARQL Challenge), under matched-condition recomputation on a QLever snapshot, QRAKEN achieves strict F1 of 0.643 $\pm$ 0.026 with GPT-4.1 mini and 0.652 $\pm$ 0.012 with GPT-5.4: relative gains of 30% and 32% over the strongest recomputed participant, outperforming systems using the same base model family. Ablations identify TTQL patterns as the dominant driver (+0.31 strict F1 over a shape-only baseline); the refinement loop provides a cheap safety net, rejecting triple patterns unsupported by the co-occurrence matrix. Compared with auto-derived SHACL, TTQL yields 64% higher strict F1, supporting the value of empirical patterns beyond schema exposure. With two local 35B 4-bit open-weight models at zero marginal cost, the same pipeline matches the strongest recomputed participant, and TTQL advantages over shape-only and SHACL baselines persist. Results on a single, relatively small benchmark provide an initial empirical signal; monolithic TTQL injection on very open cross-domain graphs remains the main limitation.

We define an intrinsic unital completely positive (ucp) map from the Cuntz algebra to the Pythagorean with finitely many generators. This permits to lift states and cyclic representations. This process restricts to the Cuntz-Toeplitz algebras and the contraction algebras. Taking inductive limits we obtain an effective machinery for constructing states on the infinite Cuntz algebra $\mathcal O_\infty$. Combining this approach with previous techniques of the first author we obtain large families of pairwise inequivalent irreducible representations of $\mathcal O_\infty$: one family being in an obvious bijection with the unit sphere of Hilbert's space.

Developing reliable models for clinical tasks, such as Medical Question Answering (QA), is severely constrained by the limited availability of high-quality, expert-annotated training data. This challenge is exacerbated by stringent privacy requirements and the impracticality of utilizing large open-source corpora or proprietary cloud APIs within resource-limited clinical settings. To address these obstacles, we introduce SAGE (Semantic Anchor-Guided Evolution), a novel data synthesis framework that enables small, locally deployed models to generate high-quality medical training data. SAGE leverages lightweight, publicly available taxonomies such as MeSH as semantic anchors, imposing a structured prior to effectively guide and ground the data generation process. At its core, SAGE iteratively interleaves atomic (individual concept-based) and associative (relation-based) synthesis, bootstrapping training data from minimal seeds. This approach eliminates the need for large collections of medical documents or reliance on external APIs, providing a practical solution for on-premises data creation. Extensive experiments across multiple medical question-answering benchmarks demonstrate that models fine-tuned with SAGE-synthesized data consistently outperform those trained using self-derived or conventional document-based paradigms, highlighting tangible improvements in data efficiency and resource utilization for medical LLM development. Code is available at https://github.com/DIaacKr/SAGE.

Canonical approaches in causal inference treat model specification as fixed, assuming that researchers directly translate all relevant domain knowledge into a causal model, which can then be used to deduce its logical implications. Yet, in practical applications, model specification is often an iterative process, and involves exploration and introspection: of the many aspects of the phenomenon one could investigate, which ones actually matter for the identification of the causal effect of interest? In this paper we study the problem of iterative identification in partially specified causal models. We focus on determining where observing variables that intercept a direct effect or a confounding path between two variables could enable identification in semi-Markovian models. We give necessary and sufficient graphical conditions for when observing such variables can render an unidentifiable query identifiable, together with an efficient algorithm for locating all such opportunities in a given causal diagram. Our results can help analysts better navigate the model space by drawing attention to the parts of their substantive knowledge that could result in a successful identification strategy.

For two bigraded spaces $k^{m||n}$ and $k^{n\wedge m}$ equipped with appropriate quadratic Poisson structures, Koszul duality identifies the mixed Poisson differential calculi and, in the unimodular case, their Poisson cohomologies as Batalin–Vilkovisky algebras. In the current paper we prove that Koszul duality induces an isomorphism of Batalin–Vilkovisky algebras between their Poisson cohomologies when the modular derivation of one algebra is diagonalizable, including non-unimodular cases.

IPv6 extension headers (EHs), such as fragmentation, segment routing, and in-situ telemetry, are operationally important yetwidely dropped in transit, and characterising their behaviour from packet captures is a recurring measurement problem. We ask whetheran explainable miner can recover human-readable rules of EH behaviour, and we contribute two reusable tools: a negative-control protocol that diagnoses whether a mined "temporal" network rule reflects genuine cross-packet dynamics or mere within-packetco-occurrence, and a sender-conditioned, per-family EH-retention measurement. Applying an interpretable temporal-logic rule miner to the JAMES paired-vantage dataset, we recover a portable Fragment-EH rule that the protocol reveals to be a within-packet,near-definitional co-occurrence rather than a temporal pattern, so the temporal-logic machinery does no work for this dominant rule;the retention measurement independently recovers the expected within-window ordering of EH observability. Our main result istherefore an honest, controlled negative finding, corroborated by executed decision-tree and large-language-model baselines: on theevaluated JAMES traces network-temporal structure does not carry the dominant Fragment-EH signal, and we supply the controls thatestablish when it would, validated on a synthetic positive control containing a genuine cross-packet dependency.

In semantic query engines, predicates are evaluated by machine-learned models, and the choice of a query plan affects not only the cost of a query but also its result. Existing systems either apply a fixed threshold to each semantic operator or tune accuracy per operator, without accounting for how errors propagate through joins. We give a formal problem definition for cost-accuracy optimization of such queries. Our starting point is the calibrated confidence that decision models such as Jev attach to each decision. It yields an expected error for every decision; weighting these errors by each decision's contribution to the output (in the simplest case, its fan-out) gives the expected output quality of a plan without any labeled data, and the same computation in reverse turns an output-level accuracy target into a price on each base or intermediate tuple. Building on this, we define an oracle semantics for relational algebra with semantic operators, physical plans as pairs of a logical plan and a decision policy, declarative output-level targets, and a hierarchy of plan equivalence. We show that accuracy is plan-invariant under pointwise-deterministic policies, and that selection pushdown is not quality-sound when escalation bands are calibrated on the plan's own candidates. Expected quality can be computed in polynomial time under bag semantics; under set semantics it follows the dichotomy of tuple-independent probabilistic databases when every relation carries a semantic predicate. Choosing which tuples to drop is NP-hard, while the optimization problem decomposes into per-tuple decisions through two Lagrange multipliers, and, with what we call confidence-centric skipping, tuples that can no longer affect the target are skipped without being scored. Simulations on a synthetic workload illustrate these effects; an evaluation on real engines is left for future work.

Phase-field equations are fundamental examples of gradient-flow systems and require numerical solvers that preserve intrinsic energy dissipation. In this work, we propose a neural network-based method that combines an SAV time discretization with a mesh-free neural representation. We establish the unconditional energy stability of the underlying SAV semi-discretization, quantify the energy defect caused by solver residuals, and derive a conditional high-probability error estimate for the Allen–Cahn equation. Numerical experiments show that our approach consistently exhibits energy-stable behavior, while outperforming existing neural network-based solvers.

This paper studies an entropy Bregman alternating direction method of multipliers (BADMM) with logarithmic dual update for solving discrete optimal transport (OT) problems. The algorithm uses simple row and column normalizations without inner iterations, allowing efficient CPU and GPU implementations. However, the convergence of this method for general OT problems has not been established. Starting from a strictly positive feasible primal point and a zero multiplier, here we establish the $R$-linear convergence of the primal–dual sequence for general OT costs with any fixed multiplier stepsize in $(0,2)$ and a sufficiently large fixed penalty, even when the primal limit lies on the boundary. Our analysis further characterizes the primal limit as the entropy Bregman projection of the initial point onto the optimal solution set and establishes strict complementarity of the limiting OT primal–dual solution. For separable costs on two-dimensional grids, we exploit the separable structure to accelerate matrix–vector products and reduce storage requirements. Numerical experiments show competitive performance of our BADMM for general cost matrices with substantial speedups over state-of-the-art solvers, including HOT and HALO, for squared Euclidean costs on two-dimensional-grid marginals. The largest tested problem, with $2048\times2048 \approx 4.19$M grid points in each marginal, is solved in approximately 100 seconds on a single GPU.

The clinical integration of AI systems in digital dermatology relies heavily on human trust. Clinically interpretable visual concepts can act as intermediate representations enhancing trust and reliability. However, research in this domain is currently limited by scattered, heterogeneous dataset annotations. In this work, we introduce SkinLex, a harmonized dataset of 48 clinical morphological attributes across four public datasets (SkinCon, DermaCon-IN, MM-Skin, and PASSION) for a total of 20,411 records. Supervised nine-partition classification of skin conditions shows that limiting features to specific visual groups, like shapes or colors alone, reduces diagnostic accuracy. Bootstrapped backward elimination reveals that the set of 48 visual concepts has some degree of redundancy for algorithmic nine-partition diagnosis on the examined dataset. This demonstrates that coarse diagnosis on the selected dataset requires a relatively small but varied combination of clinical concepts, and motivates further research to improve concept taxonomy. Results can be translated into clinical benefits by reducing inputs for concept-based models, improving efficiency for annotation and modeling, and further enhancing interpretability. Code and prompt templates are available at https://github.com/Digital-Dermatology/SkinLex.

Speech-LLMs often exhibit prompt overfitting, where models solely trained on automatic speech recognition (ASR) instruction fail to generalize to new instructions such as speech translation and continue to behave primarily as ASR system. We propose DirectSpeech2LLM, a simple end-to-end framework that preserves the instruction-following ability of the LLM on unseen tasks when conditioned on speech. It computes distance-based CTC loss over the frozen LLM embedding matrix and uses greedy CTC labels to derive geometrically and temporally aligned speech embeddings respectively as an input to the LLM. Trained solely on 960 hours of LibriSpeech ASR data, DirectSpeech2LLM outperforms the cascaded system on ASR (seen task) and generalizes zero-shot to speech translation and emotion recognition (two unseen tasks), closely matching the cascaded system upper bound on these two new instructions despite seeing neither during training. We also find that geometric alignment strength plays a smaller role than previously assumed, as our modified CTC loss is shown to provide sufficient implicit geometric grounding without requiring an explicit regression loss. Results are consistent across two LLM families and scale with both more training data and model capacity.

The high abundances of heavy elements in early, extremely metal-poor stars is still an unsolved issue in Galactic Chemical Evolution (GCE). Standard approaches, such as mergers of neutron stars, have several difficulties, and several non-merger production channels are under discussion. Here, we suggest that pre-enriched inflow might explain the heavy elements seen in low metallicity stars in the Galaxy. To characterize the conditions of the origin of such a pre-enriched infall, we apply a heavy-element freeze-out approach. We characterize the initial distribution by Lagrange parameters which are nonequilibrium generalizations of temperature and chemical potentials. We then speculate about the origin of such a pre-enriched infall: The required nonequilibrium conditions might be found in cosmological fluctuations in the early Universe, and might be connected to the formation of primordial black holes.

There are reasons to believe that the region of uniform curvature that we observe within our horizon is perhaps a tiny patch, much smaller than the length scales of inhomogeneity and global connectivity of an extremely complicated manifold. However, the recent supernova (SN) results suggest that the horizon scale could be comparable to or even much larger than curvature radius. Non trivial global structure too tends to be of the order of the local curvature scale. Probing (slightly) beyond the cosmic horizon can potentially reveal nontrivial global structure lurking around or just beyond the horizon scale. The cosmic microwave background (CMB) anisotropy is a sensitive probe of the universe on length scales up to and somewhats beyond the horizon scale and is perhaps poised to detect or put interesting limits on nontrivial features the global structure. This point is exemplified by high CMB anisotropy signal of the Elliptical topology in a large fraction of the revised parameter space of the closed FRW universe (spherical geometry) currently preferred by SN observations.

LLM tool-use agents operate in dynamic environments where many actions carry operational risk. However, most safety mechanisms react only after errors manifest. Existing pre-emptive approaches either fine-tune the agent on chain-of-thought deliberation or compile natural-language guardrails into runtime checks, but they do so without exposing a structural, auditable verdict. We propose POLAR, a guardrail framework for small tool-calling agents that assesses reversibility through a structured two-layer ontology. POLAR assigns each action a graded reversibility score by deriving a candidate inverse sequence; calls failing a threshold are pruned before execution. Evaluated on $\tau^2$-bench across six agent models, POLAR improves mean task reward by 0.11 to 0.18 points on airline for four of six agents, but only eight of eighteen model–domain cells improve overall; retail and stronger agents often regress. POLAR provides an auditable structural check and characterizes its task-utility trade-offs. Reward is not a direct measure of prevented harm.

Magnonics investigates the dynamic excitations of magnetically ordered media, known as spin waves, and their application in functionalized devices. To efficiently control spin wave based devices minimizing losses and interferences from unwanted reflections, a clear picture of the scattering mechanism is needed. Here, we focus on the reflection of spin waves produced at the interface between two ferromagnetic media. We show that it is possible to understand the reflection mechanism based on the continuity of the angular momentum density flux. This constraint allows us to analytically compute the reflection coefficient and the stationary wave envelope in the first medium, as well as the damped propagation in the second. In addition, the analytical expressions are compared with full micromagnetic simulations, showing excellent agreement.

Fourier-domain beamforming methods, such as filtered backpropagation (FBP), are beneficial in ultrafast plane-wave imaging due to their computational efficiency and high image quality. These methods use the Fourier diffraction theorem (FDT) for steered plane waves to exactly invert linear scattering models. However, these models rely on simplifying assumptions that degrade image quality. The use of linear transducer arrays, in particular, requires: (i) a two-dimensional space, and (ii) lossless tissues. Herein, Laplace-domain beamforming is proposed. This method retains the computational efficiency of the Fourier-domain methods while improving image quality for linear arrays. Specifically, the method uses a generalization of the FDT, here called Laplace diffraction theorem, to account for three spatial dimensions, finite array element heights, and lossy tissues. A phantom experiment showed that the proposed method improves image uniformity, spatial resolution, and contrast compared to FBP. Using three steering angles, the lateral and axial -6 dB-widths of wires reduced by up to 12% and 25%, respectively, while the contrast of anechoic regions improved by up to 9%.

A pronounced pyramid-shaped enhancement in the axion density power spectrum induced by the QCD phase transition is identified. The enhancement occurs near the horizon scale at the transition, with a characteristic comoving length scale comparable to the size of the Solar System, and amplifies the axion density perturbation by factors exceeding $3.5 \times 10^{13}$ relative to the CDM case. Under the hilltop initial condition, coupling to radiation triggers this enhancement. The initial condition is related to the axion mass, suggesting that observation of the axion pyramid in cosmology may constrain the QCD axion mass.

Standard causal identification methods often assume no unmeasured confounding and can fail when relevant confounders are unobserved. Proximal causal inference instead uses proxy variables to identify effects under hidden confounding. However, nonparametric proximal estimation can be challenging in practice: recovering causal estimands such as the conditional average treatment effect (CATE) requires solving an ill-posed integral equation that is data-hungry, hyperparameter-sensitive, and optimization-unstable. Bayesian inference for such models provides a desirable alternative, mitigating these difficulties by regularizing through the prior. However, computing a posterior is itself challenging, as a typical likelihood function will include latent variables. Following the recent success of tabular foundation models in backdoor, instrumental variable, and frontdoor settings, we propose that prior-data fitted networks (PFNs) are uniquely suited to resolve this bottleneck. Indeed, by training on synthetic data sampled from compliant structural causal models with access to oracle counterfactuals, we simplify the task substantially, amortizing the implied Bayesian operator inversion into a single transformer forward pass. Compared to prior literature that focuses primarily on point estimation, our model, ProximalFM, explicitly targets the Bayesian posterior distribution of the CATE. One unique aspect of this problem is that we need to provide Monte Carlo estimates of the oracle CATEs, leading to a novel variation of PFNs that accounts for the added stochastic error. Across a diverse suite of proximal regimes, ProximalFM achieves consistently strong CATE-estimation performance without dataset-specific tuning, with its largest advantage when latent confounding is substantial and the proxies are weakly informative; it also provides fast inference through a single amortized forward pass.

Reinforcement learning with verifiable rewards (RLVR) turns agent experience into learning signals primarily through scalar outcome rewards after interaction. For group-relative objectives, however, this signal vanishes when all rollouts receive the same reward, even though their trajectories may reveal useful information about what the task requires and how the agent fails. We ask a complementary question: can hindsight teach an agent what it could have anticipated before acting? We introduce prospective learning, which uses post-hoc experience to supervise foresight predictions from the pre-interaction view, and instantiate it with Self-Retrospection Distillation (SRD). Intuitively, a completed trajectory reveals knowledge that would have been useful and pitfalls that should be avoided; SRD distills this privileged hindsight into trajectory-blind foresight of the same policy. Foresight serves only as a training target and need not be explicitly generated at inference time. Across 10 tool-integrated reasoning and long-horizon agentic tasks, SRD complements RLVR and self-distillation baselines with gains of up to 24.2 pp. Its advantage is especially pronounced when reward contrast is scarce: when 37–98% of rollout groups are reward-uniform across model scales, yet SRD can still exploit learning signal from sampled trajectories. In the 2B setting, where 98% of groups are all-failure, the RLVR training ends up at 0.0% success, while adding SRD reaches 60.6% under the same rollout budget. Our results suggest that post-hoc agent experience is useful not only for evaluating or improving behavior, but also for shaping predictive representations before available interaction. Training code can be found at https://github.com/SalesforceAIResearch/SRD.

Frontier LLM agents have been shown to be capable of solving increasingly complex tasks for which humans have measurable solutions. This begs the pertinent question of whether LLM agents can go beyond what humans have already solved. The ability to develop sophisticated strategies to tackle consequential problems becomes paramount as well-trodden, human-developed solutions become insufficient for problems for which we lack context or enough training data. We study agents' capability of such strategy formation through the communal practice of video game speedrunning. In speedrunning, practitioners compete to find the fastest way to complete a video game under certain conditions, and in so doing uncovering interesting unorthodox play styles that require a thorough understanding and mastery of the underlying game mechanics. We introduce SPEEDRUNBENCH, a benchmark that evaluates frontier LLM agents across 9 different games. To perform well in this benchmark, agents must repeatedly improve their strategy, reflect on their performance, exploit their gained knowledge, and reason across a long-horizon of actions to improve on an increasingly difficult problem: being faster than themselves and everyone else. Our experiments show that while frontier agents approach human world records in simple platformer games, they remain behind human performance on longer, more complex games under practical budgets. These results suggest that SPEEDRUNBENCH is a useful testbed for studying agents' strategy formation capabilities as well as being a saturation-resistant evaluation measure, as there is almost always a faster completion time waiting to be discovered.

Conditional neural fields represent signals continuously, but their effectiveness depends on how the conditional latent representations are inferred from observed data. In meta-learning, this encoding occurs through gradient updates induced by the decoder, tying representation learning directly to decoder design. We formalize this connection by interpreting latent optimization as an optimization encoder, unifying the roles of second-order differentiation, latent parameterization, and task supervision. This concept enables second-order meta-learning for end-to-end training of the encoding procedure alongside the decoder, and clarifies which learning pathway first-order approximations discard. Guided by this view, we introduce Attentive Latent Fields (MetaLF), an equivariant transformer-based neural field that contextualizes a latent pointcloud through self-attention. These interactions shape both field predictions and the updates that construct their representation, allowing local observations to inform coherent non-local structure. Disentangling the inner encoding objective from outer task supervision unifies reconstruction, classification, and segmentation within an end-to-end meta-learning framework, using reconstruction-only latent adaptation at test time. Controlled experiments on polynomial fields link latent coordination to lower effective rank and stronger alignment with the underlying function space. Across image and 3D shape reconstruction, MetaLF improves fidelity within three to five gradient updates, while supporting semantic prediction across images, shapes, and volumes. Together, these findings position the optimization encoder perspective as a unified basis for designing neural fields around how representations are constructed, coordinated, and used.

We study the Cauchy problem for a semilinear heat equation driven by the fractional harmonic oscillator. We establish local and global well-posedness in Orlicz and Morse–Transue spaces, based on sharp semigroup estimates and an integral compatibility condition between the Young function and the nonlinearity. We identify a critical Young function separating local well-posedness from instantaneous nonexistence for suitable data. Finally, we prove a confinement effect: under a Dini condition at the origin, small data yield global solutions decaying at the sharp exponential rate, with no Fujita-type restriction, in contrast with the corresponding free equation.

Estimating causal effects with missing outcomes requires learning outcome, exposure, and selection models. Flexible propensity learners can predict treatment or missingness well while worsening target estimation by emphasizing instruments, weak-overlap regions, or variation unrelated to outcome-regression bias. We propose a collaborative representation-based targeted learning method for recovered average treatment effects under outcome selection. The method learns low-dimensional exposure and selection representations from cross-fitted pseudo-outcomes that encode outcome-regression drift. A finite candidate library alternates targeted outcome updates with representation updates, and inner cross-validation selects representation complexity, collaboration strength, and regularization using a target-aware risk. We give high-level sufficient conditions for collaborative robustness, consistency, and asymptotic linearity after outer validation-fold targeting. Simulations show finite-sample bias reduction, with explicit bias-variance trade-offs across configurations and relative to competing estimators

We maximize the average torsional rigidity among open subsets of $\mathbb{R}^2$ with fixed inradius whose complements consist of pairwise disjoint balls of fixed radius $\varepsilon$ with mutual distances bounded below. We prove that, provided $\varepsilon$ is sufficiently small, the optimal value is asymptotically attained by sequences of domains whose complements exhibit a regular honeycomb structure. The proof is reduced, via Delaunay triangulations, to the analysis of a mixed Dirichlet–Neumann problem on triangular domains with circular cutouts at their vertices. Our approach is quite general and extends to other variational energies, such as the Cheeger constant, for which we also derive an explicit bound of the ratio $\varepsilon/$ inradius.

Zilber's celebrated quasiminimality conjecture states that a subset of $\mathbb C$ defined by polynomials and exponentials is either countable, or has countable complement. Koiran has asked whether the same could be true replacing $\exp$ with any unary entire function. We give a negative answer to Koiran's question, using results from the theory of holomorphic approximation.

Recent diffusion-based image generation backbones have grown substantially in scale, making the network inference cost increase rapidly. While diffusion distillation techniques can reduce the number of inference steps, high-quality image generation within a single full-backbone-forward compute budget remains challenging. Existing one-step methods typically allocate this budget to a single evaluation of a monolithic student. However, approximating the heterogeneous coarse-to-fine transport with a single monolithic mapping is difficult and often leads to over-smoothed outputs. To address this issue, we propose Phase-wise Velocity Distillation (PVD), which partitions the generation timeline into a coarse and a fine phase, and models the transition within each phase via the average velocity. A dedicated half-sized expert is assigned to each phase, decoupling structural composition from detail refinement while keeping the cumulative computation equivalent to one full-backbone forward pass. We show that the use of two half-sized phase-specific experts outperforms a single full-size monolithic student. On class-conditional image generation, PVD achieves an FID of 1.48 on ImageNet 256 x 256. On more complex text-to-image (T2I) tasks, PVD-distilled models (Stable Diffusion 3.5-Medium, FLUX.1-dev, Qwen-Image) produce results competitive with their multi-step teachers, significantly outperforming prior distillation methods. Moreover, across the evaluated T2I backbones, PVD reduces active parameters by 49.10-50.89% and peak VRAM by 45.76-48.36% compared to the corresponding teachers. Source code and distilled models are available at https://github.com/PolyU-VCLab/PVD.

A mean shift between two data sources can be easy to detect but hard to remove without substantially changing their representations. We cast its removal as a statistical decision problem: from noisy differences between paired calibration measurements in $\mathbb{R}^d$, learn one linear map, applied to both sources under a hard distortion budget, that leaves as little of the shift as possible on fresh data. We derive the exact finite-sample minimax risk over all such maps, $(d-k) \mathbb{E}[1/(d+2J)]$ with $J\sim\mathrm{Pois}(\kappa/2)$, where the budget allows deleting $k$ directions and $\kappa$ is the calibration signal-to-noise ratio. Projecting out the mean calibration difference attains it without knowing $\kappa$ or the noise scale. This exposes a detection-repair gap: detecting the shift needs only $\kappa\gg\sqrt d$, whereas removing a fixed fraction of it at constant distortion needs $\kappa\asymp d$, as for estimating its direction. Standard linear concept erasers (MP, SAL, LEACE) remove the same calibration difference, so the formula gives, before fitting, exactly how much shift they leave on fresh data and how much calibration a target requires. The limit is robust: pairing keeps it exact for non-Gaussian shared content, the projection keeps its guarantee under anisotropic noise, and selective abstention cannot close the gap. On paired clinical and wearable sleep EEG, where differences between participants act as calibration noise, the formula predicts the device shift left in new participants, and more recordings per person soon stop helping. Together, these results tell whether a correction that falls short needs a better method, more recordings, or more participants.

Realistic physical interaction is a cornerstone of embodied intelligence, yet collecting paired visual–tactile data remains costly. Visual-to-tactile synthesis offers a promising approach to augmenting such data, but learning this mapping is complicated by the gap between visual appearance and contact-related material properties, as well as spatial misalignment in paired observations. To address these challenges, we present PhysTacGen, a visual-to-optical-tactile image generation framework that integrates material-aware descriptions with geometric conditioning. First, we introduce Group Tactile Policy Optimization (GTPO), a reinforcement learning strategy that refines a vision–language model to generate structured material descriptions using task-specific rewards. Second, we combine DINOv2-based pair curation with monocular relative-depth estimation to select training pairs and provide geometric priors. Finally, an SDXL ControlNet synthesizes optical tactile images conditioned on RGB, relative depth, and GTPO-generated text. Experiments on curated SSVTP data demonstrate improved structural similarity over the compared baselines, while a blinded user study shows a preference for GTPO-generated descriptions. Generated tactile inputs also improve performance on an attribute-derived force-coefficient prediction proxy. Together, these results demonstrate the effectiveness of PhysTacGen for optical tactile image synthesis and its utility in the evaluated downstream task.The code will be available at https://github.com/VDIGPKU/PhysTacGen.