Papers

Per-instance algorithm selection (PIAS) takes advantage of complementarity between a set of algorithms by deciding which algorithm to run on a given instance. This decision is based on features of the instances, which, in the context of black-box optimization (BBO), require a part of the optimization budget to be computed. This raises two questions: (a) from which fraction of the budget spent on feature computation does PIAS become worth it for BBO, and (b) which fraction of the budget optimizes the tradeoff between feature accuracy and PIAS performance. To this end, we perform a broad study where PIAS with varying sampling budgets for feature computation is compared to the single best algorithm on a broad range of algorithm selection scenarios. These scenarios consist of two portfolio sizes, three problem sets, 4 dimensionalities, and 10 target budgets. We find that PIAS is viable for the majority of tested scenarios, even when as much as a quarter of the total budget is spent on feature computation. The tradeoff for the fraction of the budget spent on feature computation to maximize the benefit of PIAS is highly dependent on the specific AS scenario. Further, on average 20 percent of PIAS loss to the virtual best solver is explained by the budget spent on feature computation, highlighting the importance of properly accounting for the feature budget.

Sparse Mixture-of-experts (MoE) models enable scalable transformer architectures by activating only a subset of experts per token. Recent evidence suggests that performance improves with increasingly granular experts, i.e., many small experts instead of a few large ones. However, this regime substantially increases routing cost, which can dominate computation and memory. We introduce adaptive inverted-index routing for MoE (AIR-MoE), an inverted-index-inspired routing architecture based on vector quantization (VQ). In a first stage, AIR-MoE performs coarse shortlisting by assigning tokens to VQ codewords to construct a candidate set of experts. In a second stage, fine scoring computes exact routing scores restricted to this shortlist. This two-stage procedure approximates true top-K routing while avoiding full expert scoring and, in contrast to prior work, imposing no structural constraints on expert parameters. AIR-MoE serves as a drop-in replacement for standard routers and requires no modifications to the model architecture or loss function. We further provide a lower bound on the mass recall achieved by AIR-MoE that yields insights into the inner workings. Empirically, AIR-MoE improves the perplexity-FLOPs trade-off over existing MoE routers in regimes with up to more than a million tiny experts, and achieves consistent perplexity improvements over the best existing baseline.

Batch normalization (BN) is central to modern deep networks, but its effect on the realized function during training remains less understood than its optimization benefits. We study training-time BN in continuous piecewise-affine (CPA) networks through the geometry of switching hyperplanes and the induced affine-region partition. Conditioned on a mini-batch, we show that BN defines for each neuron a reference hyperplane through the batch centroid, and that breakpoint-switching hyperplanes are parallel translates whose offsets are expressed in batch-standardized coordinates and are independent of the raw bias. This yields an exact criterion for when a switching hyperplane intersects a local $\ell_\infty$ window and motivates a local region-density functional based on exact affine-region counts. Under explicit sufficient conditions, we show that BN increases expected local partition refinement in ReLU and more general piecewise-affine networks, and that this mechanism transfers locally through depth inside parent affine regions where the upstream representation map is an affine embedding. These results provide a function-level geometric account of training-time BN as a batch-conditional recentering mechanism near the data.

We study long-horizon deployment of a frozen predictor under dynamic covariate shift. A time-domain Poincare inequality first reduces temporal risk volatility to derivative energy. A Jacobian-velocity theorem then supplies the corresponding pathwise control. Given explicit regularity and domination assumptions, the theorem identifies directional tangent energy along the deployment path as the governing quantity. Under low-rank drift, that quantity reduces to directional Jacobian energy in the drift subspace, motivating drift-aligned tangent regularization (DTR) and a matched monitoring proxy. Rather than smoothing the network isotropically, DTR penalizes sensitivity only along estimated drift directions. We validate the theorem-to-method pipeline in four experiments: a synthetic benchmark for the time-domain inequality, a controlled synthetic comparison against isotropic Jacobian regularization, and two frozen-deployment studies on the UCI Air Quality and Tetouan power-consumption datasets. DTR reduces risk volatility and directional gain in the controlled low-rank regime and beats isotropic smoothing there. It also gives validation-selected deployment gains on both real datasets, with the Air Quality subspace estimated from target-orthogonal sensor motion. Moderate drift-subspace misspecification is tolerable while orthogonal misspecification largely removes the benefit.

Despite theoretical advantages, causal methods for Gene Regulatory Network (GRN) inference from single-cell RNA-seq data consistently fail to match or outperform correlation-based baselines in many realistic benchmarks, a persistent puzzle which casts doubt on the value of causality for this task. We argue that existing benchmarks are insufficiently controlled to answer this question because they evaluate on real or semi-real data where multiple pathologies co-occur, confounding failure modes, and obscuring the specific conditions under which different inference methods excel or fail. To address this gap, we introduce a controlled diagnostic framework that isolates seven biologically motivated pathologies (dropout, latent confounders, cell-type mixing, feedback loops, network density, sample size, and pseudotime drift) and measure how six representative methods spanning three inference paradigms degrade as each pathology intensifies. Across 6,120 controlled experiments, we find that causal methods genuinely dominate in clean and structurally favorable regimes, but specific pathologies (notably dropout and latent confounders) selectively neutralize their advantages. We further introduce an error-type decomposition that reveals methods with similar aggregate accuracy commit qualitatively different errors. To probe whether single-pathology effects persist when multiple stressors co-occur, we perform an interaction sweep over the three most impactful pathologies and find that their joint effects are sub-additive, while also exposing density-conditional cross-overs invisible to single-dial analysis. Our findings offer a nuanced understanding of when and why different methods succeed or fail for GRN inference, providing actionable insights for method development and practical guidance for practitioners.

Compositional generalization refers to correctly interpret novel combinations of known primitives, which remains a major challenge. Existing approaches often rely on supervised fine-tuning, which encourages models to imitate target outputs. This token-level training paradigm fails to capture the global compositional structure required for generalizing to unseen combinations. In this work, we investigate whether compositional generalization can instead be improved through outcome-level reinforcement learning. We adopt Group Relative Policy Optimization to optimize models based on feedback on their final outputs. Within this framework, we explore both a simple binary outcome reward and a composite reward that provides additional composition feedback. Experiments on multiple compositional benchmarks show that reinforcement learning improves compositional generalization compared to supervised fine-tuning. Further analysis reveals that supervised models tend to overfit frequent training compositions, whereas reinforcement learning improves compositional generalization by reshaping the output distribution, particularly for more complex composition types.

Strichartz inequalities are a cornerstone of the modern theory of dispersive PDEs, but their extremizers are known explicitly only in a handful of sharp cases. The non-convexity of the underlying functional makes the problem hard, and to our knowledge no systematic numerical attack has been attempted. We propose a simple neural-network-based pipeline that searches for extremizers as critical points of the Strichartz ratio, and apply it in three settings. First, on the Schrödinger group we recover the Gaussian extremizers of Foschi and Hundertmark–Zharnitsky in dimensions $d=1,2$ to within $10^{-3}$ relative error, with no analytical prior. Second, on $59$ further admissible pairs in $d=1$ where the answer is conjectural, the method consistently finds Gaussians, supporting the conjecture that Gaussians are the universal extremizers in the admissible range. Third, on the critical Airy–Strichartz inequality at $\gamma=1/q$, where existence is open, the optimization does not converge to any $L^2$ profile: instead, the iterates organize themselves as mKdV breathers $B(0,\cdot;\alpha,1,0,0)$ with growing internal frequency $\alpha$, and the discovered ratio approaches the Frank–Sabin universal lower bound $\widetilde A_{q,r}$ from below with a power-law gap $\sim\alpha^{-0.9}$. We confirm the same picture with an independent Hermite-basis ansatz. We propose a precise conjecture: the supremum equals $\widetilde A_{q,r}$ and is approached, but not attained, along the breather family. The pipeline thus serves both as a validator on known cases and as a discovery tool when no extremizer exists.

Learning tractable linear representations of nonlinear dynamical systems via Koopman operator theory is often hindered by dictionary selection, temporal memory encoding, and numerical ill-conditioning. Inspired by Reservoir Computing (RC) paradigm, this paper introduces the RC-Koopman framework, which interprets reservoir as a stateful, finite-dimensional Koopman dictionary whose temporal depth is explicitly controlled by its spectral radius. We show that the Echo State Property (ESP) guarantees well-posedness and favorable numerical conditioning of the lifted Koopman approximation. A correlation-based spectral radius selection algorithm aligns reservoir memory with dominant system timescales. Analysis reveals how the finite memory of the reservoir determines which Koopman eigenfunctions remain observable from the lifted features. Evaluation on synthetic benchmarks demonstrates that RC-Koopman achieves a favorable balance between reconstruction accuracy of the underlying nonlinear dynamics and dynamical stability, compared to Extended Dynamic Mode Decomposition (EDMD) and Hankel-based lifting approaches. Code available at: https://github.com/NEAR-the-future/RC-Koopman.git

Inductive Logic Programming (ILP) learns interpretable logical rules from data. Existing methods are transductive: their learned parameters are bound to specific predicates and require retraining for each new task. We introduce Neural Rule Inducer (NRI), a pretrained model for zero-shot rule induction. Rather than encoding literal identities, NRI represents literals using domain-agnostic statistical properties such as class-conditional rates, entropy, and co-occurrence, which generalize across variable identities and counts without retraining. The model consists of a statistical encoder and a parallel slot-based decoder. Parallel decoding preserves the permutation invariance of logical disjunction; an autoregressive decoder would instead impose an arbitrary clause order. Product T-norm relaxation makes rule execution differentiable, allowing end-to-end training on prediction accuracy alone. We evaluate NRI on rule recovery, robustness to label noise and spurious correlations, and zero-shot transfer to real-world benchmarks, and we believe this work opens up the possibility of foundation models for symbolic reasoning. Code and the reference checkpoint are available at https://github.com/phuayj/neural-rule-inducer.

LLM post-training typically propagates task gradients through the full depth of the model. Although this end-to-end structure is simple and general, it couples task adaptation to full-depth activation storage, long-range backward dependencies and direct task-gradient access to pretrained representations. We argue that this full-depth backward coupling can be unnecessarily expensive and intrusive, particularly when post-training supervision is much narrower than pre-training. To this end, we propose LoPT: Local-Learning Post-Training, a simple post-training strategy that makes gradient reach an explicit design choice. LoPT places a single gradient boundary at the transformer midpoint: the second-half block learns from the task objective, while the first-half block is updated by a lightweight feature-reconstruction objective to preserve useful representations and maintain interface compatibility. LoPT shortens the task-induced backward path while limiting direct interference from narrow task gradients on early-layer representations. Extensive experiments demonstrate that LoPT achieves competitive performance with lower memory cost, higher training efficiency and better retention of pretrained capabilities. Our code is available at: https://github.com/HumyuShi/LoPT

Tabular data synthesis aims to generate high-quality data while preserving privacy. However, we find that existing tabular generative models exhibit a clear tradeoff in the small-data regime: improving data quality typically comes at the cost of increased memorization of training samples, thereby weakening privacy protection. This tradeoff arises because small training sets make it difficult for dataset-specific generative models to distinguish generalizable structure from sample-specific patterns. To address this, we propose DiffICL, which formulates tabular data generation as an in-context learning problem. Instead of fitting each dataset from scratch,DiffICL leverages pretrained structural priors learned from a large collection of datasets, enabling it to infer data distributions from limited context rather than memorizing individual samples. We evaluate DiffICL on 14 real-world datasets. Results show that DiffICL improves both data quality and privacy, and generate synthetic data that provides effective data augmentation. Our findings suggest that the quality-privacy tradeoff can be improved through better training paradigms.

Electrospinning is a highly sensitive fabrication process in which small variations in operating parameters can significantly influence fiber morphology and material performance. Machine learning (ML) methods are increasingly employed to model these process-structure relationships and to identify the relative importance of processing variables. However, most existing studies rely on a single ML model, implicitly assuming that the resulting feature importance is robust and reproducible. In this study, the consistency of feature importance across multiple ML model families was systematically evaluated using a curated dataset of 96 polyvinyl alcohol (PVA) electrospinning experiments. Twenty-one ML models representing linear, tree-based, kernel-based, neural network, and instance-based approaches were trained and compared. To provide a unified interpretability framework, SHAP (SHapley Additive exPlanations) values were used to calculate feature importance consistently across all models. A rank-based statistical analysis was then performed to quantify inter-model agreement and assess the robustness of parameter rankings. The results demonstrate that predictive performance and interpretive reliability are fundamentally distinct properties. Although several models achieved comparable predictive accuracy, substantial differences were observed in their feature importance rankings. Solution concentration emerged as the most robust and consistently influential parameter (variability = 0), whereas flow rate and applied voltage exhibited high ranking variability (variability > 0.9), indicating strong model dependence. These findings suggest that feature importance derived from a single ML model may be unreliable, particularly for small experimental datasets, and highlight the importance of cross-model validation for achieving trustworthy interpretation in ML-assisted electrospinning research.

Large language models (LLMs) show strong potential for neural architecture generation, yet existing approaches produce complete model implementations from scratch – computationally expensive and yielding verbose code. We propose Delta-Code Generation, where fine-tuned LLMs generate compact unified diffs (deltas) to refine baseline architectures rather than synthesizing entire models. Our pipeline iteratively fine-tunes the LLM via LoRA on curated architectures from the LEMUR dataset, with MinHash-Jaccard novelty filtering for structural diversity. We evaluate three 7B-class LLMs – DeepSeek-Coder-7B, Qwen2.5-Coder-7B, and Mistral-7B – across six datasets (CIFAR-10, CIFAR-100, MNIST, SVHN, ImageNette, CelebA) using a 22-cycle protocol (1,100 candidates per LLM). All three substantially surpass the full-generation baseline (50.6% valid rate, 42.3% mean first-epoch accuracy): DeepSeek-Coder reaches 75.3% valid rate and 65.8% mean accuracy; Qwen2.5-Coder 72.1%/64.6%; Mistral 66.6%/66.1%. On CIFAR-10, best first-epoch accuracies reach 85.5% (Mistral), 85.2% (DeepSeek), 80.6% (Qwen) – well above 63.98% full generation and 71.5% for the concurrent approach of Gu et al. Output lengths are 30-50 lines versus 200+ for full generation (75-85% reduction). A 50-epoch study confirms the 1-epoch proxy preserves rankings (Mistral: Spearman $\rho$ = 0.926). Delta-based generation is a token-efficient, multi-domain, LLM-agnostic alternative to full-model synthesis for LLM-driven NAS.

GPT-style language models are sensitive to single-token changes at generation points where the predicted probability distribution is spread across multiple tokens. Viewing this sensitivity as a geometric property, we derive an $\mathfrak{so}(n)$-valued 1-form that depends only on the geometry of the token embeddings. Despite this purely geometric origin, we show that its curvature is semantically meaningful: On chess reasoning tasks, the curvature couples to the world model of an off-the-shelf instruction-tuned model, with transformations clustering by board region and respecting piece importance. Our findings suggest that token space geometry directly reflects how models internally represent problems.

Published transfer-BO comparisons often estimate an average treatment effect of acquisition choice over hidden regime variables, while practitioners need the conditional effect for their specific prior quality, budget ratio, and metric. An audit of 40 transfer-BO papers from NeurIPS, ICML, ICLR, AISTATS, UAI, TMLR, JMLR, and AutoML-Conf (2022-2025) finds that 98% never vary B/|A| as a controlled axis. On the same GDSC2 benchmark, changing only the budget reverses the ranking: at B=50, Greedy outperforms UCB by 0.050 Hit@1, while at B=100, UCB outperforms Greedy by 0.035. We capture this transition with the Portable Regime Score PRS=(B/|A|)(1-rho), where rho is the prior rank correlation and can be estimated from pilot contexts before the main comparison. Across 79 conditions spanning chemistry, drug-response biology, and HPO, a hierarchical model gives beta=0.50 (p=1.1e-9), and 19% of conditions fall in an equivalence zone where |advantage|<0.01 Hit@1. In five published reversal cases, PRS predicts the winner from pre-comparison observables. A No-Free-Leaderboard proposition explains why unconditional rankings are unstable: when CATE changes sign across regimes, the reported ATE becomes a function of benchmark mixture. RegimePlanner, which estimates rho online and switches acquisition accordingly, wins all 16 HPO-B search spaces at B=100 and exceeds the matched {Greedy,UCB} per-context oracle on GDSC2 by 18%. Pre-registered predictions achieve 27/40=67.5% overall accuracy and above 90% within EMA prior families. The practical protocol is simple: report B/|A|, rho, K, and metric alongside any claimed acquisition advantage.

Every attention head defines a degree-normalized transport operator, and a growing family of diagnostics reads model behavior (hallucination among them) from its spectrum. We ask what such diagnostics can and cannot infer. The operator splits orthogonally into a symmetric part governing transport capacity and an antisymmetric part encoding orientation. We prove an identifiability limit: every transpose-invariant spectral diagnostic is orientation-blind (unable to distinguish an operator from its transpose, hence blind to the orientation of information flow), with a transpose-stability bound limiting any Lipschitz diagnostic's transpose sensitivity by the asymmetry coefficient $G$. This bounds what spectral diagnostics of the attention operator can resolve (e.g.\ LapEigvals and the attention-spectral branch of LLM-Check). On the surviving axis, a closed-form bipartite-Cheeger landscape shows uniform causal attention obeys an $n$-independent temporal-cut floor $\phi \ge 1/5$ while window attention pierces it as $O(w/n)$; the floor is an idealized benchmark, not an empirical attractor, and the fraction of real heads falling below it is itself an empirically stable architectural descriptor. The two-axis diagnostic ($\phi$ for capacity, $G$ for asymmetry magnitude) yields a falsifiable polarity prediction, borne out in sign under length-controlled, forced-scoring evaluation across decoder-only, encoder-only, and encoder–decoder models (capacity-axis signal 0.62–0.84 LC-AUROC): polarity reverses between HaluEval and MedHallu, directionally as predicted though asymmetric in strength, with decision polarity calibrated per regime.

Automated glaucoma detection is critical for preventing irreversible vision loss and reducing the burden on healthcare systems. However, ensuring fairness across diverse patient populations remains a significant challenge. In this paper, we propose FairEnc, a fair pretraining method for vision-language models (VLMs) that enables simultaneous debiasing across multiple sensitive attributes. FairEnc jointly mitigates biases in both textual and visual modalities with respect to multiple sensitive attributes, including race, gender, ethnicity, and language. Specifically, for the textual encoder, we leverage a large language model to generate synthetic clinical descriptions with varied sensitive attributes while preserving disease semantics, and employ a contrastive alignment objective to encourage demographic-invariant representations. For the visual encoder, we propose a dual-level fairness strategy that combines mutual information regularization to reduce statistical dependence between learned features and demographic groups, with multi-discriminator adversarial debiasing. Comprehensive experiments on the publicly available Harvard-FairVLMed dataset demonstrate that FairEnc effectively reduces demographic disparity as measured by DPD and DEOdds while achieving strong diagnostic performance under both zero-shot and linear probing evaluations. Additional experiments on the private FairFundus dataset show that FairEnc consistently preserves fairness advantages under cross-domain and cross-modality settings and maintains diagnostic performance within a competitive range. These results highlight FairEnc's ability to generalize fairness under distribution shifts, supporting its potential for more equitable deployment in real-world clinical settings. Our codebase and synthetic clinical notes are available at https://github.com/Mohamed-Elhabebe/FairEnc

Recent research has revived and amplified interest in algorithms for undiscounted average reward reinforcement learning in infinite-horizon, non-episodic (continuing) tasks. Semi-Markov decision processes (SMDPs) are of particular interest. In SMDPs, discrete actions stochastically generate both rewards and durations, and the objective is to optimize the average reward rate. Existing algorithms approach this by optimizing the ratio of rewards to durations. However, when rewards and durations are non-stationary (in the infinite horizon), this can be incorrect. This paper presents a novel modified harmonic mean operator that correctly computes reward rates even under such conditions. This yields model-free learning algorithms that can work with SMDPs, while maintaining robustness to non-stationary reward and duration distributions over time. We prove theoretical properties of the modified harmonic mean operator, and empirically demonstrate its efficacy in comparison to existing algorithms.

Multimodal emotion recognition (MER) benefits from combining text, audio, and vision, yet standard fusion often fails when modalities conflict. Crucially, conflicts differ in resolvability: benign conflicts stem from missing, weak, or ambiguous cues and can be mitigated by cross-modal calibration, while severe conflicts arise from intrinsically contradictory (e.g., sarcasm) or misleading signals, for which forced fusion may amplify errors. Recognizing this, we propose Dual-Path Conflict Resolution (DCR), a unified framework that learns when to fuse and when to drop modalities. Path I (Affective Fusion Distiller, AFD) performs reverse distillation from audio/visual teachers to a textual student using temporally weighted class evidence, thereby enhancing representation-level calibration and improving fusion when alignment is beneficial. Path II (Affective Discernment Agent, ADA) formulates MER as a contextual bandit that selects among fusion and unimodal predictions based on a dual-view state and a calibration-aware reward, enabling decision-level arbitration under irreconcilable conflicts without requiring per-modality reliability labels. By taking into account the full multimodal context and coupling soft calibration with hard arbitration, DCR reconciles conflicts that can be aligned while bypassing misleading modalities when fusion is harmful. Across five benchmarks covering both dialogue-level and clip-level MER, DCR consistently outperforms competitive baselines or achieves highly competitive results. Further ablations, conflict-specific subset evaluation, and modality-selection analysis verify that AFD and ADA are complementary and jointly improve robust conflict-aware emotion recognition.

Direct Preference Optimization (DPO) has proven to be an effective solution for mitigating hallucination in Multimodal Large Language Models (MLLMs) by learning from preference pairs. One of its key challenges lies in how to transfer the sequence-level preference into fine-grained supervision on visual fidelity. To safeguard vision-related tokens that are prone to hallucination, existing methods typically allocate training emphasis according to the model's self-assessed visual sensitivity signals. However, such sensitivity, estimated by a model still under training, introduces self-referential bias: reinforcing already well-learned visual cues while neglecting hard-to-perceive but critical details, thereby limiting deeper alignment. In this work, we propose an Uncertainty-aware Exploratory Direct Preference Optimization (UE-DPO) method for MLLMs, which enables the model to uncover its cognitive deficiencies and actively explore for self-correction, guided by token-level epistemic uncertainty. Specifically, we first quantify the uncertainty from the model's failure to ground token predictions in the given image. Then, based on an uncertainty-aware exploration intensity, we encourage more learning pressure on visually deficient tokens in preferred samples, and alleviate the over-penalization of beneficial knowledge in dispreferred samples. Further, we provide a theoretical justification for our method, and extensive experiments demonstrate its effectiveness and robustness.

We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error. A base low-regularity integrator provides a consistent first-order approximation to nonlinear dispersive PDEs, while a lightweight neural network, operating on a low-dimensional latent manifold, learns the residual defect that analytical methods cannot close. An explicit time-step scaling on the neural correction ensures that its Lipschitz contribution remains $\mathcal{O}(\tau)$, yielding a Gronwall stability factor bounded uniformly in the step size and independent of the spatial resolution. The network is trained end-to-end through a solver-in-the-loop objective that unrolls the full iteration and penalises trajectory error in a Bourgain-type norm, aligning learning with multi-step solver dynamics rather than isolated one-step targets. Under stated assumptions, the global error satisfies $C(\varepsilon_{net}+\delta)\,\tau^\gamma\ln(1/\tau)$, where $\varepsilon_{net}$ measures the network approximation quality and $\delta$ the training shortfall. Experiments on three dispersive benchmarks with rough data show that HIN-LRI improves accuracy over analytical integrators, splitting methods, and neural PDE surrogates, with stable spatial refinement, effective out-of-distribution transfer, and modest online overhead.

Uncertainty quantification (UQ) in graph neural networks (GNNs) is crucial in high-stakes domains but remains a significant challenge. In graph settings, message passing often relies on strong assumptions such as exchangeability, which are rarely satisfied in practice, and achieving reliable UQ typically requires costly resampling or post-hoc calibration. To address these issues, we introduce Quantile-free Prediction Interval GNN (QpiGNN), a framework that builds on quantile regression (QR) to enable GNN-based UQ by directly optimizing coverage and interval width without requiring quantile inputs or post-processing. QpiGNN employs a dual-head architecture that decouples prediction and uncertainty, and is trained with label-only supervision through a quantile-free joint loss. This design allows efficient training and yields robust prediction intervals, with theoretical guarantees of asymptotic coverage and near-optimal width under mild assumptions. Experiments on 19 synthetic and real-world benchmarks show QpiGNN achieves average 22% higher coverage and 50% narrower intervals than baselines, while ensuring efficiency and robustness to noise and structural shifts.

The standard constraint-based paradigm for causal discovery with incomplete data – impute first, test second – is frequently miscalibrated: any consistent conditional independence (CI) test rejects a true null with probability approaching 1 when imputation error induces spurious conditional dependence. We introduce PAIR-CI, a nonparametric CI test that restores calibration by integrating multiple imputation directly into the inferential procedure via a paired permutation design. PAIR-CI compares cross-validated models that include and exclude the candidate variable while receiving the same imputed conditioning set, forcing imputation error to cancel in their loss difference rather than contaminate the test statistic. A provably consistent variance estimator jointly accounts for uncertainty arising from cross-validation and multiple imputation – to our knowledge, the first formal unification of these two inferential frameworks. In simulations, existing imputation-based CI tests exhibit false positive rates of 28–45% when data are missing not at random (MNAR), whereas PAIR-CI averages below the nominal 5% level across data-generating processes and missingness mechanisms. These gains are largest in nonlinear settings and grow with causal graph size: when integrated into the PC algorithm, PAIR-CI reduces structural Hamming distance by 8% on 10-variable nonlinear graphs, 15% on 30-variable equivalents, and up to 44% on the 56-variable HAILFINDER network, with stable performance in all settings.

Unlike vision and language domains, graph learning lacks a shared input space, as input features differ across graph datasets not only in semantics, but also in value ranges and dimensionality. This misalignment prevents graph models from generalizing across datasets, limiting their use as foundation models. In this work, we propose ALL-IN, a simple and theoretically grounded method that enables transferability across datasets with different input features. Our approach projects node features into a shared random space and constructs representations via covariance-based statistics, thus eliminating dependence on the original feature space. We show that the computed node-covariance operators and the resulting node representations are invariant in distribution to permutations of the input features. We further demonstrate that the expected operator exhibits invariance to general orthogonal transformations of the input features. Empirically, ALL-IN achieves strong performance across diverse node- and graph-level tasks on unseen datasets with new input features, without requiring architecture changes or retraining. These results point to a promising direction for input-agnostic, transferable graph models.

Neural operators generally demonstrate strong predictive performance on in-distribution (ID) problems. However, a critical limitation of existing methods is their significant performance degradation when encountering out-of-distribution (OOD) data. To address this issue, this work introduces continual learning into physics-informed neural operators, with particular emphasis on neural operators built upon the Transolver architecture, and proposes a simple yet effective replay-based continual learning strategy. The proposed method is fully physics-informed and does not require labeled data, relying solely on input fields together with physical constraints for training. When new OOD data become available, a small number of past data are incorporated through a distillation-based constraint to preserve previously acquired knowledge and alleviate catastrophic forgetting. Meanwhile, a transfer learning LoRA is employed to enable rapid adaptation to the new data. The proposed framework is systematically validated on three representative physical problems, including the Darcy flow problem in fluid mechanics, a two-dimensional hyperelastic brain tumor problem in biomechanics, and a three-dimensional linear elastic Triply Periodic Minimal Surfaces problem in solid mechanics. The results demonstrate that the proposed method effectively mitigates catastrophic forgetting on previously learned data while maintaining fast adaptability to new data. Compared with conventional joint training strategies, the proposed method significantly improves training efficiency while reducing additional memory usage and computational cost.

Diffusion models undergo a phase transition in a critical time window during generation dynamics, with two complementary diagnoses of criticality. The symmetry breaking picture views the critical window as when trajectories bifurcate into different semantic minima of the energy landscape, whereas the nonlocality picture views the critical window as when local denoising fails. We study whether two notions of such phase transitions are concurrent in modern diffusion transformers. By evaluating the dynamics and outcomes of the generation trajectory, we observe a near-simultaneous occurrence of the non-locality and symmetry breaking critical times. Our work is the first to unify the two notions of phase transitions in practice: it provides a concrete diagnostic for when and why diffusion models rely on conditioning and global denoising, enabling principled evaluation of model efficiency and guiding the design of architectures and sampling schemes that avoid unnecessary computation.

Label Distribution Learning (LDL) models supervision as an instance-wise probability distribution, enabling fine-grained learning under inherent ambiguity, but its success relies on high-fidelity label distributions that are costly to obtain and thus often noisy. Motivated by privacy-sensitive applications, we study Federated Label Distribution Learning (Fed-LDL), where data isolation further induces heterogeneous annotation quality across clients, making local updates unevenly reliable and breaking sample-size-based aggregation (e.g., FedAvg). To address this trust dilemma, we propose FedQual, a quality-aware Fed-LDL framework with two coupled mechanisms: (i) quality-adaptive client training guided by a global semantic anchor that calibrates low-quality clients while preserving high-quality autonomy, and (ii) reliability-aware server aggregation that reweights client contributions by effective reliable information rather than raw sample size. To enable rigorous evaluation, we construct four new Fed-LDL benchmarks (FER-LDL, FI-LDL, PIPAL-LDL, and KADID-LDL) with controlled annotation quality disparity. We further provide a theoretical guarantee showing that under heterogeneous supervision quality, client-specific calibration is strictly better than any uniform calibration. Extensive experiments on the proposed benchmarks demonstrate the effectiveness of FedQual.

Factorization machine with quadratic-optimization annealing (FMQA) is a black-box optimization method that combines a factorization machine (FM) surrogate with QUBO-based search by an Ising machine. When FMQA is applied to integer or discretized continuous variables via one-hot encoding, uniform random initial sampling can leave many binary variables never active in the initial training data, and the corresponding FM parameters receive no direct gradient updates from the observed responses. We address this by designing the initial training data to achieve complete marginal bit coverage, namely, ensuring that every binary variable obtained by one-hot encoding takes the value one at least once. We use two space-filling sampling methods, Latin hypercube sampling (LHS) and the Sobol' sequence, yielding LHS-FMQA and Sobol'-FMQA. On the human-powered aircraft wing-shape optimization benchmark with 17 and 32 design variables, both proposed methods achieved numerically higher mean final cruising speeds than the baseline FMQA, with the advantage more pronounced on the 32-variable problem.

Graph neural networks have been widely used in Boolean satisfiability (SAT) tasks to learn structural information from SAT formulas. The goal of these studies is to solve SAT instances or to enhance SAT solvers, including tasks such as unsat-core prediction. However, most existing approaches model a SAT formula as a bipartite graph or a directed acyclic graph, which are less direct in capturing clause-level and higher-order interactions among literals and clauses. Moreover, these approaches are limited in modeling intrinsic polarity-related properties of SAT, such as the complementary relationship between the positive and negative literals of a variable. To address these limitations, we propose a polarity-aware representation learning framework over clause-literal hypergraphs. We model SAT formulas as clause-literal hypergraphs augmented with a clause incidence graph to capture higher-order structural interactions. We then introduce a polarity-aware decomposition mechanism that separates variable representations into polarity invariant and equivariant components, explicitly modeling the relationship between positive and negative literals, with the resulting literal representations propagated along the hypergraph structure. We further incorporate a polarity-inversion consistency regularization to reinforce polarity-consistent representations during training. Experimental results on multiple SAT datasets demonstrate the effectiveness of the proposed approach.

With the rapid development of cloud computing and Web services, Quality of Service (QoS) has become a key criterion for service selection and recommendation. Tensor latent feature analysis provides an effective way to model multidimensional QoS data, and most existing QoS prediction methods are mainly based on Canonical Polyadic (CP) decomposition or Tucker decomposition. However, constrained by their inherent structural properties, these methods cannot accurately capture the complex and dynamic dependencies in user-service interactions, which limits their prediction performance. To address this issue, this paper proposes a dynamic QoS prediction framework based on the Biased Nonnegative Block Term Tensor Decomposition Model, termed BNBT. Specifically, the proposed framework is developed from three aspects: (1) block term tensor decomposition is employed to enhance the representation capability of latent feature learning; (2) linear bias terms are incorporated to further improve prediction accuracy; and (3) a tensor-oriented single-element-dependent nonnegative multiplicative update algorithm, called SLF-NMUT, is designed for efficient parameter estimation. Extensive experiments on real-world QoS datasets demonstrate that the proposed BNBT framework consistently outperforms several state-of-the-art QoS prediction methods in terms of prediction accuracy.