Papers

Statistical learning is a fascinating field that has long been the mainstream of machine learning/artificial intelligence. A large number of results have been produced which can be widely applied to real-world problems. It also leads to many research topics and also stimulates new research. This report summarizes some classical statistical learning models and well-known algorithms, especially for amateurs, and provides a category-theoretic perspective on understanding statistical learning models. The aim is to attract researchers from other fields, including basic mathematics, to participate in the research related to statistical learning.

Real-time bidding (RTB) ad exchanges typically forward nearly all incoming requests to demand-side platforms (DSPs), even though only a small fraction receive bids. This over-distribution weakens auction outcomes: DSPs throttle participation under compute and budget constraints, reducing the effective use of limited bidding capacity. We present a competition-aware request dispatch framework that uses distributional bid prediction and probabilistic forwarding to decide whether each request should be sent to each DSP. The system adapts per-DSP thresholds over time through lightweight policy optimization to track non-stationary market conditions. We evaluate the framework through four sequential online experiments on a production platform serving over 20 billion daily requests. A full multi-DSP deployment reduces DSP request volume under the policy by 34.2% while increasing net revenue by 4.6% (p<0.001) in a recent 14-day window after an initial DSP adaptation period. Further analysis highlights strong heterogeneity across traffic segments and reveals that aggregate metrics can be misleading. Segment-level and per-DSP analyses suggest that the policy surfaces comparative advantages among DSPs, improving monetized outcomes without increasing overall request volume.

This work focuses on the problem of learning on temporal graphs, with particular emphasis on the task of clustering: obtaining coarse-grained representations by aggregating information from nodes, edges, and temporal dynamics - a task related to pooling in machine learning on graphs, or community detection in network science. Although graph neural networks reach state-of-the-art performance across many downstream graph tasks, their advantage over established descriptive and inferential clustering algorithms is far less settled, especially under demands of efficiency and recovery accuracy. We frame this tension through three linked perspectives: principles, connecting graph learning and community detection through shared spectral foundations and detectability thresholds in stochastic block model regimes; primitives, making spectral clustering and multislice modularity optimization tractable through GPU-accelerated temporal backends; and pooling, viewing principled community detection as a theory-grounded coarse-graining operator for temporal graphs. Our results indicate that algorithmic methods remain the appropriate tool where attributes are absent or weak - scalability rather than accuracy being the binding obstacle - while neural models are most compelling when structural, temporal, and attribute signals align. By making temporal clustering scalable, GPU-accelerated primitives suggest a route toward theory-grounded pooling, while raising a central question: when does community-based coarse-graining preserve the dynamics needed for downstream learning tasks?

This work addresses community detection in temporal networks through GPU-accelerated extensions of spectral clustering and modularity-based algorithms originally designed for static graphs. Built on the NVIDIA RAPIDS ecosystem, the framework enables the characterization and tracking of communities in snapshot-based dynamic graphs, either by Leiden greedy optimization with multi-GPU support via Dask-based workload distribution, or eigendecomposition of a symmetric Bethe-Hessian operator. Our multislice modularity backend achieves up to roughly three orders of magnitude speedup over the CPU reference under an equal-work budget, depending on graph density and snapshot count, while preserving compatibility with existing graph analytics pipelines. We demonstrate its applicability on real-world and synthetic datasets, facilitating exploratory analysis of structural network properties over time. Such capabilities are relevant across several application domains, such as epidemic spreading, financial systems, cybersecurity, and trajectory and mobility analysis. We release our implementation as free and open-source software, including Python bindings through the NetworkX-Temporal library for ease of use and zero-code acceleration with existing codebases.

Point-of-care cardiac devices such as smartwatches and handheld ECG recorders typically capture 1–2 leads, yet existing ECG foundation models are architecturally constrained to fixed 12-lead inputs, degrading or failing under these reduced configurations. We introduce LAEF (Lead-Agnostic ECG Foundation), a 7M-parameter ECG foundation model that can natively process any lead subset without zero-padding or architectural modification. LAEF represents ECGs as variable-size spatiotemporal graphs with physiologically motivated intra- and inter-lead connectivity, processed by a Graph Attention Network that scales naturally with active lead count.Pre-trained on 9.2M 12-lead ECGs via masked node modelling with stochastic lead sampling, LAEF learns representations robust to lead configuration. Across 18 downstream datasets, LAEF is on par with specialized 12-lead baselines over 12$\times$ larger at full lead availability. Under direct point-of-care-oriented diagnostics (1–2 leads), it outperforms all zero-padded alternatives on 17 out of 18 datasets with with a single randomly sampled lead and on 14 out of 18 with 2 leads, with an average AUROC gain of +3.2 points. Representation analysis links this advantage to architectural lead-agnosticism, and a lead-importance study across 164 cardiovascular conditions shows population-level performance is stable across single standard input leads while still recovering established clinically lead-condition associations.

Causal diagnostic models must explain how conclusions follow from evidence because diagnoses guide repairs and treatments. Yet serious cases are scarce, records rarely contain reasoning paths, and data transfer poorly across configurations, complicating local deployment. We present DiagLoop, a counterfactual data flywheel that converts codified physical relations or clinical guidelines, authored once per mechanism family, into training supervision beyond recorded cases. A training-only teacher proposes counterfactual worlds by varying causes, contexts, and observations, while an independent hybrid checker admits only valid worlds. The student reasons through symptom abstraction, causal-chain construction, and root-cause attribution. Stage-specific criteria identify its earliest failure. For nonterminal failures, a bounded repair probes downstream competence, and the resulting weakness profile guides subsequent data generation. Stage-localized reinforcement learning updates only the model-generated continuation, while replay and preservation reduce forgetting. The same criteria govern admission, attribution, reward, and regeneration through checks separate from the proposer. Using only synthesized scenarios and no case-level expert reasoning annotations, the resulting 8B model improves strict path correctness over the strongest conventional baseline. Gains are 11.6 points across eight industrial systems and 5.5 points across ten disease categories. Gains over a deranged-routing control are 3.9 and 2.3 points, respectively. The model also exceeds the evaluated proprietary references in both domains, even when they receive few-shot examples or the specification in context.

Many critical reasoning tasks, including clinical diagnosis, legal judgment, and industrial fault diagnosis, require step-dependent causal chains in which early errors propagate and correct conclusions can mask invalid reasoning. Although large language models perform well on such tasks, privacy, latency, and controllability motivate distillation into locally deployable models. Standard trajectory imitation does not correct process errors on the student's own rollout distribution. We propose CausalOPD, a curriculum online process distillation framework. A knowledge-augmented teacher first provides trajectories grounded in domain-specific causal rules, entity relations, and structural constraints. The student then generates on-policy trajectories, and the teacher identifies the first wrong step, defined as the earliest transition that verifiably violates available constraints. Starting from the verified prefix, short-horizon reinforcement learning repairs this localized failure. A causal-stage curriculum advances from evidence-level to mechanism-level and conclusion-level errors, following their propagation order. Across three domains, CausalOPD improves average path correctness by 23.4 percentage points over sequence-level online process distillation and reduces the right-label-wrong-reasoning rate from 15.7% to 4.4%. The domain-specific 8B students also surpass both evaluated proprietary references in path correctness across all domains.

Out-of-distribution (OOD) recommendation is vulnerable to preference shifts induced by a latent environment. Existing methods can infer latent states from logged interactions, yet the statistical meaning of the latent environment and its effect on preference remain underdetermined. We formulate this task as conditionally identifiable risk-aware recommendation (CI-RR) and propose Conditionally Identifiable Latent-Environment Recommendation (CILER). CILER uses a user-conditioned exponential family to model the latent environment and a feature-indexed polynomial to specify how it changes preference. It predicts by marginalizing item probabilities over the inferred environment distribution. Under sufficient variation, correct specification, and decoder regularity, CILER identifies the environment-sensitive representation up to the stated equivalence class. We further bound excess deployment log-risk by environment-inference error. Controlled studies test the observable consequences of sufficient variation and model specification. Experiments on three datasets show that CILER improves all twelve OOD ranking metrics under feature, temporal, and geographical shifts within shared support.

Deep learning has advanced time series forecasting, but periodicity drift, in which cycle timing and phase vary over time, remains a challenging problem. Existing methods predominantly model these sequences on fixed time grids, suffering from a limited ability to accommodate phase-related variation. To address this limitation, we propose POEM, a phase-aware forecasting framework based on latent feature rotation using the special orthogonal group in two dimensions, denoted by $\mathrm{SO}(2)$. POEM aims to reduce the phase-related variability by learning a phase-correction coordinate and applying an invertible $\mathrm{SO}(2)$-based rotation to paired latent features. To extrapolate this correction coordinate, Directional Phase Increment Attention (DPIA) retrieves historical phase increments from similar temporal contexts and integrates them into future phase corrections. Experiments demonstrate that POEM achieves competitive performance, while qualitative visualizations suggest that the learned phase-aware transformation makes latent trajectories more regular.

A companion paper studies when activation patching and weight-space ablation agree, inside an idealized model where a conditional computation is carried additively through a residual stream. For the one composition in that model where two carriers are architecturally dependent, an attention head and its own layer's normalization-MLP composition, it derives an exact first-order interaction formula, zero when only the MLP is ablated and second-order bounded when the head is also ablated. That result is confined to a single residual block and checked only on small transformers on a synthetic task. This paper extends the result past both limits. First, the interaction from ablating carriers spanning several layers decomposes exactly into same-block terms, one per touched layer, plus a cross-layer remainder on which the decomposition makes no claim of smallness. Second, we isolate that remainder exactly, for two layers, as a double integral of a mixed second derivative, and name the missing ingredient needed to bound it: a Jacobian bound for the attention sub-block. We derive this bound in closed form and verify it, without a single violation, against Qwen2.5-1.5B-Instruct's real weights, though we do not yet chain it across layers. We also give, in closed form, the curvature constant the companion paper's bound leaves unexhibited. Third, on that same model, we search for and find an emergent circuit for indirect object identification, never designed into it, using the original activation-patching method for this task, and test collapse, dissociation, and interaction on it. The result is mixed: a shared carrier emerges across all five tested instances, collapse and dissociation hold on most but not all, and a nonzero interaction is measurable on three of five, at layer pairs outside the same-block case the companion theorem covers.

Adaptive conformal prediction can recover clinically important heartbeat classes missed by a point classifier, but delayed feedback makes its decisions sensitive to event order. We introduce ConformalShift, a bounded event-reordering attack that suppresses the ventricular class for rescued events without modifying ECG waveforms, labels, classifier scores, or the event multiset. ConformalShift searches for feasible permutations of authentic preceding events that lower the ventricular threshold before a selected target is evaluated. On disjoint MIT–BIH confirmation records, the attack suppressed 66.7% of eligible targets for Extra Trees and 60.0% for HistGradientBoosting, compared with random-schedule rates of 4.4% and 12.0%, respectively. Transferred configurations also outperformed random scheduling on INCART, while reducing the displacement budget weakened the attack on both datasets. These results show that adaptive monitors in healthcare can be compromised through the timing of authentic information, even when waveforms, labels, classifier outputs, and event contents remain unchanged.

Activation patching and weight-space ablation both claim a component is causally responsible for a behavior, yet they act on different objects: one forward pass versus the parameters behind every forward pass. We ask when they agree. We study an idealized model where a conditional computation is carried additively through a residual stream, $F(x)=F_0(x)+\sum_i\alpha_i(x)v_i$, read out by a linear functional, and prove three exact results. First, deleting a subset of carriers collapses a matched input pair onto the same unconditional output if and only if the removal is symmetric on the pair and leaves no outside contrast; the error is deterministic, and we give its exact form even when the two conditions hold only approximately. Second, patching a carrier moves the readout by its donor-receiver contrast, while ablating it moves the readout by its absolute level; neither bounds the other, and we construct pairs where every single-carrier patch flips the decision while no single-carrier ablation does. Third, for an attention head composed with its own layer's normalization and MLP, we derive an exact first-order interaction formula with a provably second-order remainder, vanishing identically when only the MLP is ablated but not, in general, when a head is. Small transformers trained on a synthetic conditional task illustrate all three predictions: across thirty-nine ablation configurations the measured interaction is strongly rank-correlated with the idealized model's predictive accuracy (Spearman $-0.83$), and a second task and architecture reproduces the same pattern, including a further polarity reversal. The single-block interaction result extends past one residual block, and the synthetic validation is tested against a real pretrained model, in a companion paper that takes this theory further along both axes.

Clinical development is sequential decision-making under uncertainty, where a sponsor must plan a portfolio of experiments from heterogeneous evidence. We study this setting by framing oncology clinical development as an offline decision-making problem in which an agent predicts the next six-month trial portfolio of an oncology drug program from information available at the decision date. To support this, we construct a temporal dataset that combines 31.7k heterogeneous public data records, including trial registries, regulatory reviews, sponsor filings, utilization data, and epidemiology, into 881 offline decision episodes across 45 historical programs. We compare four offline objectives: behavioral cloning, reward-weighted behavioral cloning, learned-reward training, and value-based implicit Q-learning against four frontier LLM agents that share a common date-gated retrieval scaffold across held-out drug, sponsor, drug-class, and temporal splits. Models trained offline outperform the non-fine-tuned baselines, particularly in the post-August 2025 contamination-clean holdout. Reward-weighted behavioral cloning performs the best, obtaining 46.2% indication F1 and 14.2% strict F1 against 25.0% and 2.1%, respectively, for the best-performing tool agent on each metric. These results suggest that structured offline learning can teach agents to plan clinical experiments.

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia and is associated with increased risks of stroke, heart failure, and mortality. Recent ECG foundation models offer transferable representations for automated AF detection. However, their relative effectiveness remains unclear because existing studies use different datasets, preprocessing procedures, classifiers, and validation protocols. This study presents FOUND-AF, a unified, leakage-controlled, and deployment-oriented benchmarking framework that evaluates the quality of pretrained ECG representations under identical experimental conditions. Nine publicly available foundation models from five families, including HuBERT-ECG, CLEF, ST-MEM, ECG-JEPA, and ECGFounder, were evaluated across four heterogeneous ECG datasets, namely AFDB, CinC2017, CPSC2021, and LTAFDB. All models were used as frozen feature extractors with standardized preprocessing, model-native resampling, a fixed XGBoost classifier, and recording-level grouped cross-validation. The evaluation included classification metrics, receiver operating characteristic analysis, paired recording-level bootstrap comparisons with Holm correction, embedding-space visualization, and computational efficiency profiling. The ECGFounder model consistently achieved the strongest overall performance across datasets while offering a favorable trade-off between accuracy, model size, inference time, and memory usage. FOUND-AF therefore provides a reproducible framework for selecting ECG foundation models and demonstrates that compact, clinically pretrained encoders can support robust and computationally efficient AF detection across heterogeneous acquisition settings.

We present a method for designing deep neural networks (DNNs) for intermittent, energy-autonomous, on-device learning on microcontroller units (MCUs). In mobile applications where the energy can run out, e.g., when solar-powered, executing artificial intelligence (AI) faces a technical issue as learning can be interrupted at any time. Our approach combines a hardware-aware energy prediction model with multi-objective optimization (MOO), enabling offline DNN optimization at the design stage without repeated deployment and online testing on the target MCU. Our proposed energy predictor estimates per-layer energy consumption for both DNN inference and training, including the intermittent checkpointing overhead, based on implementation-specific compute and memory features extracted from the DNN model. We validate our approach using autoencoders for anomaly detection on a Cortex-M4 MCU, where our predictor achieves a weighted absolute percentage error of 16.6%, which is sufficient for reliable architecture selection under intermittency constraints. As a result, this work bridges the gap between MOO, automated DNN design, deployment on energy-harvesting systems, and intermittent learning, truly enabling autonomous AI at the edge.

Modern multi-tenant Low-Rank Adapters (LoRAs) serving systems concurrently host tens to hundreds of LoRA adapters. Though powerful, this introduces a critical system dilemma between serving efficiency and task performance: higher-rank adapters generally achieve better downstream task performance, but their GPU VRAM footprint and Host-to-Device PCIe swapping overhead severely constrain scalability. Conversely, ultra-low-rank adapters ($r \le 2$) minimize both VRAM footprint and PCIe transfer overhead, but suffer from downstream task performance degradation. To solve this problem, we propose Subspace-Aligned LoRA Training (SALT), a serving efficiency-aware hierarchical fine-tuning framework. Our solution operates in three phases. First, a provider jointly trains high-capacity domain centroids on public data within the domain using a novel alignment regularizer that coheres in-domain task subspaces into a unified basis. Next, users fine-tune ultra-low-rank task residual adapters on private data atop those frozen centroids. Finally, during inference, the provider pins the centroid in GPU VRAM and dynamically swaps in each user's task residual on demand. Across LLMs of varying scales, SALT recovers high-rank accuracy using $r \le 2$ residuals, achieving up to 18.5% absolute accuracy gains over state-of-the-art compression baselines and reducing per-adapter memory by up to 16x. When integrated into vLLM, SALT improves serving throughput by up to 51% under PCIe bandwidth pressure and 28% under GPU VRAM constraints for Llama-3.2-3B.

Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) exhibit fundamentally different behaviors in enhancing multi-task reasoning for large language models (LLMs). Our preliminary experiments revealed a phenomenon: SFT suffers from severe task conflicts under multi-stage training, whereas RL enables stable coexistence across diverse tasks. Empirically, we trace this to the parameter level, observing that RL induces sparse and approximately orthogonal updates across tasks. We provide a theoretical explanation for this mechanism by analyzing multi-task gradient interference. Our results reveal a distinction: interference in SFT is norm-limited, scaling with the absolute gradient magnitude, whereas interference in RL is variance-limited, bounded by the gradient variance induced by advantage normalization and on-policy optimization. This small variance bound yields near-orthogonal optimization directions across tasks. Leveraging this insight, we propose Parallel-RL, a paradigm that decouples multi-task training, significantly improving efficiency and flexibility.

Benchmarking the ability of AI scientists to generate novel ideas is notoriously difficult. Existing benchmarks in this field have made progress in evaluating scientific reasoning and research replication, but often rely on synthetic tasks or retrospective targets, which may be confounded by prior exposure. We hypothesize that complex, adversarial, fast-moving real-world domains where expert practitioners independently generate observable outputs can provide a practical solution to fill this gap and evaluate the capabilities needed for AI scientists, including reasoning, novelty, and hypothesis formulation. We instantiate this framework in two structurally different domains, Formula 1 (F1), where models ideate around car design concepts for the 2026 season, and real pre-season innovations provide a ground truth, and Magic: The Gathering (MTG), where models propose decks from a recently updated card pool and are evaluated against 19 Pro Tour (PT) decklists. Across both domains, models produce plausible outputs, but few align with real-world expert solutions. In F1, the best model, GPT-5.2 matched 10 of 40 real innovations with 166 ideas proposed across runs. In MTG, the best deck from Gemini 3 Flash recovered 5 of 7 new-set cards from the third-place PT deck, and across all 108 decks, the cards models selected most often were also the cards most widely adopted by PT decks (Spearman $\rho = 0.74$, $p = 0.0003$). These results suggest that a key capability gap for AI scientists is not idea generation, but filtering, prioritization, and coherent novelty.

The drift diffusion model (DDM) is a cornerstone of cognitive decision-making research. Although numerous estimation methods exist, researchers continue to seek inference approaches that are both fast and flexible across diverse study designs. Amortized Bayesian inference (ABI) can provide nearly instantaneous inference for complex stochastic models like the DDM, but neural networks trained for one study design cannot generalize to others. In this paper, we propose a divide-and-conquer framework that address this limitation. The core idea is that the DDM's independence assumption allows the full dataset to be decomposed into pairwise shards, each sharing a common structure that a single neural network can learn. Inference is performed on each shard separately and the resulting posteriors are combined via consensus MCMC to approximate the full posterior. Using simulated datasets, we evaluate the accuracy and uncertainty of this method. Our results show that the proposed divide-and-conquer approach achieves accuracy and uncertainty comparable to MCMC while reducing computational cost by several orders of magnitude. This work not only advances DDM estimation but also demonstrates a general strategy for improving the scalability and generalizability of ABI methods across diverse applications.

While modern tabular learners excel at capturing statistical patterns, they frequently operate in a semantic vacuum, treating textual features as discrete symbols, ignoring the rich semantics inherent in feature names or cell entries. We propose CASE (Context-Aware Semantic Embeddings), a novel framework that bridges the gap between the semantic understanding of Large Language Models (LLMs) and the statistical capabilities of tabular learners. Unlike existing methods that embed rows in isolation, CASE utilizes a contextualization strategy: we pre-fill the KV cache of a custom-trained Gemma 3-based Tabular Language Model with a representative sample of rows to establish a persistent anchor of the dataset's semantics. This ensures that generated row embeddings are dynamically contextualized, resolving semantic ambiguities and anchoring representations in domain-specific context. Our experiments across several benchmarks (CARTE, TextTab, and TabArena) demonstrate that CASE substantially improves the performance of tabular learners on semantically rich datasets, particularly in low-data regimes.

Reinforcement learning (RL) with general utility extends classic RL by optimizing an arbitrary utility functional of the policy-induced occupancy measure, thereby enabling a broader range of applications. However, previous work on general utility RL typically assumes the evaluation utility is fixed and correctly specified. In practice, the utility used at deployment can deviate from the training one, creating a robustness gap that prior work does not address. Motivated by this, we propose robust general-utility RL, a minimax learning framework that trains policies against utility misspecification within a prescribed uncertainty set. Our framework strictly generalizes standard general-utility RL while also providing a unified view of many existing RL frameworks, including reward-robust RL and constrained RL, through appropriate choices of the utility uncertainty set. We further develop provably convergent stochastic algorithms for two regimes. For concave utilities, we develop a projected stochastic gradient descent-ascent method and establish stationarity guarantees. For the more challenging nonconcave regime, we propose a stochastic prox-extragradient algorithm that mitigates ill-posed behavior induced by nonconcavity, with convergence guarantees to approximate first-order stationarity. Experiments on LLM safety alignment and exploration maximization tasks further corroborate the convergence behavior consistent with our theory.

Tabular-to-image methods that convert tabular data into visual representations have emerged as a novel paradigm for leveraging the high performance of deep learning models. Despite their advantages, the robustness of these methods under distribution shifts remains under explored. Test-Time Augmentation (TTA) is an effective approach in image classification to improve model generalization and robustness, where predictions over multiple transformed views of each input are aggregated. This work evaluates the impact of TTA techniques on predictive performance under Out-Of-Distribution (OOD) for representations generated by tabular-to-image methods. Six tabular-to-image encoding methods were considered: TINTO, IGTD, DeepInsight, BIE, DistanceMatrix, Fotomics. Twenty-five TTA techniques were used, organized into six types: Geometric, Photometric, Structural, Frequency/Encoding, Mixup, and Composite. We employed two datasets from the TableShift benchmark (HELOC and Voting) that provide in-distribution and OOD test subsets designed to evaluate the effect of distribution shifts on tabular data. The results indicate that TTA improves OOD performance, with composite and photometric strategies providing the best trade-off between robustness and variance. In contrast, frequency-domain transformations that alter the encoder's feature-to-intensity mapping consistently degrade performance. These findings highlight TTA as a promising approach for improving the robustness and generalization of classifiers trained on image representations derived from tabular data, particularly under distribution shifts.

Active learning (AL) promises to reduce the cost of medical imaging projects by lowering the number of clinical labels required. However, practical deployment requires committing to a sampling strategy before the full annotation budget is spent, and choosing the wrong strategy can increase rather than decrease costs. We propose Active-Learning Deployment Advisor (ALDA), a deployment-oriented framework for AL method selection under clinical performance constraints. Given a short pilot phase, ALDA fits a parametric learning-curve model to each candidate strategy, estimates whether that strategy is expected to reach a required clinical performance target, and predicts the number of expert annotations needed to do so. In addition to absolute annotation cost, ALDA introduces a deployment window that quantifies the sensitivity of this cost estimate to uncertainty in the clinical threshold. The final recommendation follows a risk-aware rule: among strategies with near-optimal predicted cost, ALDA prefers the strategy with the narrowest deployment window, the most robust to threshold revisions. Experiments on four medical imaging classification domains show that ALDA predicts the deployment-optimal method from a pilot of 15-30% of the intended budget and reduces annotation costs by up to 82% compared with a poor strategy choice. Rather than introducing a new sampling heuristic, ALDA provides a practical decision layer that answers a deployment-critical question: how many labels are enough?

Large Language Models (LLMs) have recently shown strong capabilities in reasoning, planning, and tool-use, enabling new forms of autonomous agents. However, LLM-based agents struggle with long-horizon sequential decision tasks that require precise action optimization and environment interaction. Reinforcement Learning (RL), while effective for sequential control, often lacks the high-level abstraction and task decomposition abilities needed for complex scenarios. This paper introduces an LLM-Augmented Reinforcement Learning Agent that integrates LLM-driven planning with RL-based action optimization. The proposed architecture leverages the LLM to generate subgoals, structured plans, and contextual guidance, while the RL agent refines low-level actions through interaction with the environment. Experiments on sequential decision tasks demonstrate improved sample efficiency, higher success rates, and more coherent action trajectories compared to RL-only and LLM-only baselines. This hybrid paradigm highlights a promising direction for building more capable autonomous systems.

Federated Learning (FL) enables collaborative model training across distributed healthcare institutions without centralising sensitive patient data. However, real-world healthcare federations are often characterised not only by non-IID data, but also by heterogeneous clinical objectives and partially overlapping feature spaces. Different hospitals may optimise distinct and potentially conflicting objectives, such as mortality risk prediction, readmission reduction, or length-of-stay estimation, while also retaining institution-specific clinical features that cannot be shared with other participants. Existing personalised FL methods mainly address statistical heterogeneity, whereas multi-objective FL approaches typically learn a shared global model without explicit client-level adaptation. To address these limitations, we propose FedCARE, a multi-objective personalised FL framework for smart healthcare services. FedCARE follows a two-stage training strategy. First, it learns a shared global backbone from common clinical features using Pareto-driven multi-objective federated optimisation. Second, each client independently fine-tunes the shared backbone using its private features and local clinical objectives, enabling institution-specific personalisation without additional communication overhead. We implement FedCARE in a cloud-based client-server federated deployment on the Melbourne Research Cloud and evaluate it on two real-world healthcare datasets, MIMIC-III and Diabetes 130-US Hospitals. Experimental results show that FedCARE consistently outperforms standard FL, multi-objective FL, and personalised FL baselines, achieving up to 12.5% AUROC improvement and 32.0% MAE reduction over FedAvg.

Vocabulary extension is an efficient way to adapt pretrained large language models (LLMs) to new languages, but the initialization of newly added token embeddings can strongly affect continued pre-training (CPT) efficiency. We present a systematic study of more than 20 initialization strategies for Hindi vocabulary extension in Nemotron-3-Nano-30B-A3B. Our comparison spans vocabulary-averaging baselines; external and learned initialization methods, including FOCUS, top-k semantic retrieval, and residual MLP mappings; subword composition; norm calibration; and input-output asymmetry. We find that subword composition methods outperform both vocabulary averaging and external/learned initialization approaches. Within subword composition, asymmetric variants achieve the lowest observed early validation loss and reveal distinct preferences for input and output embedding initialization. The best observed configuration initializes the input embedding matrix with uniform subword averaging and Hindi-specific norm calibration, and the output language modeling head with character-length-weighted subword averaging. Relative to the standard Mean-all baseline, this full initialization pipeline reaches comparable validation loss with over a 6x reduction in CPT steps and exceeds the baseline's 3,500-step MILU-Hindi accuracy after only 500 steps. Finally, we show that initialization loss and initialization bits-per-byte (Init BPB) are unreliable predictors of downstream convergence, whereas lightweight CPT, as few as 50 steps, provides a cost-effective and reliable signal for selecting the best initialization strategy.

Existing chunk-based Vision-Language-Action (VLA) models execute a fixed number of actions (i.e., execution horizon) before replanning, turning replanning into a task-agnostic periodic schedule that is independent of task progress. As a result, when no replanning boundary falls before a critical manipulation stage, it is executed from a stale chunk rather than a freshly replanned one. To address this limitation, we propose Bernoulli-Continuation Policy (BCP), a lightweight, plug-and-play framework for adaptive horizon execution that keeps the base VLA frozen. Given a fixed-length action chunk, its continuation head decomposes execution-horizon selection into a sequence of continue-or-replan decisions, which imposes an ordinal, prefix-sharing inductive bias over candidate horizons rather than treating them as independent classes. Since the optimal horizon for each chunk is not observable, we train this head with reinforcement learning from trajectory-level outcomes and introduce a Replanning-Efficiency Reward that jointly rewards task success and efficient VLA usage, discouraging the policy from collapsing to unnecessarily short horizons. On RoboTwin 2.0 with LingBot-VLA as the base policy, BCP improves the average success rate by +11.08% on 13 low-success tasks and from 89.88% to 93.94% (+4.06%) across all 50 tasks. Although trained only under the Clean setting, BCP generalizes to the Randomized setting, raising the average success rate by +4.06%. It also transfers to a different base policy $\pi_{0.5}$, achieving a better result on LIBERO (+1.7%) and, notably, on the harder LIBERO-PRO (+6.8%). On a real robot, BCP lifts success from 74% to 92% and from 44% to 84% on two manipulation tasks. Meanwhile, its negligible overhead, combined with higher success, makes BCP's overall runtime even lower than the fixed-horizon baselines.

The performance of Support Vector Machines (SVMs) critically depends on the kernel function choice, which enables implicit mapping of data into high-dimensional feature spaces. While classical kernels like Radial Basis Function (RBF) remain popular, orthogonal polynomial kernels offer mathematically interpretable alternatives that can incorporate structured prior knowledge. This work extends the orthogonal polynomial kernel paradigm by introducing a novel family based on discrete $q$-Hermite I polynomials, a class of $q$-orthogonal polynomials that generalize classical Hermite polynomials through a deformation parameter $q$. We formally define the q-Hermite kernel and establish its validity under Mercer's theorem. The kernel's inherent boundedness properties naturally prevent annihilation and explosion effects without requiring explicit scaling mechanisms. Extensive experiments across 20 benchmark datasets demonstrate that the proposed kernel achieves competitive performance compared to both classical kernels and other orthogonal polynomial kernels, while offering advantages in numerical stability and computational simplicity. Our results confirm that $q$-orthogonal polynomials constitute a promising direction for kernel design, bridging mathematical elegance with practical machine learning applications, that provides conceptual and algorithmic resources that may be further extended to emerging quantum computing paradigms. To facilitate full reproducibility, we provide the complete implementation and experimental pipeline in an open-access GitHub repository at https://github.com/Kokechacho/SVMs-QSVMs.

We study score learning for reflected diffusion on bounded domains. Reflection keeps trajectories feasible but does not ensure that the learned score satisfies the boundary behavior implied by the forward process. With implicit score matching, integration by parts leaves a boundary term, and we show that it depends on one scalar at each boundary point: the diffusion- weighted normal component of the score, or conormal trace. The no-flux condition fixes this value while leaving the re- maining boundary components unrestricted; under anisotropic diffusion it generally differs from the ordinary normal score component. On hyperrectangles, our parametrization enforces the required trace without additional trainable parameters or a stochastic boundary estimator and, under regularity assump- tions, can represent the true score, whereas fixing an incorrect value creates an error that more data cannot remove. We ex- tend the construction to simplices and polygonal domains and identify reflection masking: hard reflection can keep samples feasible even when the learned trace is wrong, so post-reflection metrics may hide the error. Experiments show the clearest separation with less frequent reflection, anisotropic diffusion, and mass near intersections of constraints; under full reflection, final sample placement improves inconsistently, illustrating how hard repair can mask boundary-score errors and decouple score accuracy from downstream generation quality.

Reinforcement learning with verifiable rewards (RLVR) com- monly optimizes each correct completion as an independent learning signal. In GRPO, this completion-level uniformity creates structure-level skew: recurring correct solution forms accumulate positive coefficient mass in proportion to how often they are sampled, while rare forms receive limited credit. We formalize this behavior as multiplicity-induced structure-level credit concentration and introduce a partition- conditioned rule that redistributes positive advantages accord- ing to cluster rarity. Cue-GRPO instantiates this rule with- out auxiliary-model inference by using deterministic Strategy Cues to construct rollout-local partitions of verified-correct traces. Across Qwen2.5-Math-7B and Llama-3.1-8B-Instruct, Cue-GRPO improves AIME repeated-sampling performance, with the largest gains at high sampling budgets. Credit Re- distribution (CR) under Judge Partitions (JP) further indi- cates that the proposed redistribution mechanism can oper- ate with judge-derived partitions. Cue-GRPO adds only 6% wall-clock training overhead over GRPO. These results sup- port structure-level credit redistribution as a practical design axis for RLVR, with Strategy Cues providing a low-overhead implementation for competition mathematics. Code is avail- able at https://github.com/CzZ12/When-Correct-Solutions- Repeat-Rarity-Aware-Credit-Redistribution-for-GRPO.