Papers

In recent years, the rapid development of foundation models and graph pre-training technologies has spurred increasing interest in constructing a universal pre-trained graph model or Graph Foundation Model (GFM). However, a significant challenge is that existing models are unable to address feature heterogeneity in graph data without textual information, which hinders the transferability of graph models across different datasets. To bridge this gap, we propose the concept of learnable graph patches, which we regard as the smallest semantic units of any graph data. We decompose the graph into learnable graph patches by unfolding the node features and constructing corresponding patch structures separately. We then design a framework that mines transferable information from graph data across domains. Specifically, after extracting graph patches, we propose a patch encoder to extract knowledge from each unit and a patch aggregator to learn how the units are combined into a whole. Due to its domain-agnostic nature, the model can be applied to downstream data across different domains. Furthermore, we analyze the connection between our method and existing graph models, as well as the transferability of the node embeddings it generates. Empirically, our method not only achieves the capability to use multi-domain graphs for pre-training, but also shows enhanced performance across various downstream datasets and tasks. Moreover, we observe consistent improvement in downstream performance as the volume of pre-training data increases.

Fine-tuning large language models (LLMs) is compute-intensive and error-prone: model performance depends sensitively on data quality and hyperparameter choices, and naïve runs can even degrade model performance. This raises a practical question:can we predict fine-tuning performance before committing to a full training run? We present TUNEAHEAD, a lightweight framework for pre-hoc prediction of fine-tuning performance. TUNEAHEAD encodes each candidate run as a meta-feature vector that combines static dataset descriptors with dynamic probe features from a short standardized probe. A predictor maps these features to performance estimates, while SHAP-based attributions provide interpretable diagnostics that reveal which specific features drive the prediction. Across 1,300+ fine-tuning runs on Qwen2.5-7B-Instruct, TUNEAHEAD consistently outperforms strong baselines such as Early-Stop Extrapolation and ProxyLM. On a held-out test set of 370 runs, TUNEAHEAD achieves an RMSE of 1.47 percentage points and places 95.1% of predictions within +3/-3 percentage points of the true score. These accurate continuous predictions support practical go/no-go screening policies that can reduce unnecessary full fine-tuning while retaining most promising runs.

This study introduces enhancements to physics-constrained neural networks (PCNNs) that improve the accuracy and stability of hybrid short-term weather forecasting models. Building on the WeatherGFT architecture, three innovations are proposed. First, an upgraded numerical solver, combining a fifth-order weighted essentially non-oscillatory scheme (WENO-5), a beta-plane approximation, and subgrid-scale viscosity, permits a fourfold increase in the integration time step to 1200 s while reducing the daily mean squared error by up to 26%. Second, a unified autoregressive hybrid block replaces the original chain of 24 specialised modules, eliminating overfitting to specific lead times. Third, the physical core is integrated with two state-of-the-art neural backbones, resulting in PI-PredFormer and PI-IAM4VP. Evaluation on the WeatherBench South Pacific subset from 2000 to 2004 shows that these hybrids reduce root mean squared error at 1-12 h lead times by 8-22% compared to purely neural counterparts, while better preserving physical consistency. These results demonstrate that incremental refinement of hybrid components offers a practical route toward more accurate and efficient short-range weather forecasting.

The high cost of fine-tuning LLMs poses a significant economic barrier; pre-hoc performance prediction offers a critical solution to substantially reduce this expense. However, the theoretical limits of pre-hoc performance prediction remain unexplored. We formulate it as a stochastic estimation problem under information constraints, decomposing prediction risk into two components: an intrinsic limit (static data-model compatibility) and a reducible optimization variance. We prove that optimization variance admits a necessary lower bound on its decay rate, implying fundamental constraints on how quickly uncertainty dissipates, regardless of the predictor used. Based on these dynamics, we derive a budget-optimal probing principle and introduce a predictability phase diagram that organizes tasks into three distinct regimes: Static-Sufficient, Dynamic-Critical, and Noise-Dominant. Extensive experiments on synthetic and real-world benchmarks validate these theoretical regimes and demonstrate the efficiency of our probing strategy.

Large language model (LLM) web agents are usually deployed as tool callers: each turn, the model reads a fresh page observation and emits one structured tool action. When every action is a low-level primitive, horizons grow quickly and so do policy-facing LLM completions, dominating latency and cost on benchmarks such as Mind2Web and WebArena. Recent systems therefore wrap repeated interaction fragments as web skills: callable tools built from successful trajectories or induced programs, so one call can replace several primitives. However, prior skill libraries are still triggered mainly by instruction similarity or coarse site metadata, which yields low skill reuse on held-out sites and leaves much of the potential step and token reduction on the table. We present SkillMigrator, an agent that learns reusable web skills and transfers them across sites by matching layout structure rather than specific element references. Each induced skill is stored as a transferable interaction pattern (TIP): the skill paired with a structural sketch of the snapshot at induction time. At test time, SkillMigrator retrieves TIPs by layout similarity and grounds their references on the live page. The rest of the stack is standard: accessibility-snapshot observations with stable references, and fixed tool calling over primitives plus skill invocations. Compared with the state-of-the-art approaches, SkillMigrator reduces the average LLM-action count on successful trajectories by 8-10% across both WebArena and Mind2Web at matched success rate.

In Self-Supervised Learning (SSL), preventing representation collapse by explicitly enforcing a uniform distribution on the unit hypersphere has proven to be effective. However, current frameworks typically rely on sliced statistical regularizers such as SIGReg (used in LeJEPA) and SUSReg (used in SPHERE-JEPA), which approximate this continuous objective via Monte Carlo sampling along random 1D directions. This stochasticity injects projection variance into the training gradients, destabilizing optimization, and hindering convergence. In this work, we first show that analytically integrating out these random projections natively yields a deterministic Maximum Mean Discrepancy (MMD), bypassing the variance of sliced methods. Motivated by this equivalence, we formulate full-dimensional objectives for MMD, Kernel Stein Discrepancy (KSD), and Kullback-Leibler (KL) divergence directly on the sphere to enforce a uniform distribution. To prevent spatial bias, we equip these tests with rotationally invariant kernels constructed via spectral theory, systematically evaluating two canonical families: smooth exponential decay (Heat) and strict frequency cutoff (Bandlimited) filters. Empirically, removing projection-induced noise results in more stable optimization, faster convergence, and consistent improvements over stochastic sliced regularizers on ImageNet and Galaxy10. Furthermore, we reveal that the choice of the statistical test shapes the geometry of the learned latent space: MMD and KSD favor locally clustered organization suitable for object-centric domains, whereas the continuous KDE-based KL divergence promotes fine-grained instance separation, yielding the strongest results on unclustered procedural texture retrieval.

Finding the initial noise that generates a given data sample, known as inversion, is a key component for downstream applications such as training-free image editing. Existing fixed-point inversion methods improve inversion accuracy by formulating each inversion step as a fixed-point problem, but they lack a principled mechanism for selecting among multiple fixed-point solutions that can arise in practice. We observe that different selections induce different inversion trajectories, leading to substantial variation in reconstruction and editing quality. For rectified flows, we further find that this variation is closely associated with trajectory straightness, motivating straightness as a principled selection criterion. We propose SelFix, a fixed-point inversion method that selects fixed-point solutions inducing straighter inverse trajectories while retaining convergence to an exact inverse root under standard local assumptions. Experiments on FLUX.1-dev and PIE-Bench show that SelFix improves fixed-point inversion, achieving stronger real-image reconstruction and better source-preserving prompt-based editing than prior inversion baselines. The code is available at https://github.com/seminkim/selfix.

Adding LLM-generated node features to graph neural networks (GNNs) is widely reported to improve accuracy on standard benchmarks. We document a contrasting observation: when LLM features are introduced through pure input concatenation (rather than joint training, distillation, or prompt-conditioning), they can systematically degrade accuracy on the same homophilous benchmarks where end-to-end LLM pipelines succeed. With an MLP backbone on the Planetoid public split and bag-of-words original features, concatenating SBERT-encoded GPT-4o-mini TAPE features reduces PubMed test accuracy by -17.0 +/- 0.3 pp and Cora by -4.3 +/- 0.6 pp (CiteSeer -0.6 +/- 0.8 pp, within seed noise). The drop attenuates as we relax each condition (GCN / GCNII / GAT backbones, random splits, smaller encoders) and reverses on medium-homophily WikiCS (+4.4 pp) and ogbn-arxiv (+11.7 pp). To predict when concatenation helps versus hurts, we report a simple measure of LLM-alone discriminability, Delta_sig. Across 9 datasets Delta_sig correlates with the concatenation cost more strongly than homophily at point estimate (r^2 = 0.38 vs. 0.06; N=9, bootstrap CIs overlap). The bootstrap-best change-point is tau = 13.8 pp, and the rule "Delta_sig <= tau predicts non-positive concat cost" classifies 7/9 datasets correctly; since 60% of bootstrap samples place tau in [5, 30] pp, we treat Delta_sig as an interpretive lens rather than a precision filter. A dimension-controlled ablation on PubMed places the LLM-feature drop between same-source PCA (-2.3 pp) and same-dim Gaussian noise (-37.3 pp), ruling out dimensionality and weight-decay artifacts. Nine PubMed configurations fit a power law |Delta_concat| proportional to (sqrt(d_l/n))^1.31 with r^2 = 0.97; the low-Delta_sig, small-n corner is exactly where the headline -17 pp PubMed deficit appears.

Learned dynamics models often answer global physical questions, such as fault severity or impact stiffness, by pooling a per-step feature sequence into one readout vector. This sequence-to-global interface creates an under-studied temporal credit problem: with only trajectory-level supervision, a model can predict accurately in training conditions while reading from abundant smooth correlates rather than the brief physical events that determine the target. We call this failure temporal credit dilution. It is not exposed by the training loss and is not removed by standard physics-informed residuals, because the error lies in where the global readout assigns functional credit. We introduce Credit-in-Event, an interface-level probe for measuring how much pooled credit lands on event steps, and prove in closed form that a pooled linear reader routes credit to a spurious background channel as the event fraction shrinks. We then propose CREST, a training-free and label-free readout that estimates a transient event core from learned features and re-anchors the pooled representation through event-versus-rest contrast. Across simulated gear and impact systems, recurrent and attention encoders, and public bearing vibration data, CREST reduces out-of-distribution error while restoring event credit. Ablations show that stable-step selection and receptive-field shrinking fail, confirming that the gain comes from event-core credit re-anchoring rather than a generic locality or stability prior.

While sequential residual fitting is the bedrock of standard boosting frameworks, it inherently breeds learner redundancy by repeatedly revisiting correlated error components. To address this bottleneck, we propose a shift from residual fitting to residual orthogonalization and introduce SCBoost. Our framework tackles redundancy through two complementary mechanisms: Spectral Residual Projection (SRP) and Covariance-Regularized Weighting (CRW). During training, SRP projects each residual target onto the orthogonal complement of the historical prediction subspace, forcing successive learners to capture only novel empirical innovations. During aggregation, CRW optimizes ensemble weights on a validation set with an explicit covariance penalty to mitigate remaining correlations. Theoretically, we provide a finite-sample geometric characterization proving that SRP yields an exact additive residual-energy decomposition. Furthermore, under an isotropic-noise assumption, we rigorously establish the conditions under which this projection improves the effective Signal-to-Noise Ratio. Extensive experiments across ten benchmark datasets demonstrate that SCBoost delivers strong out-of-the-box performance, particularly in accuracy and F1 score. This work reinterprets boosting through a geometric lens, suggesting that explicit redundancy control is a principled and necessary step toward more efficient ensemble architectures.

Video diffusion transformers (DiTs) process tens of thousands of spatio-temporal tokens per denoising step, so low-latency inference and training commonly spread them across several accelerators. Auto-parallelization systems price a sharding on its logical graph, but its cost depends on the program the compiler generates and, on direct networks such as TPU sub-slices, on which chip runs each logical rank; both are visible only after compilation, while the chip assignment must be fixed before it. We present AoiZora, a compiler-agnostic auto-parallelization framework built on two IRs, one for the program a partitioner shards and one for the program a compiler emits; it chooses the logical mesh, the layout of every tensor and operation, and the device assignment of an unsharded model by pricing its compiled programs, without executing any candidate. At the core of AoiZora is evidence, a compiler-neutral record of a compiled program that leaves its placement open, so that one compilation can be priced under many placements by a calibrated model of the accelerator network and the placement can determine which sharding is selected. On TPU v5e, AoiZora reduces the denoising latency of Wan 2.1 and HunyuanVideo by 1.23x and 1.32x on average over expert configurations and Alpa, finding each plan within 10 minutes; it also speeds up training on TPU v5p by 1.11x on 4 chips and 1.21x on 8 chips on average and parallelizes PyTorch programs on GPUs with the same core.

Geographic tipping points in ecosystems, climate subsystems, or ice sheets pose severe challenges for localized early warning. Classical spatial indicators such as Moran's I summarize global spatial structure, but they struggle with three issues: spatial dilution, Euclidean assumptions, and correlated noise. This paper introduces SpatioTemporal Causal Network Diagnostics (ST-CND), a framework that addresses these three issues by representing the geographic field as a time-evolving directed causal network. The core workflow is as follows: (1) infer which spatial nodes help predict other nodes via transfer entropy, replacing fixed Euclidean neighborhoods with data-driven information-flow topology; (2) estimate local recovery rates within each candidate subnetwork via dynamic mode decomposition; and (3) identify the most vulnerable subnetwork by combining three signals, namely high internal fluctuation, high internal synchronization, and low external coupling, thereby suppressing false alarms from spatially correlated noise. Validated on synthetic bifurcations and two observational sea-surface temperature benchmarks, namely Indo-Pacific SST and North Atlantic AMOC, ST-CND delivers localized and interpretable warnings. On the AMOC task, it achieves an AUROC of 0.783 and a critical-subnetwork IoU of 0.378, outperforming recurrence-network and lambda-AR1 baselines. The framework provides an interpretable and scalable pipeline for spatial early warning in Earth system science.

Iterative generative modeling techniques, such as flow matching, provide powerful tools to model complex behaviors for effective offline reinforcement learning (RL). In this work, we propose a new off-policy RL algorithm that trains a flow policy based on prior data. Our idea starts from the "expanded" Markov decision process (MDP) framework, which treats individual flow refinement steps as separate actions in an MDP. To enable off-policy RL within this framework, we apply two techniques: we generate virtual on-policy trajectories (by "reversing" flows) to make this framework compatible with prior data, and we apply a bias-and-variance reduction technique to mitigate the curse of horizon in off-policy RL. We call the resulting algorithm Reversal Q-learning (RQL). RQL has several advantages over previous flow-based RL methods: it does not suffer from backpropagation through time, makes better use of the learned value function, and directly trains the full, expressive flow policy. Through our experiments on 50 challenging simulated robotic tasks, we show that RQL leads to the best average offline RL performance compared to state-of-the-art flow-based offline RL algorithms.

Simulation based solvers for optimal stopping problems must discretize the stopping decision. Under classical dynamic programming, a coarse exercise grid with only a few stopping opportunities can materially undervalue the optimal expected reward, whereas on a very fine grid, approximation errors accumulate through the backward recursion. To remove this limitation, we develop a new reinforcement-learning inspired algorithm that enables us to learn the exercise rule at arbitrarily fine time resolution. Our CARLOS (Continuous-time Adaptive Reinforcement Learning for Optimal Stopping) algorithm utilizes an aggregate deep neural network (ADNN) to learn a joint space-time decision boundary. Starting from a coarse time grid, we progressively increase the frequency of stopping opportunities, while in parallel training the ADNN to refine its timing-value estimates. We moreover design an adaptive sampling strategy that gradually concentrates training effort near the stopping boundary. Benchmarked results show that CARLOS delivers higher prices than existing Bermudan solvers, approaching the American upper bound, and achieves high computational efficiency relative to non-RL comparators.

Offline evaluation of agentic systems often collapses trajectories to terminal success, discarding information about partial progress and inducing widespread ties, creating substantial statistical inefficiency by reducing effective sample size and weakening the ability to distinguish systems. We propose preference-based trajectory evaluation, which compares trajectories directly through temporal preferences over progress and time-to-return profiles. We find that, across diverse agentic and interactive benchmarks, standard success-based metrics produce tied comparisons on roughly 75% of instances, whereas trajectory-aware preferences reduce ties to roughly 35%, improving discriminative power, ranking stability, and data efficiency. Our results suggest that benchmark saturation, often attributed to poor data collection or problem difficulty, may also be explained by the choice of evaluation measure.

Non-negative matrix factorisation (NMF) learns additive representations from data, but non-negativity alone does not ensure interpretable basis functions. We introduce Top-NMF, which guides basis learning through general topological preferences without prescribing the detailed form of the components. Observations and basis vectors are treated as non-negative functions on structured domains. Discrete topological conditions are difficult to optimise directly. Our guiding viewpoint is that persistent homology provides a stable, continuous relaxation of ordinary homological invariants: it tracks connected components and loops across thresholds, allowing structural preferences to be expressed through continuous scores suitable for optimisation. We construct such scores for connected image parts, clique-like graph structure, and periodic time-series components, and incorporate them into a common NMF objective. For graph data, we derive an exact maximum-weight-spanning-tree formula and characterise all local minimisers of the score, showing that their positive-weight edges form disjoint cliques. We establish the regularity of the scores, describe their derivatives, and analyse projected first-order optimisation. Numerical studies on synthetic and real data demonstrate how these priors guide basis learning and examine the balance between structural agreement, atom recovery, and reconstruction accuracy.

New York City implemented the nation's first cordon-based congestion pricing program in January 2025, providing an opportunity to evaluate how system-wide urban mobility responds to large-scale pricing interventions. Because such policies generate spillovers across modes and locations, credible control groups are difficult to construct. We address this challenge using time series foundation models to generate probabilistic counterfactual demand forecasts with calibrated uncertainty. Applying this framework to bus, subway, and aggregate trip volume data, we find that post-policy bus and subway ridership increased significantly relative to expected no-policy demand, while overall travel demand decreased modestly. The effects are spatially heterogeneous: while reductions in overall travel demand are concentrated within the Congestion Relief Zone, transit gains extend beyond Manhattan's core. Socio-demographic analyses further reveal uneven adaptation across neighborhoods, highlighting spatial equity implications. Our framework provides a scalable approach for the uncertainty-aware evaluation of system-wide urban interventions when clean control groups are unavailable.

Scientific machine-learning (SciML) surrogates approximate expensive simulations, but exact expected outputs for arbitrary inputs are unavailable (the oracle problem). Metamorphic testing checks relations across executions, yet a candidate relation is not automatically valid: its preconditions, output mapping, and the numerical floor of the scoring operator determine whether a violation is meaningful. We study how candidate metamorphic relations (MRs) can be screened for domain validity and turned into executable, oracle-free test assets for SciML surrogates. We propose (i) a domain-validity rubric that admits a candidate only when its tolerance dominates the operator's numerical floor and its preconditions hold; (ii) an MR-card executable-asset format recording source cases, transformations, metrics, tolerances, and typed relation-level verdicts; and (iii) a case-study protocol on MeshGraphNets cylinder-flow surrogates, with a claim ledger binding every result to a tracked artifact. On a MeshGraphNets checkpoint, node permutation holds to machine precision, mirror-y is a bounded out-of-distribution stress finding rather than an exact symmetry, and absolute conservation stays deferred while a reference-relative guard passes. The same readings hold across held-out trajectories, a checkpoint roster, three further architectures, and PhysicsNeMo. On a second CFD task (compressible airfoil) the predicate instead rejects incompressible continuity on physical grounds, showing it reasons about domain validity rather than running a fixed checklist. On a second PDE family, FNO Burgers and heat surrogates run full admit/reject/execute verdicts. The evidence spans two CFD tasks and a second PDE family, supporting a validity-aware bridge from candidate MRs to auditable SciML test assets that separates model-level violations from out-of-domain applications.

Efficient optimization is essential for training large language models. Although intra-layer selective updates have been explored, a general mechanism that enables fine-grained control while ensuring convergence guarantees is still lacking. To bridge this gap, we propose MGUP, a novel mechanism for selective updates. MGUP augments standard momentum-based optimizers by applying larger step-sizes to a selected fixed proportion of parameters in each iteration, while applying smaller, non-zero step-sizes to the rest. As a nearly {plug-and-play} module, MGUP seamlessly integrates with optimizers such as AdamW, Lion, and Muon. This yields powerful variants such as MGUP-AdamW, MGUP-Lion, and MGUP-Muon. Under standard assumptions, we provide theoretical convergence guarantees for MGUP-AdamW (without weight decay) in stochastic optimization. Extensive experiments across diverse tasks, including MAE pretraining, LLM pretraining, and downstream fine-tuning, demonstrate that our MGUP-enhanced optimizers achieve superior or more stable performance compared to their original base optimizers. We offer a principled, versatile, and theoretically grounded strategy for efficient intra-layer selective updates, accelerating and stabilizing the training of large-scale models. The code is publicly available at https://github.com/MaeChd/MGUP.

Large language models show strong reasoning ability, but their internal reasoning process can remain unstable in complex multi-step settings, where early hidden-state errors may propagate to incorrect predictions. We propose ReLAR, a reinforcement-guided latent refinement framework that iteratively updates hidden representations before decoding. ReLAR maintains a compact latent reasoning state and uses learned depth and action controllers to adaptively determine both the number and direction of refinement steps. The controllers are trained with a policy gradient objective based on step-wise likelihood improvement, enabling efficient input-dependent reasoning without explicit chain-of-thought generation. Experiments on medical, mathematical, multi-hop reasoning, and open-ended generation benchmarks show that ReLAR improves accuracy, generation quality, and reasoning stability with substantially lower inference overhead than explicit reasoning baselines.

Information-Geometric Optimization (IGO) provides a unified framework for black-box optimization by interpreting the adaptation of a search distribution as a natural gradient update. Despite its conceptual importance, the convergence theory of IGO remains limited: most existing results concern continuous-time idealizations such as the IGO flow, rather than discrete-time updates with non-infinitesimal learning rates. In this paper, we study discrete-time IGO in continuous spaces, formulated as natural gradient updates in the expectation-parameter coordinates of an exponential family. In particular, we analyze IGO over the multivariate Gaussian family on strongly convex quadratic objective functions. Our analysis covers a setting that simultaneously incorporates full covariance adaptation, a fixed positive learning rate, and quantile-based weights. In this setting, we prove that the covariance matrix converges to the zero matrix. We further show that the mean vector converges to the global optimum, provided that the condition number of the appropriately scaled covariance matrix is bounded at sufficiently frequent iterations. These results advance the convergence theory of IGO and help bridge the gap between the mathematical theory of IGO and practical covariance-adaptive search methods such as CMA-ES.

Deep neural networks are widely believed to derive their expressive power from their ability to form hierarchical representations, capturing progressively more abstract and compositional features across layers. In language modeling, transformers have emerged as the dominant architecture, with early layers capturing local syntactic patterns and later layers encoding more complex clause-level dependencies. While this intuition has shaped model design, there remains a lack of rigorous theoretical work demonstrating how deep transformers represent such hierarchical structures. In this work, we analyze the expressiveness of deep transformer models through the formal lens of bounded-depth, non-recursive context-free grammars. For this class of grammars, we explicitly construct transformers with positional attention whose depth grows linearly with grammar depth, while the neuron count scales with the number of derivation-tree shapes and quadratically with the number of production rules. Our theoretical results support the linear representation hypothesis by demonstrating that these architectures possess the structural capacity to encode abstract grammatical states into low-dimensional, linearly separable subspaces within the residual stream.

Causal discovery from observational data remains challenging due to the need to recover directed structure and latent confounding without interventions. We propose FoundCause, an amortized causal discovery model trained entirely on synthetic data that maps datasets directly to causal graphs in a single forward pass. By learning from large collections of simulated structural causal models, FoundCause captures transferable statistical patterns that generalize beyond individual datasets. The architecture incorporates several key inductive biases for causal discovery. It uses a permutation-invariant transformer encoder with alternating attention over samples and variables to jointly model cross-variable dependence and per-variable distributions. Pairwise statistical features derived from classical asymmetry measures are injected through statistics-conditioned attention, guiding the model toward known causal signals. A factorized decoder separates edge existence from direction, while a triangular refinement module enables reasoning over higher-order causal motifs such as chains and colliders. In addition, a dedicated confounder module based on learnable latent tokens explicitly models hidden common causes, and the model explicitly handles missing data via its masked input representation. To our knowledge, FoundCause is the first amortized causal discovery approach to explicitly model latent confounding. FoundCause outperforms 11 classical non-amortized methods (e.g., PC, GES, NOTEARS-style optimization) and 4 amortized causal discovery methods on 15 real-world datasets, achieving +9.6% improvement in $F_1$, +1.2% in AUROC, and an 18.9% reduction in structural Hamming distance relative to the strongest non-amortized methods, while performing inference in a single forward pass.

Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability. Existing approaches primarily model uncertainty in network parameters, largely overlooking the geometry-aware representations learned by the operator itself. We propose REEF-GP (Residual on Embedded Features Gaussian Process), a post-hoc UQ framework that fits a GP to the residuals of a frozen neural operator whose internal embeddings define the kernel feature space. Rather than learning a separate feature map, REEF-GP adapts the operator's intrinsic coordinate-feature representations to construct geometry-aware uncertainties. To ensure stability and scalability on unstructured domains, REEF-GP incorporates spectral-normalized projections, heteroscedastic geometry-aware noise, and efficient subset-based training that avoids restrictive low-rank approximations. Across five PDE benchmarks with varying geometries, REEF-GP preserves predictive accuracy while achieving calibrated uncertainty estimates competitive with deep ensembles but at a fraction of their cost. Our approach remains robust under geometric distribution shift, with uncertainty concentrating in physically meaningful regions (e.g., shock fronts). Our results demonstrate that accurate and scalable post-hoc UQ for neural operators can be achieved directly in their learned feature space, offering a practical alternative to parameter-centric approaches.

Training a model to predict the next step in a concurrent program is harder than it looks: two runs of the same program from the same trace prefix can produce different next events, both valid, because the scheduler is nondeterministic. A model trained against a single label is learning to guess one outcome of a random process. We turn this around and use the nondeterminism as a training signal. We run each program many times, aggregate the observed next events into an empirical distribution, and fine-tune a 7B model to match that distribution with a KL objective. On 798 held-out predictions drawn from real production Go bugs (CockroachDB, Kubernetes, gRPC, etcd), fine-tuning on fewer than a thousand traces reaches 36.2% accuracy, ahead of Gemini 3.5 Flash used zero-shot (34.8%) and the same model without fine-tuning (28.6%). Distribution training matches cross-entropy on accuracy (35.8% vs. 36.2%) while reducing Expected Calibration Error from 0.205 to 0.169. We also derive a formal goroutine-leak signature for a class of select-blocked goroutines where P(GoUnblock)=0 holds by scheduler semantics, not by learning. We release the dataset, trained adapters, and all tooling.

Transformer-based models achieve strong performance for jet tagging at the CERN LHC, but deploying them in low-latency, resource-constrained trigger systems is challenging. We present an initial implementation of a quantized, integer-only transformer for jet tagging on the AMD Versal AI Engine (AIE), mapping dense and multi-head attention (MHA) layers to AIE tiles. The main contribution is a reusable software framework that represents transformer layers as composable AIE building blocks and automatically generates the corresponding Vitis graph code from a high-level Python model description. This framework provides a foundation for future research and is released as open-source software at https://github.com/KastnerRG/particle_transformer_aie.

Binary data factorization is common, but real-valued methods ignore discreteness and yield hard-to-interpret factors. Boolean Matrix Factorization (BooMF) instead decomposes a binary matrix into two lower-rank binary matrices via logical AND and OR, expressing the data as a Boolean disjunction of interpretable patterns. In cancer genomics, BooMF can reveal coordinated feature changes that may drive tumor evolution, unlike rotational or additive decompositions. Most existing BooMF methods are heuristic, greedy, sensitive to initialization, prone to local optima, and do not support principled model selection or uncertainty quantification. We introduce Bayesian Boolean Matrix Factorization (BBMF), a fully conjugate generative model with sparsity-inducing priors. It enforces Boolean constraints, yields interpretable latent factors with coherent uncertainty quantification, and admits Gibbs sampling with closed-form full conditionals. Because cancer evolution often involves widespread, near-simultaneous chromosome-number changes (e.g., whole-genome duplication followed by instability and selection), Boolean factorizations capture these patterns more naturally than additive models. Applied to arm-level copy-number alteration data in multiple myeloma, where entries indicate presence/absence of chromosomal-arm amplifications, BBMF finds a small set of interpretable bicliques linking patient subsets to recurrently co-altered chromosomal arms, providing a compact, biologically meaningful summary of tumor heterogeneity and demonstrating BBMF's utility for uncovering discrete latent structure in complex binary data.

Large Language Models (LLMs) are increasingly deployed in edge-cloud inference systems to handle diverse user tasks with heterogeneous accuracy, latency, and cost profiles. Selecting the appropriate LLM for each incoming task is critical for ensuring service quality and efficient resource utilization. However, model heterogeneity, stochastic and unknown performance characteristics, and time-varying task demands make static selection strategies inadequate. Real-world deployments often impose hard resource budgets such as monetary expenditure limits, along with soft service-level requirements such as latency guarantees. These constraints introduce additional challenges for online decision-making. We formulate this problem as a constrained stochastic bandit learning task, where the learner sequentially selects models under both packing-type (hard) and covering-type (soft) constraints, while adapting to time-varying task demand. The learner operates without access to the underlying reward, cost, or latency distributions and must rely on partial feedback. We develop a novel online learning algorithm that leverages confidence-bound estimates and demand predictions to balance reward maximization with long-term constraint satisfaction. We provide theoretical guarantees showing sublinear regret and sublinear covering constraint violations compared to an offline benchmark with full information. Experimental results on synthetic workloads demonstrate the effectiveness and robustness of our approach in dynamic, resource-constrained environments.

Out-of-distribution (OOD) detection in dynamic open-world environments requires a model to continually adapt to evolving data distributions while generalizing to covariate-shifted inputs and rejecting semantic-shifted OOD examples. Most existing OOD detection methods optimize only the current-step objective and do not explicitly account for how post-deployment environment changes affect future OOD behavior. In this paper, we establish a theoretical grounding for dynamic OOD detection using a reinforcement learning (RL)-guided optimizer that explicitly favors updates that reduce the semantic OOD false positive rate over time. We develop a novel augmented optimizer that uses an RL-guided correction term on top of standard gradient descent (GD) and show its improvement over both future-domain generalization and semantic-OOD rejection. We analyze temporal error decomposition in terms of model-change and environment-change generalization errors and develop a new theoretical framework for comparing the generalization errors under both GD and RL-guided optimizers.

Laser-induced breakdown spectroscopy (LIBS) quantitative analysis faces critical challenges in wavelength selection due to high-dimensional spectral data and the fundamental trade-off between prediction accuracy and feature efficiency. This paper presents a novel Multi-Adapter PPO framework that transforms wavelength selection into a reinforcement learning problem, leveraging cross-attention mechanisms and multiple specialized adapters to capture complex spectral relationships. Our approach outperforms traditional Particle Swarm Optimization (PSO) by an average of 28.4% in comprehensive score and 45.2% in prediction accuracy across steel and coal datasets. The proposed method demonstrates superior performance in balancing prediction accuracy with feature efficiency, achieving state-of-the-art results in LIBS quantitative analysis while maintaining interpretability and computational efficiency. We released our code and dataset here: https://github.com/Hflying/MAPPO