Search research

Given only observational data $X = g(Z)$, where both the latent variables $Z$ and the generating process $g$ are unknown, recovering $Z$ is ill-posed without additional assumptions. Existing methods often assume linearity or rely on auxiliary supervision and functional constraints. However, such assumptions are rarely verifiable in practice, and most theoretical guarantees break down under even mild violations, leaving uncertainty about how to reliably understand the hidden world. To make identifiability actionable in the real-world scenarios, we take a complementary view: in the general settings where full identifiability is unattainable, what can still be recovered with guarantees, and what biases could be universally adopted? We introduce the problem of diverse dictionary learning to formalize this view. Specifically, we show that intersections, complements, and symmetric differences of latent variables linked to arbitrary observations, along with the latent-to-observed dependency structure, are still identifiable up to appropriate indeterminacies even without strong assumptions. These set-theoretic results can be composed using set algebra to construct structured and essential views of the hidden world, such as genus-differentia definitions. When sufficient structural diversity is present, they further imply full identifiability of all latent variables. Notably, all identifiability benefits follow from a simple inductive bias during estimation that can be readily integrated into most models. We validate the theory and demonstrate the benefits of the bias on both synthetic and real-world data.

Competitive programming remains challenging for code LLMs. Despite recent progress, many training pipelines still depend on scarce real-world data, raising concerns about scalability and near-duplicate benchmark contamination. In this paper, we examine whether synthetic training artifacts can support the complete SFT-to-RL cycle for competitive programming: no real-world tasks, solutions, or test cases are directly used for post-training. To this end, we synthesize tasks, verified solutions, and reliable test cases that serve as reward signals for reinforcement learning. To improve reward reliability, we introduce a dual-verification strategy that reduces noise in both selected solutions and test outputs. Using this high-quality data, we train the X-Coder model series. X-Coder-14B achieves 67.5% avg@8 on LiveCodeBench v5 and 63.4% on v6, outperforming its base model by over 40 points. Further analysis provides practical insights into synthetic post-training, highlighting the value of diverse tasks, verified long-CoT supervision, and code-centric reinforcement. Our data and models are released at https://github.com/JieWu02/X-Coder

Differentially private optimization suffers from a fundamental geometric mismatch: deep networks have highly anisotropic loss landscapes, yet DP-SGD injects isotropic noise. Second-order preconditioning can resolve this, but estimating curvature typically requires private data (consuming privacy budget) or public data (introducing distribution shift). We show that the Fisher Information Matrix decouples into architectural sensitivity, recoverable via synthetic noise, and input correlations, approximable from modality-specific frequency statistics. We propose DP-KFC, which constructs KFAC preconditioners by probing networks with structured synthetic noise, requiring neither private nor public data. Empirically, DP-KFC consistently outperforms DP-SGD and adaptive baselines across diverse modalities in strong privacy regimes ($\varepsilon \leq 3$). DP-KFC matches private-data preconditioners while public-data variants degrade by up to $4.8\%$, showing that curvature can be estimated without consuming privacy budget or introducing distribution shift. This enables privacy-preserving learning in specialized domains (e.g., medical applications) where regulatory constraints make data scarce.

Gromov--Wasserstein optimal transport (GW-OT) extends classical optimal transport by introducing structure-aware transport cost. This is particularly relevant for spatial transcriptomics, where dynamical reconstruction should preserve tissue structure in addition to matching expression patterns. While static formulations have been widely used for such structure-aware alignment, a general dynamic formulation for reconstructing continuous trajectories is still missing. We introduce Travelling Pair Dynamical Alignment and Trajectory Estimation (TP-DATE), a theoretical and computational framework to generalize GW-OT dynamically in a simulation-free manner. We formulate a broad class of static and dynamic Quadratic-form OT (QOT) through path actions and prove the static dynamic equivalence. We further develop travelling-pair flow matching, which allows interacting conditional paths and marginalizes their interactions into a single vector field. On synthetic and real spatial transcriptomics data, TP-DATE better preserves spatial structure and improves continuous 3D dynamics reconstruction.

Single Ventricle Physiology (SVP) is a rare subtype of congenital heart disease characterized by the presence of a single functional cardiac ventricle with atypical anatomic configurations that challenge conventional image segmentation approaches. The scarcity of clinical data and the morphological diversity across SVP subtypes make the development of robust segmentation methods particularly difficult. To address these limitations, we propose a cardiac MRI segmentation framework focused on ventricular chambers and myocardium segmentation tailored for SVP. First, we introduce a data augmentation pipeline that generates synthetic 3D cardiac meshes using SDF4CHD and corresponding synthetic cardiac MRI through generative modeling. Second, we introduce SV-Cine, a diagnosis-conditioned adaptation of the foundation model CineMA that incorporates patient-level diagnostic information through Feature-wise Linear Modulation layers, enabling diagnosis-aware feature adaptation during segmentation. We evaluated the framework on an internal cohort with varying SVP subtypes. SV-Cine achieved median Dice scores of 0.89 (IQR: 0.80--0.91) for the left ventricle and 0.72 (IQR: 0.54--0.84) for the right ventricle, outperforming the strongest baseline, nnU-Net, by 0.39 Dice points on right ventricle segmentation. It also yields a median ejection fraction error of 5.55 percentage points (IQR: 3.41--7.69) for the dominant ventricle. Compared with the internal cohort, LV and myocardium segmentation performance was lower for the external cohort; whereas RV Dice scores were comparable for both cohorts. Our findings suggest that a pretrained foundation model can be adapted for highly specialized downstream tasks through usage of diagnosis priors while leveraging anatomic knowledge learned from large-scale MRI datasets during pretraining.

The energy transition is reshaping residential electricity consumption through the increasing adoption of distributed generation, electrified appliances, and demand-response programs. Understanding these evolving behaviors requires access to granular smart-meter data for applications such as load forecasting, appliance detection, and demand-side flexibility analysis. However, such data are subject to strict access restrictions and data-protection regulations. Thus, realistic synthetic alternatives are necessary. In this paper, we introduce LoaDiff, a diffusion-based generative model for year-long, sub-hourly smart-meter load curves. LoaDiff supports flexible conditioning on static household attributes, such as appliance ownership, and dynamic contextual variables, including calendar information and outdoor temperature. We evaluate the model against multiple generative baselines on three residential electricity-consumption datasets. Our experiments assess four complementary dimensions: fidelity and diversity, training-record memorization risk, downstream utility for load forecasting and appliance detection, and conditional controllability under alternative temperature conditions. The results show that LoaDiff generates realistic and diverse load profiles, achieves a favorable trade-off between generation quality and limited evidence of memorization, preserves information useful for downstream energy applications, and responds coherently to changes in conditioning variables.

Feature-based explanations quantify features' influence on model predictions, but are primarily designed for scalar outputs. In many applications, however, outputs are functional or multivariate, such as time-dependent trajectories in demand forecasting. Consequently, existing approaches typically explain each output location independently, ignoring dependencies across the output components. We address this limitation by developing a unified framework for feature-based explanations of time-dependent outputs. Specifically, we generalize functional decomposition to Hilbert-valued prediction functions and extend an existing feature-based explanation framework to this setting. Our framework introduces kernel-based output representations that enable time-dependency-aware explanations at multiple levels of temporal granularity, including time-specific, time-resolved, and time-aggregated, while providing a unified view in which existing methods arise as special cases. We validate our framework on synthetic and real-world data, including intraday financial market volatility prediction and energy demand forecasting.

Automatic modulation classification (AMC) models are frequently trained and validated on synthetic or channel-cabled data, leaving open the question of how they behave once path loss and antenna pointing error are introduced by a genuine free-space link. We report a curriculum fine-tuning study of a hybrid CNN-Transformer AMC model. The general-purpose, all-32-class dataset underlying the model was built entirely at 915 MHz, on a controlled, clock/PPS-synchronized MIMO-expansion-cable link (not spatial-multiplexing transmission); all subsequent free-space, real-hardware experimentation - the sequential fine-tuning curriculum, matched-distance evaluation, and every reported over-the-air accuracy figure - was carried out at 4 GHz, across five directional-antenna distances (25, 35, 50, 70, 75 cm) under fixed TX/RX gain. Three distances used near-ideal antenna alignment (~99%) and two used a deliberately introduced partial misalignment (~85%), fine-tuned last in the curriculum. We report matched-distance test accuracy (91.8-93.7% across all five 4 GHz conditions) and confusion-matrix analysis grounded in RF theory, and report honestly where our sequential fine-tuning order confounds cumulative link adaptation with antenna alignment, rather than overstating what the data can support.

Machine learning systems deployed for credit, hiring, and resource distribution are increasingly subject to regulatory oversight from policies such as the EU AI Act and GDPR. Current fairness governance practices rely on observational fairness metrics, post-hoc explainability, and immutable audit logs, but provide limited support for causal attribution and efficient evidentiary verification. We introduce Causal Evidentiary Governance (CEG), a framework in which regulated institutions commit to a versioned directed acyclic graph (DAG) that partitions causal pathways into allowable and disallowed groups. The Causal Harm Rate measures prediction variation attributable to disallowed causal pathways. Each decision is accompanied by a signed Decision-Evidence Packet (DEP), cryptographically binding the prediction to a digest of the published DAG and path-specific attributions. DEP digests can be appended to a Merkle tree to enable logarithmic-cost inclusion proofs. We validate CEG through a two-layer empirical methodology using demographic summaries from four years of PMA credit supervisory data to construct 10,000 synthetic credit applicants across four strategic DAG counterfactuals. Causal Harm Rate isolates injected causal effects more clearly than demographic parity or equalized odds. Cross-model validation and ablation studies assess robustness. Evaluation on the German Credit dataset shows that harm associated with specific causal pathways can be substantially understated by associational fairness metrics. Finally, a proof-of-concept implementation demonstrates operationally plausible throughput and highlights relevant performance tradeoffs.

Modern data science increasingly gives rise to hypothesis-testing problems that are not naturally formulated in terms of parameters within prespecified statistical models. One important example is the dynamic evaluation of optimization algorithms, where decisions must be made during training about whether further updates remain beneficial or the algorithm should switch to a different phase. This issue is particularly relevant in stochastic min-max optimization. Generative adversarial networks (GANs) provide a canonical example, as their training requires repeated decisions about when to switch between discriminator and generator updates, yet existing methods typically rely on fixed update ratios or heuristic criteria. We formulate this switching problem as sequential hypothesis testing and develop an e-process-based adaptive training procedure. During discriminator updates, one e-process tests the null that the discriminator-induced separation between the empirical data distribution and the generator law remains below a target level. During generator updates, with the discriminator fixed, a second e-process tests the reverse null that this separation remains above a refresh level. Conditional on the observed training sample, we prove that fresh empirical indices and latent draws yield conditional e-values that can be accumulated into e-processes, providing anytime-valid Type I error control under adaptive model updates and data-dependent switching. Across multimodal synthetic distributions and image benchmark datasets, the proposed method matches or outperforms the best fixed-ratio baselines under several widely used GAN objectives.

The difficulty of collective action remains a central challenge in the design of policies for multifamily residential redevelopment. Stakeholders continually adjust their decisions in response to evolving negotiation contexts and the reactions of others, meaning that when a policy intervenes and which stakeholders it targets can substantially reshape collective outcomes. Assessing these adaptive responses ex ante remains difficult because existing simulation models often rely on predefined behavioral rules. Here, we present CoRenew, an open-source platform that uses LLM-based agents to simulate negotiations among multiple stakeholders and evaluate the effects of alternative policy combinations. Integrating open source geographic and demographic data, the platform can generate synthetic residents, simulate negotiation dynamics under alternative policy settings and compares policy performance across competing objectives. It supports both numerical and semantic policy inputs and includes built-in tools for visualization and result export. We validate its behavioral realism against survey responses from 324 residents and a nine-month observed negotiation process from a real redevelopment case. With its modular and adaptable architecture, CoRenew can be used to assess policies across different institutional and cultural contexts.

The use of variable well perforation and injection strategies can improve the efficiency of geological carbon storage operations. We develop a new multimodal auto-regressive transformer surrogate to model these operations under geological uncertainty. A modified SEAM CO2 geomodel, which involves a faulted system with three stacked aquifers, is considered. The two injection wells are perforated in stages, from bottom to top, with the stage durations and individual well injection rates treated as control variables. The surrogate model processes three input modalities - the 3D geomodel, scalar parameters characterizing relative permeability functions, and control variables - through separate encoders. These are fused via self-attention in a transformer encoder, and a temporal decoder generates predictions auto-regressively through encoder-decoder cross-attention. The surrogate is trained, using 4000 GEOS flow simulations, to predict saturation and pressure at monitoring locations, total injected and mobile CO2 mass, and saturation footprints. For a new test set, involving randomly sampled geomodels and control variables, the surrogate achieves a median saturation MAE of 0.028 and median relative errors of 0.2-5% for the other quantities of interest. Importantly, it captures the switch from rate to bottom-hole-pressure control. The surrogate model is used within a hierarchical Markov chain Monte Carlo data assimilation procedure for a synthetic true model under three operational strategies. Substantial uncertainty reduction is achieved for key metaparameters, particularly the fault permeabilities. Posterior predictions for saturation footprints and total injected and mobile CO2 mass are also shown to be generally consistent with true model results.

Spatial understanding is crucial for foundation models (FMs), and maps have long helped humans organize and reason about geographic information. This study examines whether choropleth maps remain useful for machine spatial understanding when models can directly process structured geodata. We introduce ChoroplethMap-Bench, a controlled benchmark containing 2,400 synthetic choropleth maps, corresponding GeoJSON data, and 12,000 questions across five cognitive dimensions: Identify, Spatial Recognition, Compare, Rank, and Delineate. We evaluate 22 open-source and proprietary models under three input conditions: Data Only, Map Only, and Data + Map. The results show that maps substantially improve spatial reasoning, especially when combined with symbolic data and for tasks requiring higher-level understanding of spatial patterns. We further analyze the effects of map type, color hue, and spatial structure, as well as prompting strategies, language, geographic context, decoding settings, classification methods, and response stability. Overall, the Data + Map condition achieves the strongest performance, demonstrating that maps remain valuable external representations for foundation model spatial reasoning.

Creating realistic 3D human-human interactions in virtual environments is challenging due to the high degrees of freedom in the human body and the need for physically accurate poses that do not collide with each other. Traditional methods for human-human interaction are based on motion tracking or 3D body reconstruction, but lack generative capabilities. Recent generative methods enable the synthesis of individual or interacting motions via text or image input, but generally fall short in modeling close interactions. This paper introduces a novel generative model for close 3D human-human interactions using a conditional variational autoencoder (cVAE), which generates poses for one human conditioned on the pose of another, allowing for controlled and diverse interaction synthesis. To train our model, we address two underlying long-standing challenges in the field of human-human interaction: data scarcity, for which we propose an automated supervised data augmentation strategy that generates synthetic yet realistic interaction poses; and collision awareness in generative approaches, for which we propose a self-supervised loss based on a collision resolution technique using volumetric proxies to ensure physically correct interactions. We extensively evaluate the capabilities of our model, and demonstrate a wide variety of plausible and physically correct interactions, not possible to generate with current state-of-the-art methods.

Recent advances in video diffusion models have enabled either long single-view generation through temporal autoregression, or short multi-view synthesis through bidirectional attention. However, generating long, multi-view consistent videos of dynamic scenes remains unsolved. In this work, we present MV-Forcing, a framework that composes temporal and view-wise autoregression within a single diffusion model by introducing a 4D geometric bridge between sequentially generated views. Our key insight is that an autoregressive 3D reconstruction model naturally interfaces between autoregressively generated views. Given a completed source view, we reconstruct its 3D structure and render a geometric prior of the next target viewpoint, which the diffusion model refines into a high-quality video. To extend generation beyond the teacher's fixed temporal window, we introduce a joint denoising regime where both view slots are initialized from noise during training, enabling temporally unbounded generation. We distill the model via Distribution Matching Distillation with Spatio-Temporal Self-Forcing, closing the train-inference exposure bias gap for both temporal and view-sequential autoregression. Extensive experiments on both synthetic and real-world data demonstrate that MV-Forcing produces geometrically consistent multi-view videos of dynamic scenes at arbitrary lengths and viewpoint counts using a single few-step student model.

Conditional inference trees (CIT) and conditional inference forests (CIF) reduce split-selection bias by testing features before choosing split thresholds, but repeated permutation tests and threshold searches can make these methods computationally expensive. We study CIT and CIF as top-$k$ feature-ranking methods for downstream prediction using real-data benchmarks, runtime ablations, and synthetic feature-recovery experiments. At a fixed node, if the features and permutation budget do not depend on the node responses, Bonferroni-corrected $+1$ Monte Carlo permutation $p$-values control nodewise rejection under the complete permutation null. CIF ranks 4th among 17 classification methods on 22 datasets and 3rd among 18 regression methods on 8 datasets. With Bonferroni correction held fixed, the CIF runtime ablations indicate that adaptive stopping and the number of thresholds searched have the largest measured effect on runtime: turning off adaptive stopping and using exact threshold search increase fitting time by 4.0--8.4$\times$ and 1.9--10.8$\times$, respectively, while downstream score changes are at most 0.011. Sparse high-$p$ simulations indicate that forest feature sampling can leave informative features out of many split decisions. Overall, the results support CIF as a top-$k$ feature-ranking method in the evaluated downstream prediction benchmarks.

Climate governance processes involve complex interactions between heterogeneous citizens, advocacy groups, media actors, and political decision-makers. While agent-based models (ABMs) have been widely used to study environmental policy and socio-ecological systems, many existing approaches focus either on institutional dynamics or individual behavioural mechanisms in isolation. This paper presents a modular multi-level agent-based architecture that integrates empirically grounded cognitive decision models with strategic institutional behaviour within a unified simulation framework. The architecture combines (i) motive-based individual decision-making operationalised through the HUMAT and MOA frameworks, (ii) socially embedded influence processes via demographic homophily networks, and (iii) institutional strategy modules for environmental non-governmental organisations (NGOs), media agents, and politicians. Political decisions emerge from the aggregation of multiple signals, including expert input, public mobilisation, party alignment, and media framing. The model is designed to be empirically calibrated through synthetic populations derived from survey data and and institutional parameters informed through Living Lab stakeholder engagement, and to support scenario-based exploration of climate-relevant land-use governance processes. Rather than presenting empirical results, this paper focuses on the architectural design principles, modular structure, and integration logic of the model. We discuss how this multi-layered approach contributes to the modelling of democratic climate governance and outline pathways for generalization and future validation.

Hybrid attention models improve long-context efficiency by retaining only a subset of full-attention layers and replacing the remaining layers with linear attention. However, the effectiveness of Transformer-to-hybrid conversion critically depends on which layers preserve full attention. Existing hybrid layer selection methods typically rely on heuristic strategies such as fixed placement patterns or layerwise scoring, implicitly treating layer importance as isolated and overlooking the interdependent layer effect under a global hybrid configuration. In this work, we formulate hybrid layer selection as a budget-constrained subset optimization problem. We further propose FlashMorph (Fast LAyer Selection for Hybrid MORPHing), an effective, efficient and scalable layer selection method for Transformer-to-hybrid conversion. FlashMorph first constructs a morphable model by equipping each full-attention layer with a converted linear-attention branch. It then freezes all model weights and jointly optimizes layerwise gates on synthetic long-context retrieval data, with a linearization regularization that encourages the model to rely on linear attention for efficiency. The learned gates are discretized under a preset full-attention budget to instantiate the hybrid architecture, followed by standard logits distillation and long-context finetuning. Extensive experiments show that FlashMorph discovers more effective hybrid configurations, preserves strong long-context recall and general benchmark performance while substantially reducing layer selection cost compared with existing layer selection methods, demonstrating its effectiveness, efficiency, and scalability.

We address the problem of inferring a directed network from nodal measurements generated by linear diffusion dynamics on the sought graph. Observations are modeled as the outputs of a graph convolutional filter, i.e., a polynomial (with unknown coefficients) of a local diffusion graph-shift operator encoding the latent graph topology, excited with an ensemble of independent graph signals with arbitrarily-correlated nodal components. Unlike prior efforts that considered undirected graphs and white signal excitations, here the graph-shift operator and the observations' covariance matrix are not simultaneously diagonalizable. In this challenging context, we first rely on measurements of the output signals along with prior statistical information on the inputs to identify the diffusion filter. Such system identification problem involves solving a system of quadratic matrix equations, which we show is identifiable under spectral-diversity assumptions on the input covariances. For algorithmic purposes we recast it as a smooth quadratic minimization subject to Stiefel manifold constraints. Subsequent identification of the network topology given the graph filter estimate boils down to finding a sparse and structurally admissible shift that commutes with the given filter, thus, forcing the latter to be a polynomial in the sought graph-shift operator. A joint graph filter and topology identification algorithm is also proposed, which alternates between the aforementioned steps in a mutually reinforcing fashion to offer improved sample complexity. Numerical tests corroborate the effectiveness of the proposed algorithms in recovering synthetic digraphs and real-data case studies, and illustrate their potential utility on urban mobility analyses as well as portfolio optimization.

Recent Large Audio Language Models (LALMs) have achieved remarkable progress in audio perceptual tasks across individual acoustic layers, including speech, sound, and music. However, existing benchmarks predominantly evaluate these layers in isolation, overlooking the complex contextual relationships that arise when multiple acoustic sources co-occur in real-world auditory scenes. Real-world auditory interpretation requires Context-Aware Auditory Scene Understanding (CASU): the ability to comprehend the holistic scene by integrating sound layers. To evaluate this capability, we introduce the CASU benchmark, which assesses whether Audio LLMs can interpret auditory scenes composed of speech, acoustic events (e.g., announcements), and background environments (e.g., traffic), and reason about the logical relationships between these layers. We propose a scalable pipeline for constructing time-accurate, semi-synthetic audio streams by composing real-world scene sounds with synthetic speech. Building on this data, we design four tasks that probe scene understanding: contextual question answering, entity extraction from the scene, speaker role inference, and counterfactual reasoning where scene is manipulated. Experiments across multiple LALMs demonstrate that effective auditory scene understanding requires integration over all auditory layers, rather than reliance on speech or sound alone, underscoring the necessity of CASU for advancing complex audio understanding in LALMs.

Targeted advertising systems can pair audiences selected by advertisers with ad units that expose visible user actions. When an interaction remains linked to the campaign that elicited it, the advertiser may receive an observation tied to a user rather than only an aggregate report. We model that channel as a noisy oracle for attribute inference. The model separates targeting predicates, exposure, interaction, and disclosure. These boundaries capture the gap between eligibility and delivery, and the gap between interaction and advertiser visibility. We build a reproducible benchmark using synthetic populations calibrated with public data, each with known sensitive labels. A generated campaign semantics layer provides topic variants and response priors. The simulator generates the ground truth, event traces, disclosed observations, and metrics. The evaluation compares Bayesian, supervised, positive and unlabeled, and adaptive attacks under common campaign and disclosure definitions. The final evaluation uses four topic variants, seven simulator seeds, and two interaction settings. Repeated campaigns with identity exposure produce measurable but bounded inference signal. At $160$ campaigns, Bayesian and supervised attacks reach about $0.64$ AUC in the main setting and about $0.65$ AUC in the higher interaction setting. Disclosure policy is the strongest control. Aggregate reporting removes the evaluated oracle input tied to users. Type filtering and randomized disclosure reduce the released signal. The result is a model, artifact, and defense evaluation method for privacy in interactive targeted advertising. The code is available at https://github.com/P-HOW/Interactive-Ad-Oracle.

Matrix completion has been extensively studied for real-valued data, but existing methods are often limited in handling categorical variables. We propose LCMC, a double-loop optimization framework for categorical matrix completion via latent factorization based on a binary tensor representation. In this setting, each categorical entry is encoded as a one-hot vector along a third tensor mode, thereby preserving its discrete, non-ordinal nature. The outer loop adaptively estimates the latent dimension by iteratively updating it with feedback from the inner loop, while the inner loop reconstructs the categorical matrix through tensor factorization, supported by a corresponding theoretical analysis. To further improve scalability and robustness, we introduce enhancements including a split-merge-refine strategy and an adaptive data reduction technique. Experiments on synthetic and real-world datasets in viral quasispecies reconstruction, demonstrate that LCMC achieves superior accuracy and efficiency compared to existing methods.

It is well established that ReLU networks define continuous piecewise-linear functions, and that their linear regions are polyhedra in the input space. These regions form a complex that fully partitions the input space. The way these regions fit together is fundamental to the behavior of the network, as nonlinearities occur only at the boundaries where these regions connect. However, relatively little is known about the geometry of these complexes beyond bounds on the total number of regions, and calculating the complex exactly is intractable for most networks. In this work, we prove new theoretical results about these complexes that hold for all fully-connected ReLU networks, specifically about their connectivity graphs in which nodes correspond to regions and edges exist between each pair of regions connected by a face. We find that the average degree of this graph is upper bounded by twice the input dimension regardless of the width and depth of the network, and that the diameter of this graph has an upper bound that does not depend on input dimension, despite the number of regions increasing exponentially with input dimension. We corroborate our findings through experiments with networks trained on both synthetic and real-world data, which provide additional insight into the geometry of ReLU networks. Code to reproduce our results can be found at https://github.com/bl-ake/ICLR-2026.

Causal discovery aims to recover directed causal relations from observational and interventional data, providing a basis for mechanistic understanding and reliable decision-making. Causal discovery foundation models (CDFMs) seek to amortize this problem by mapping a dataset directly to a causal graph in a single forward pass, avoiding per-dataset testing, search, or optimization. However, existing CDFMs remain limited, often failing to consistently match strong classical methods, and we find that a key bottleneck is how causal pretraining tasks are constructed. Based on this observation, we propose TabCausal, a data-driven CDFM trained with broad causal pretraining over diverse graph priors, structural mechanisms, noise models, dimensions, sample sizes, and intervention regimes. A dynamic task construction strategy composes these causal environments into varied discovery tasks, enabling more transferable structural learning from observational and mixed-interventional data. On large-scale synthetic benchmarks, TabCausal achieves better macro-averaged performance than a diverse set of causal discovery baselines. To further bridge abstract synthetic generators and realistic causal reasoning scenarios, we introduce a protocol-guided and LLM-audited semantic causal environment benchmark, where domain-grounded SCMs generate interpretable observational and interventional datasets for out-of-distribution analysis. Across both synthetic and semantic environments, TabCausal demonstrates robust structure recovery, especially under interventional evidence, highlighting broad causal pretraining as a key ingredient for transferable amortized causal discovery.

This paper studies adaptive targeting under network interference in a bandit setting, where treatments applied to one individual may affect others through spillover effects. We consider a linear model in a sparse regime, where each individual's outcome can be affected by at most a few others. We first establish a regret lower bound showing that ignoring the network structure and reducing the problem to a standard linear bandit inevitably leads to inefficient learning, particularly in large populations. To understand how structural information can be leveraged, we analyze regimes with varying levels of knowledge of the interference structure: (1) full support knowledge, (2) knowledge of the column support sizes, and (3) no prior knowledge. For each regime, we establish regret lower bounds characterizing the fundamental limits of learning, and develop algorithms that achieve near-optimal regret. Together, our results provide a unified view of how knowledge of the interference structure governs the efficiency of online learning under interference, and offer practical adaptive targeting algorithms in each setting. Numerical experiments on synthetic and real-world data demonstrate the practical benefits of our algorithms.

Neural networks are known to develop latent representations that are $aligned$, namely structurally similar across networks trained with different architectures, training protocols, or training datasets. We study this phenomenon in a controlled setting, where we train an ensemble of networks on regression and classification tasks using training sets perturbed by independent realizations of a noise process. We show that the signal-to-noise ratio (SNR) and the training sample size influence the alignment in qualitatively similar ways in networks trained on real-world datasets and in an extremely simple $linear$ network with a single hidden layer, for which the alignment can be estimated analytically. Across linear and nonlinear networks, regression and classification tasks, and both synthetic and real-world data, we consistently observe that alignment varies monotonically with SNR but non-monotonically with training sample size. In particular, the alignment is minimized near the interpolation threshold, and a stronger alignment does not necessarily correspond to better generalization error. These findings reveal a non-trivial dependence of alignment on data quality and quantity, decoupled from generalization performance.

Large-scale search, recommendation, and retrieval-augmented generation (RAG) systems typically employ a two-stage architecture: an early-stage ranker (ESR) generates a candidate set, which is subsequently re-ranked by a late-stage ranker (LSR). While there are many reinforcement learning (RL) methods for training the LSR, end-to-end training of the ESR has proven challenging. In particular, naive application of "vanilla" policy gradient (V-PG) is not scalable for candidate-set sizes relevant for practical use due to exploding variance. This issue arises because V-PG propagates the gradient to the joint probability of the candidate sets, ignoring the contribution of each specific item in the candidate set to the reward. To mitigate this issue, we propose a novel "credit-assigned" policy gradient (CA-PG), which computes gradients with respect to the probability that the target item is chosen in any candidate set, i.e. marginalizing over all candidate sets that contain it. Our theoretical analysis reveals that CA-PG significantly reduces the variance of V-PG by marginalizing over the specific composition of the candidate set, while preserving the ability to learn the correct ranking of items under a reasonably aligned LSR policy. Experiments on both synthetic and real-world data demonstrate that CA-PG improves the convergence speed and training stability for ESRs utilizing the canonical Plackett-Luce model, especially when the candidate-set size is large.

Message-passing neural networks (MPNNs) are a powerful framework for learning representations of graph-structured domains. However, weights in MPNNs act on features only, limiting their ability to capture structural patterns. We introduce a novel structure-aware weight sharing principle that explicitly incorporates information inherent to the graph structure. Weights are indexed directly by user-chosen graph invariants, i.e., functions preserved under node permutations, enabling systematic reuse across structurally equivalent subgraphs. We present ShareGNNs, which instantiate this principle within a simple encoder-decoder architecture, resulting in an MPNN with learnable adjacency and transformer-like connectivity. We show that their expressivity is at least as strong as the discriminative power of the chosen invariants, providing explicit control over the model complexity. Experiments on synthetic and real-world data, as well as subgraph counting tasks, demonstrate consistent improvements over standard MPNNs, competitive expressivity beyond the 1-WL test, and scalability to large datasets.

Lipid nanoparticles (LNPs) are efficient delivery systems for negatively charged nucleic acids. Their multi-component architecture yields a core-shell structure. Small-angle X-ray scattering (SAXS) is an important characterization technique for LNPs, but recovering internal structure and size distribution from SAXS is an inverse problem with non-unique solutions. Realistic models are often too expensive for systematic exploration. We introduce a machine-learning-accelerated, differentiable framework for SAXS analysis of heterogeneous, polydisperse LNPs. The forward model combines a core-shell particle with a Gaussian random-field interior, a neural surrogate for the monodisperse SAXS map, and a differentiable layer integrating over particle-size distributions. The surrogate reduces prediction cost by four orders of magnitude, while differentiability enables large-scale multi-start fitting and ensemble identifiability analysis. Applied to synthetic and experimental MC3 LNP data, the framework shows that near-identical SAXS fits can arise from distinct parameter modes, with the experimental fits dominated by a trade-off between size-distribution and interior-structure parameters.

Firms increasingly rely on dynamic pricing to respond to evolving customer demand, yet in many applications they observe only the revenue generated by a single posted price in each period. At the same time, market conditions may shift gradually or abruptly due to changes in customer preferences, competition, or external shocks. These features create two intertwined challenges: learning the revenue--demand relationship from limited feedback and adapting pricing decisions to a changing environment. We study how a seller can learn and earn effectively under these constraints, without assuming a specific parametric form for demand. We develop a learning framework that updates prices using revenue-based gradient approximations constructed from one observation per period. To address environmental changes, we incorporate a restarting mechanism that periodically refreshes the learning process so that outdated information is discounted. When the degree of nonstationarity is unknown, we further introduce a meta-learning layer to adaptively hedge across multiple restarting schedules. We provide performance guarantees for our approach, showing how cumulative revenue loss relative to a fully informed benchmark depends on both the time horizon and the magnitude of market variation. Simulation experiments using synthetic and real-world data illustrate the effectiveness of the proposed procedures.