Papers

The paradigm of Weak-to-Strong Generalization (W2SG) suggests that a pre-trained strong model can surpass its weak supervisor, yet the decisive role of pre-training remains theoretically and empirically under-explored. In this work, we identify pre-training as the essential prerequisite for the emergence of W2SG. Theoretically, we formalize the W2SG problem within a high-dimensional single-index model framework using spiked Gaussian data, modeling pre-training as a spectral initialization step. Building upon prior impossibility results regarding the failure of learning under random initialization, we prove that W2SG is achievable when pre-training provides a geometric warm start that places the model within an "effective region" characterized by a perturbed strong-convexity geometry. Within this region, we derive a rigorous generalization bound that naturally captures the optimization dynamics: an initial performance improvement followed by a saturation bottleneck dictated by the weak supervisor's bias. Empirically, we first validate all our assumptions and theoretical insights through controlled synthetic simulations. Finally, through a massive-scale evaluation of hundreds of intermediate pre-training checkpoints from large language models, we demonstrate that W2SG is not an innate capability but emerges via a phase transition tightly coupled with the progression of pre-training.

Kernel quadrature can exploit RKHS spectral structure and outperform Monte Carlo on smooth integrands, but optimized quadrature weights are generally signed and may be numerically unstable. We study whether spectral acceleration remains possible when the weights are constrained to be positive, i.e., simplex weights. In the exact-target fixed-pool setting, an evaluated i.i.d. candidate pool of size $N$ is already available and the task is to reweight it so as to approximate the kernel mean embedding. We show that this positive reweighting problem is governed not by the equal-weight empirical average, but by the random convex hull generated by the pool. Our main geometric result shows that the mean of a bounded $d$-dimensional random vector can be approximated by a convex combination of $N$ i.i.d. samples at accuracy $O(d/N)$ with high probability, sharper than equal-weight averaging in the fixed-dimensional regime. We transfer this $d$-dimensional convex-hull approximation to full RKHS worst-case error through an augmented Mercer-truncation argument. The resulting positive-weight KQ bounds consist of a spectral tail term and a finite-sample convex-hull term, yielding Monte-Carlo-beating rates in favorable spectral regimes, including near-$O(1/N)$ rates up to logarithmic factors under exponential spectral decay. We also provide a constructive Frank–Wolfe algorithm that operates directly on the pool atoms, maintains simplex weights, and admits an explicit optimization-error bound.

Optimizing the communication structure of large language model based multi-agent systems (LLM-MAS) has been shown to improve downstream performance and reduce token usage. Existing methods typically rely on randomly sampled training tasks. However, tasks may differ substantially in difficulty and domain, and thus they are not equally informative for updating communication structure, making optimization often unstable and highly sensitive to the particular training set. To actively identify the most valuable tasks for communication-structure optimization, we propose an ensemble-based information-theoretic task selection framework. The proposed method estimates task informativeness by how much a candidate task changes the distribution over graph parameters, using ensemble Kalman inversion as an efficient and derivative-free approximation of the corresponding Bayesian update. The resulting estimator is especially suitable for black-box and noisy multi-agent systems. To enhance scalability, we construct a compact candidate pool through embedding-based representative selection and combine the informative selection with surrogate modeling and batch Thompson sampling. We validate the proposed framework across both benign and adversarial settings and multiple task formats. It consistently outperforms random training, demonstrating more effective task selection and greater overall cost efficiency.

Transformers usually expose one inference cost per trained model, while deployed systems often need multiple cost-quality operating points. We study Budgeted Attention Allocation, a monotone head-gating mechanism conditioned on a requested attention budget. Dense warm-starting is important for stability: on a robust synthetic sequence task, one budgeted model reaches 99.7% accuracy at 0.303 estimated attention cost and 100.0% accuracy at 0.504 cost. On held-out AG News with a custom word-level transformer, hard-gate adaptation turns soft cost control into measured single-thread CPU speed, reaching 82.1% accuracy with 1.28x speedup at budget 0.50. In pretrained BERT-Mini AG News, budgeted structural pruning reaches 87.6% accuracy with 1.20x speedup at budget 0.50; a validation-ranked zero-shot dense post-hoc structural baseline reaches 86.1%, and one recovery epoch raises that per-budget specialist to 87.9%. On DBpedia14, BERT-Mini budgeted gates reach 97.4% at exact budget 0.50 versus 96.6% for dense full attention. Static fixed-budget gates and recovered dense specialists remain strong. The contribution is therefore not universal dominance, but a reproducible feasibility study of one controllable checkpoint across budgets that can trade attention cost for accuracy and be converted into measured structural speedups on small CPU benchmarks.

Agentic LLM workloads put bit-identical tokens at shifted positions every turn, voiding prefix caches at the first byte of divergence. Operators report cache-hit regressions ranging from moderate slowdowns to severe TTFT spikes of 10-16s on unchanged content. Prior position-independent caching systems correct RoPE on the full $d_K$-dimensional key, an architectural cost imposed by GQA, not by caching itself. Multi-Head Latent Attention, deployed at scale in DeepSeek-V2/V3/R1, Kimi-K2/Moonlight, GLM-5, and Mistral Large 3, factors each KV row into a position-free $c_{KV}$ and a 64-dim $k_r$ correctable in closed form; this structure motivates content-addressed caching as a natural fit rather than a GQA workaround. We present Irminsul, which extends SGLang's radix cache with content-hash keying over CDC-chunked segments and a $\delta$-rotation rule for $k_r$. We evaluate three native MLA-MoE deployments - DeepSeek-V2-Lite (16B/2.4B), Kimi Moonlight-16B-A3B, and JoyAI-Flash (48B/3B) - with output-consistency on all three and recovery measured on the two endpoints; Irminsul recovers up to ~83% of prompt tokens above exact-prefix on agentic traffic while delivering 63% prefill energy savings per cache hit. We argue that content-addressed caching belongs in the serving stack as a first-class primitive, not a retrofit over prefix matching.

Post-training quantization (PTQ) is an effective approach for deploying large language models (LLMs) under memory and latency constraints. Most existing PTQ methods determine quantization parameters by minimizing a layer-wise reconstruction error on a predetermined calibration dataset, typically optimized via either scale search or Gram-based methods. However, from the perspective of generalization risk, existing PTQ calibration objectives based solely on empirical reconstruction error over limited or unrepresentative calibration data may move the quantized weights away from the original floating-point weights, potentially degrading downstream performance. To address this issue, we propose Regularized Quantization Calibration (RQC), a unified framework that augments standard PTQ objectives with a regularizer that explicitly controls weight deviation from the original weights. We further generalize this framework to incorporate a saliency-aware regularizer, resulting in Saliency-Aware Regularized Quantization Calibration (SARQC). The proposed regularization encourages quantized weights to remain close to the original weights during calibration, leading to improved generalization at inference time. SARQC integrates seamlessly into existing PTQ pipelines and enhances both scale-search-based and Gram-based methods under a unified formulation. Extensive experiments on dense and Mixture-of-Experts LLMs demonstrate consistent improvements in perplexity and zero-shot accuracy, without introducing additional inference overhead.

Unlike MLPs, Kolmogorov-Arnold Networks (KANs) expose explicit learnable edge functions on every connection, enabling mechanistic explanation in time-series forecasting. This paper introduces Temporal Functional Circuits, a framework that transforms KAN edge functions from latent visualizations into faithful, temporally grounded explanations. Built on a gated residual KAN that decomposes forecasts into a linear base and a sparsely activated KAN correction, the framework (i) maps each edge to input lags via output-aware attribution, (ii) ranks edges by learned activation range, and (iii) validates faithfulness through edge-level interventions including zeroing and spline removal. Removing the learned B-spline component while retaining the base SiLU term degrades forecasts, providing evidence that the spline shape itself carries predictive value beyond the base activation. On four synthetic regimes of increasing complexity, the learned gate opens progressively wider as signal complexity grows. On regime-switching signals, gated KAN achieves 59% lower MSE than linear-only models. Across eight benchmarks, the gated architecture is competitive with linear, attention, and MLP alternatives, while providing interpretable edge functions that MLP-based corrections cannot offer.

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of decoder-only models adapted from the modded NanoGPT codebase, we introduce an empirical protocol based on activation covariance and per-sample gradient SVD spectra. This dual-view reveals three empirical findings and one mechanistic explanation. First, batch size acts as a latent determinant of representation geometry: runs that reach equal loss settle into systematically distinct activation spectra. Second, the activation covariance tail measured early in training reliably forecasts downstream token efficiency. Third, movement of the activation spectrum head (leading modes), together with gradient spectra, characterizes underlying learning-dynamics changes, separating learning-side architectural improvements from primarily execution-side gains. These predictive and diagnostic signals persist across the 12-, 36-, and 48-layer model tiers. Finally, a mechanistic model proves the main observations and explains how activation covariance spectra correlate with task-aligned feature learning.

Vector search systems built on frozen vision encoders face queries from unseen classes at deployment, yet existing adapter training collapses under this shift: high-capacity adapters with global contrastive losses silently reassign unseen-class samples to wrong seen-class clusters, dropping worst-case Label Precision by over 40 points below the frozen baseline in our tests. We propose Euclidean Geodesic Alignment (EGA), a residual adapter that couples three principles: zero initialization, local triplet loss, and hypersphere projection. These collectively induce a self-limiting dynamic: triplets that already satisfy a small margin stop producing gradients, so the adapter automatically stops updating where the local geometry is already correct. Our experiments show that at convergence $96.5\%$ of triplets are gradient-free, leaving unseen-class regions largely untouched while still enabling full-capacity refinement of seen classes. Across five diverse out-of-distribution (OOD) benchmarks, EGA achieves the highest worst-case Label Precision on the four primary splits and a consistent improvement on the fifth. The design also transfers to stronger backbones in addition to CLIP, and we provide an analytical justification linking gradient sparsity to bounded OOD perturbation.

Multi-objective optimization (MOO) has received growing attention in applications that require learning under multiple criteria. However, most existing MOO formulations do not explicitly account for distributional shifts in the data. We introduce distributionally robust multi-objective optimization (DR-MOO), which minimizes multiple objectives under their respective worst-case distributions. We propose Pareto-type solution concepts for DR-MOO and develop multi-gradient descent algorithms (MGDA) with provable guarantees. Leveraging a Lagrangian dual reformulation, we first design a double-loop MGDA that uses an inner loop to estimate dual variables and achieves a total sample complexity $\mathcal{O}(\epsilon^{-8})$ for reaching an $\epsilon$-Pareto-stationary point. To further improve convergence, we combine large-batch sampling with gradient clipping to accommodate generalized smoothness and control bias in stochastic preference updates, eliminating the need for double sampling. This yields a single-loop double-clip MGDA with substantially improved sample complexity $\mathcal{O}(\epsilon^{-4})$. Our theory applies to nonconvex problems without requiring uniformly bounded gradients of the dual objectives. Experiments demonstrate that our methods are competitive with state-of-the-art MGDA baselines.

Structured low-rank and sparse-plus-low-rank parameterizations, motivated by methods such as LoRA and low-rank factorization, impose strong structural constraints on the linear transformations within neural networks. We study the expressive consequences of these constrained structures from the perspective of universal approximation. We first characterize that purely low-rank neural networks, despite being able to exactly interpolate arbitrary finite scalar datasets, can fail to approximate continuous functions that vary along directions ignored by the low-rank hidden mapping. We show that augmenting the low-rank structure with a one-parameter diagonal component suffices to overcome this geometric bottleneck, yielding a Diagonal-plus-Low-Rank (DLoR) structure. We show that a full-rank linear transformation can be reconstructed using DLoR components either by expanding network width through additive decomposition or by extending network depth through multiplicative decomposition. We term this correspondence between additive width expansion and multiplicative depth extension the Structural Correspondence framework. By combining these constructions with local linearization of the activation function, we prove that DLoR neural networks restore universal approximation for general activation functions. These results characterize how architectural width and depth can compensate for severe rank constraints without requiring unrestricted dense hidden transformations. Diagonal terms are required for multiplicative construction, while additive expansion works with purely low-rank terms. We further determine its exact cost: both the minimal number of rank-$r$ DLoR factors representing $W$ and the minimal network depth for that layer equal $\lceil\kappa(W)/r\rceil$, where $\kappa(W)=\min_{\gamma\ne0}rank(W-\gamma I)$, achieving a lower cost than its dense representation when $W$ is identity-centered.

Simulation-based inference (SBI) provides amortized Bayesian parameter inference from simulator-generated data without requiring explicit likelihood evaluation. Its reliability can degrade under model misspecification, where real-world observations are not well represented by the simulator used for training. Existing methods using unlabeled real-world data often align simulated and real-world data distributions, but marginal alignment alone does not directly preserve parameter-relevant information needed for posterior inference. We propose SPIN, an SBI framework with parameter-relevant information-preserving domain transfer using unlabeled, unpaired real-world observations. During training, SPIN translates labeled simulator observations toward the real-world domain and back to the simulator domain, using the original simulator labels to encourage domain transfer that preserves parameter-relevant mutual information. At test time, the learned real-to-simulator transport maps real-world observations into the simulator domain for posterior inference, without requiring real-world parameter labels or paired real–simulator observations. Across controlled synthetic and physical real-world benchmarks, SPIN improves real-world posterior inference, with the improvement becoming clearer as misspecification increases.

Models trained with deep learning often fail to signal when inputs fall outside their training data manifold, leading to unreliable predictions under distribution shift. Prior work suggests that effective out-of-distribution (OOD) detection often requires class-conditional modeling or specialized models obtained through supervised fine-tuning. We revisit this assumption in modern pretrained models and show that their frozen representations already encode sufficient geometric structure for accurate label-free OOD detection. Across 59 backbone-task pairings spanning vision and language, we compare two complementary label-free detectors: a global Mahalanobis estimator fit on unlabeled latent representations, and ReSCOPED, a lightweight, diffusion-based typicality estimator operating on the same features at a local level. Despite their different detection mechanisms, representation scaling reveals a consistent regime-dependent pattern: both local and global detectors' absolute performance improves with better representation quality, and performance gaps between the two detectors disappear across both language and vision tasks as representations scale. These results suggest that label-free OOD detection depends strongly on the geometry exposed by frozen pretrained backbones, reducing the importance of detector choice as backbone scale increases and enabling efficient deployment directly on frozen models.

Retrieval-Augmented Generation (RAG) systems are vulnerable to knowledge base poisoning, yet existing attacks have been evaluated almost exclusively against vanilla retrieve-then-generate pipelines. Architectures designed to handle conflicting retrieved information - multi-agent debate, agentic retrieval, recursive language models - remain untested against adversarially optimized contradictions. We evaluate four RAG architectures (vanilla RAG, agentic RAG, MADAM-RAG, and Recursive Language Models) under controlled single-document (N=1) poisoning on 921 Natural Questions QA pairs, comparing a clean baseline, naive injection, and CorruptRAG-AK - an adversarial attack whose meta-epistemic framing targets credibility assessment. Architecture is a high-impact variable in adversarial robustness: under CorruptRAG-AK, attack success rates range from 81.9% (vanilla) to 24.4% (RLM) - a spread of nearly 58 percentage points across architectures with comparable clean accuracy (~92%). Decomposing this gap, once the poisoned document is retrieved, adversarial framing - not retrieval optimization - drives the majority of CorruptRAG-AK's advantage for three of four architectures, localizing the cross-architecture vulnerability at the content-reasoning stage. Our MADAM-RAG reimplementation shows the highest apparent contradiction detection rate, though our LLM judge over-identifies this behavior (~48.5% precision), so reported rates are upper bounds. Regardless of detection, MADAM-RAG cannot resolve contradictions reliably, producing a 41.4% non-answer rate even on clean inputs - though implementation divergences from the original may contribute. We introduce a seven-category behavioral taxonomy capturing contradiction detection, hedging, and failure modes beyond binary accuracy. Code, data, and analysis notebooks are publicly available.

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere $\mathbb S^{d-1}$. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on $\mathbb S^{d-1}$ to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on $(\mathbb S^{d-1})^L$ both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The vMF path especially in combination with PC sampling significantly improves results on Sudoku, language modeling, and mathematical reasoning.

Sustainable forest management relies on precise species composition mapping, yet traditional ground surveys are labour-intensive and geographically constrained. While Uncrewed Aerial Vehicles (UAVs) offer scalable data collection, the transition to deep learning-based interpretation is bottlenecked by the severe scarcity of expert-annotated imagery, particularly in complex, visually heterogeneous regeneration zones. This paper addresses the dual challenges of data scarcity and extreme class imbalance in the fine-grained semantic segmentation of plants by providing a scalable framework that reduces reliance on manual photo-interpretation for high-resolution, millimetre-level aerial imagery. Importantly, we leverage the large-scale Nano Banana Pro model to simultaneously generate high-fidelity images and their corresponding pixel-aligned semantic masks from prompts. We introduce WilDReF-Q-V2, an expansion of a natural forest dataset with 13 977 new unlabelled and 50 hand-labelled real images, as well as the Gen4Regen dataset, featuring 2101 pairs of synthetic images and semantic masks. Our methodology integrates real-world data with AI-generated images, highlighting that AI-generated data is highly complementary to real-world data, with unified training yielding an F1 score improvement of over 15 %pt compared to purely supervised baselines. Furthermore, we demonstrate that even small quantities of prompt-generated data significantly improve performance for underrepresented classes, some of which see per-class F1 score gains of over 30 %pt. We conclude that large-scale vision models can serve as agile data generators, effectively bootstrapping perception tasks for niche AI domains where expert labels are scarce or unavailable. Our datasets, source code, and models will be available at https://norlab-ulaval.github.io/gen4regen.

Parity (XOR) classification requires detecting discrete, high-order feature interactions that smooth classical kernels cannot efficiently capture. We study how quantum kernel advantage depends on parity complexity, the number of features entering the XOR rule, and find a clear threshold behavior. We pair a ZZ quantum feature map with binary {0, pi} encoding (features median thresholded before circuit input) to expose parity structure. A binary encoding ablation, RBF SVM trained on the identical {0, pi} features, separates encoding from circuit effects: at low complexity (n = 5 features), binary RBF achieves 83.4% +/- 1.7% and the quantum kernel 81.2% +/- 1.9%, showing encoding drives performance there. At high complexity (n = 11 features, 11 qubits, r = 3 ZZ repetitions), all classical methods collapse to near-random (approx. 50%), binary RBF reaches only 54.3% +/- 1.1%, and the quantum ZZ kernel achieves 66.3% +/- 3.2% (mean +/- std, 10 seeds), a +12.0 percentage-point margin over the binary ablation and approx. 7x higher kernel-target alignment (0.094 +/- 0.020 vs. 0.013 +/- 0.001). These results identify parity complexity as a concrete axis along which genuine quantum kernel advantage, not attributable to encoding alone, emerges.

Hyperspectral in situ sensing has shown promise in retrieving aquatic biogeochemical (BGC) parameters, such as total suspended solids, dissolved organic carbon, and total chlorophyll-a, for cost-effective monitoring of coastal water quality. However, generalising such retrieval algorithms across water bodies remains challenging, as the relationship between remote sensing reflectance (Rrs) and BGC parameters can vary considerably from one region to another due to regional distinctions in environmental conditions and biogeochemistry that lead to different BGC ranges and bio-optical properties. In this study, we propose a two-stage physics-aware meta-learning framework for retrieving coastal BGC parameters from near-surface Rrs observations. In the first stage, a bio-optical forward model is used to generate a large synthetic dataset based on an in situ bio-optical spectral library with broad representativeness of Australian coastal waters. This dataset is then used to pretrain a region-agnostic base model with meta-learning, allowing the model to learn fundamental physical relationships. In the second stage, the pretrained base model is fine-tuned for specific regions with local samples. We collected in situ hyperspectral Rrs and BGC measurements from five geographically distinct sites in Australian coastal waters. Our experimental results suggest: (1) the BGC parameters and their corresponding hyperspectral Rrs signatures exhibited clear regional distinctions among the experimental sites; (2) the synthetic dataset was physically plausible and closely aligned with real-world samples in both parameter distributions and inter-parameter correlations; (3) the proposed approach outperformed five benchmark models in BGC retrieval; and (4) time series of in situ measured and model-predicted BGC parameters showed good agreement in both magnitude and temporal dynamics.

Rheumatoid arthritis (RA) assessment from hand radiographs requires multi-level analysis and modeling of anatomical structures and fine-grained local pathological changes. However, existing public resources do not support such unified multi-level analysis, often lacking full-hand coverage, fine-grained annotations, and consistent integration with clinical scoring systems. In particular, annotations that enable quantitative analysis of bone erosion (BE) remain scarce. RAM-H1200 contains 1,200 hand radiographs collected from six medical centers, with multi-level annotations including (i) whole-hand bone structure instance segmentation, (ii) pixel-level BE masks, (iii) SvdH-defined joint regions of interest, and (iv) joint-level SvdH scores for both BE and joint space narrowing (JSN). It is designed to evaluate whether models can jointly capture anatomical structure, localized erosive pathology, and clinically standardized RA severity from hand radiographs. The proposed BE masks enable, for the first time, quantitative BE analysis beyond coarse categorical grading by providing explicit spatial supervision for lesion extent and morphology. To our knowledge, RAM-H1200 is the first public large-scale benchmark that jointly supports whole-hand bone structure instance segmentation, pixel-level BE delineation, and clinically grounded joint-level SvdH scoring for both BE and JSN. Results across benchmark tasks show that anatomical modeling is substantially more mature than quantitative BE analysis: whole-hand bone segmentation achieves strong performance, whereas BE segmentation remains a major open challenge. By unifying anatomical structure modeling, quantitative lesion analysis, and clinically grounded SvdH scoring, RAM-H1200 provides a single benchmark for comprehensive RA analysis on hand radiographs.

Large language models (LLMs) impose rapidly growing energy demands, creating an emerging energy and carbon crisis driven by large-scale inference. Solar-powered, AI-enabled low Earth orbit (LEO) satellites have been proposed to mitigate terrestrial electricity consumption, but their lifecycle carbon footprint remains poorly understood due to launch emissions, satellite manufacturing, and radiation-hardened hardware requirements. This paper presents LLMSpace, the first carbon modeling framework for LLM inference on AI-enabled LEO satellites. LLMSpace jointly models operational and embodied carbon, peripheral subsystems, radiation-hardened accelerators and memories, and LLM-specific workload characteristics such as prefill-decode behavior and token generation. Using realistic satellite and GPU configurations, LLMSpace reveals key trade-offs among carbon footprint, inference latency, hardware design, and operational lifetime for sustainable space-based LLM inference. Source code: https://github.com/UnchartedRLab/LLMSpace.

We study contextual dynamic pricing with linear valuations and bounded-support agnostic noise, whose induced demand curve may be non-Lipschitz with arbitrary jumps and atoms. Such discontinuities break the cross-context interpolation arguments used by smooth-demand pricing algorithms, while the best previous method achieved only $\tilde O(T^{3/4})$ regret. We propose Conservative-Markdown Redirect-UCB Pricing, a polynomial-time algorithm that combines randomized parameter estimation, conservative residual-grid probing, and confidence-based one-step redirection. Our algorithm achieves $\tilde O(T^{2/3})$ optimal regret, matching the known lower bounds of Kleinberg and Leighton (2003) up to logarithmic factors and improving over the previous upper bound of Xu and Wang (2022). Under stochastic well-conditioned contexts, this closes the long-existing open regret gap in linear-valuation contextual pricing under agnostic non-Lipschitz noise distribution.

Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and parameters from sparse, noisy observations. Classical smoothing methods for this problem are often limited by path degeneracy and poor scalability. In this work, we developed a novel method based on characterization of the posterior SDE in terms of conditional backward-in-time score defined as the gradient of a function solving a Kolmogorov backward equation with multiplicative updates at observation times. We learn this conditional score using neural networks trained to satisfy both the governing PDE and the observation-induced jump conditions, thereby integrating continuous-time dynamics with discrete Bayesian updates. The resulting score induces a posterior SDE with the same diffusion coefficient but a modified drift, enabling efficient posterior trajectory sampling. We further derive a likelihood-based objective for learning the SDE parameters, yielding an evidence lower bound (ELBO) for joint state smoothing and parameter estimation. This leads to a variational EM-style procedure, where the neural conditional score is optimized to approximate the smoothing distribution, followed by a maximization step over the SDE parameters using samples from the induced posterior. Experiments on nonlinear systems demonstrate accurate and stable inference with a very few observations demonstrating significant improved scalability compared to classical MCMC methods.

While Multimodal Large Language Models (MLLMs) are increasingly integrated with Retrieval-Augmented Generation (RAG) to mitigate hallucinations, the introduction of external documents can conceal severe failure modes at the instance level. We identify and formalize the phenomenon of recorruption, where the introduction of even perfectly accurate "oracle" context causes a capable model to abandon an initially correct prediction. Through a mechanistic diagnosis of internal attention matrices, we show that recorruption is driven by a two-fold attentional collapse: (1) visual blindness, characterized by the systemic suppression of visual attention mass ($M_{vis}$) and sharpness ($S_{vis}$), and (2) a structural positional bias that forces the model to prioritize boundary tokens over semantic relevance. Our analysis reveals an Illusion of Success, demonstrating that many seemingly correct RAG outcomes are merely positional coincidences where the model's textual copying bias happens to align with the ground-truth location. To address these vulnerabilities, we propose Bottleneck Attention Intervention for Recovery (BAIR), a parameter-free, inference-time framework that restores visual saliency and applies position-aware penalties to textual distractors. Across medical factuality, social fairness, and geospatial benchmarks, BAIR successfully restores multimodal grounding and improves diagnostic reliability without requiring model retraining or fine-tuning.

Increasing a voting budget can improve or reduce population accuracy, and an initial gain or loss need not persist. We give a complete structural classification of these curves for binary unweighted majority under infinitely exchangeable correctness indicators, with an arbitrary latent success-probability law $\Pi$. The classification is encoded by the signed voting signature $ \omega_\Pi(B)=\int \mathbf{1}\{q(1-q)\in B\}(2q-1)\,\Pi(\,\mathrm{d} q). $ The complete odd-budget curve and this signature determine each other: the initial accuracy gives its total signed mass, and successive budget increments give its higher moments. Reflection-symmetric differences between latent laws are exactly the changes invisible to voting. A weighted total-variation constraint characterizes every attainable signature, and a minimum-mass allocation to the two reflected branches, completed by symmetric probability mass, gives every population producing its curve. Consequently, the full curve identifies the latent population precisely when no symmetric mass remains to redistribute.

Positive-unlabeled (PU) learning addresses binary classification when only a set of labeled positives is available alongside a pool of unlabeled samples drawn from a mixture of positives and negatives. Existing PU methods typically require dataset-specific training or iterative optimization, which limits their applicability when many tasks must be solved quickly or with little tuning. We introduce PUICL, a pretrained transformer that solves PU classification entirely through in-context learning. PUICL is pretrained on synthetic PU datasets generated from randomly instantiated structural causal models, exposing it to a wide range of feature-label relationships and class-prior configurations. At inference time, PUICL receives the labeled positives and the unlabeled samples as a single input and returns class probabilities for the unlabeled rows in one forward pass, with no gradient updates or per-task fitting. On 20 semi-synthetic PU benchmarks derived from the UCI Machine Learning Repository, OpenML, and scikit-learn, PUICL outperforms four standard PU learning baselines in average AUC and accuracy, and is competitive on F1-score. These results show that the in-context learning paradigm extends naturally beyond fully supervised tabular prediction to the semi-supervised PU setting.

High-fidelity CFD is essential for aerodynamic design, but repeated simulations are computationally expensive, motivating surrogate models for rapid evaluation across geometries and operating conditions. Most existing surrogates are designed for direct field regression, requiring the evaluation of millions of field points even when only an aerodynamic quantity or a localized region is needed, while their internal representations are not intended for direct use in downstream tasks. We introduce AeroJEPA, a framework inspired by joint-embedding predictive architectures that represents the problem in two distinct latent spaces: context tokens encode geometry, while predicted tokens encode the aerodynamic state. Both representations remain directly accessible for downstream tasks, such as linear readouts of design variables and aerodynamic quantities without decoding and integrating the full field. When spatial detail is needed, a continuous implicit decoder evaluates the field only at the requested coordinates while reusing the encoded geometry. We evaluate AeroJEPA on HiLiftAeroML, with multi-million-point fields, and SuperWing, which spans a broad family of transonic wings. Compared with state-of-the-art direct-regression surrogates, AeroJEPA trades peak full-field accuracy for compact, reusable representations. In our selective-decoding experiment, however, AeroJEPA substantially outperforms the evaluated direct-regression surrogates while avoiding predictions over the remainder of the aircraft. The learned representations further support controlled interpolation, concept-vector arithmetic, and preliminary constrained latent-space optimization. These results show how predictive representations can support aerodynamic analysis with or without full-field reconstruction.

This study proposes a scalable Digital Twin framework for energy optimization in data centers.The framework integrates IoT-based data acquisition, cloud computing, and machine learning techniques to enable real-time monitoring, forecasting, and intelligent energy management. A controlled small-scale data center environment was developed to monitor variables such as power consumption, temperature, and computational workload. Long Short-Term Memory (LSTM) models were employed to predict energy demand and support operational decision-making. Experimental results demonstrated improvements in energy efficiency, including reductions in power consumption and enhancements in Power Usage Effectiveness (PUE). Despite being evaluated in a constrained environment, the proposed framework demonstrates strong potential as a scalable and cost-effective solution for sustainable data center management.

Recent optimizers such as Lion and Muon have demonstrated strong empirical performance by normalizing gradient momentum via linear minimization oracles (LMOs). While variance reduction has been explored to accelerate LMO-based methods, it typically incurs substantial computational overhead due to additional gradient evaluations. At the same time, the theoretical understanding of LMO-based methods remains fragmented across unconstrained and constrained formulations. Motivated by these limitations, we propose LMO-IGT, a new class of stochastic LMO-based methods leveraging implicit gradient transport (IGT). We further introduce a unified framework for stochastic LMO-based optimization together with a new stationarity measure, the regularized support function (RSF), which bridges gradient-norm and Frank–Wolfe-gap notions within a common framework. By evaluating stochastic gradients at transported points, LMO-IGT accelerates convergence while retaining the single-gradient-per-iteration structure of standard stochastic LMO. Our analysis establishes that stochastic LMO achieves an iteration complexity of $\mathcal{O}(\varepsilon^{-4})$, variance-reduced LMO achieves $\mathcal{O}(\varepsilon^{-3})$ at the cost of additional gradient evaluations, and LMO-IGT achieves $\mathcal{O}(\varepsilon^{-3.5})$ using only a single stochastic gradient per iteration. Empirically, LMO-IGT consistently improves over stochastic LMO counterparts with negligible overhead. Among its instantiations, Muon-IGT achieves the strongest overall performance across evaluated settings, demonstrating that IGT provides an effective and practical acceleration mechanism for modern LMO-based optimization.

This paper shows that the semi-dual formulation of the optimal transport problem has a degenerate saddle-point structure, and that its numerical solution is equivalent to solving a constrained optimization problem. We derive necessary and sufficient conditions for the convergence of Monge maps without requiring optimality of the dual potential. This analysis helps explain why, in practice, numerical algorithms often require more iterations to update the transport map than the potential.

Despite the growing availability of large datasets, causal structure learning remains computationally prohibitive at scale. We revisit sparsest-permutation learning for linear structural equation models and show that exact Cholesky factorization is unnecessary for structure recovery. This observation motivates a support-level relaxation that searches for sparse triangular factors over a precision-support screening graph. The relaxed formulation can be efficiently evaluated via masked zero-fill incomplete Cholesky factorization, enabling scalable comparison of candidate orderings. At the population level, we establish soundness for Markov equivalence class (MEC) recovery under no-cancellation and sparsest Markov representation assumptions, as well as robustness to ordering misspecification. Motivated by these guarantees, we introduce SCOPE, a sparse-Cholesky pipeline that provides a scalable implementation of the relaxed formulation. Experiments on synthetic and real datasets demonstrate that SCOPE matches the MEC recovery accuracy of substantially slower baselines, while achieving significantly reduced runtime and scaling to 10k variables.