Papers

We investigate the best $L_2$ approximation of mixed Sobolev spaces by shallow neural networks with $n$ neurons and general activation functions. We first establish an activation-independent Fourier-block principle: if an activation has univariate approximation order $\rho$ in the sense of the Fourier-block property, then the global approximation rate has algebraic order $\min\{\alpha,\rho\}$ for target functions of mixed smoothness $\alpha$, up to explicit logarithmic factors. To verify this property for concrete activations, we introduce a structured univariate approximation condition that implies the Fourier-block property with explicit parameters. For $\mathrm{ReLU}^k$, a matching algebraic lower bound identifies $\min\{\alpha,k+1\}$ as the optimal algebraic approximation exponent in any dimension, up to logarithmic factors in the upper bound. The framework also yields the exponent $\min\{\alpha,k+1\}$ for cardinal B-splines and soft-$\mathrm{ReLU}^k$, and the full mixed-smoothness exponent $\alpha$ for ELU and cosine activations, again up to logarithmic~factors.

We introduce GLASS, a framework for graph-level anomaly detection (GLAD) that achieves robust cross-domain transferability through graph-language alignment on the unit hypersphere. GLASS builds a unified representation space by aligning a structure-aware graph encoder with an instruction-aware text embedding via a multi-slice soft cosine objective. Our framework serializes local, global, and semantic graph properties into a compact Graph Descriptor Prompt (GraphDP), creating a text bridge that enables domain-agnostic anomaly scoring. By enforcing multi-scale consistency through Matryoshka representation slices, the model captures anomalous deviations at multiple levels of granularity. We formulate anomaly detection as density estimation on the aligned hypersphere and introduce Spherical Multi-Modal Scoring (SMS), which instantiates von Mises-Fisher kernel density estimators in both graph and text embedding spaces. This probabilistic formulation recovers angular 1-nearest-neighbor scoring in the high-concentration limit, motivates the practical mean k-nearest-neighbor scorer, and provides a principled fusion of structural and semantic anomaly signals. The shared text embedding space further serves as a cross-domain bridge: by encoding a target domain's GraphDP without target-domain training data, GLASS performs zero-shot anomaly detection, and with only a handful of normal examples, few-shot adaptation via reference-set calibration. For privacy-sensitive deployment, we extend reference-set calibration with a bounded joint graph-text kernel summary that provides graph-record differential privacy while keeping the encoders fixed independently of the private target references. Across twelve benchmarks and three meta-domains, GLASS obtains the best average AUROC and rank compared with recent advanced GLAD baselines and enables effective cross-domain transfer.

As spaceborne computing systems increasingly rely on neural network (NN) accelerators, the opacity of commercial, black-box architectures severely restricts the development of verifiable radiation mitigation strategies. Open-source, register-transfer level (RTL)-accessible accelerators resolve this limitation by enabling user-defined instrumentation, yet few have empirical radiation-response baselines. This work establishes a foundational system-level proton-irradiation baseline for an unmitigated open-source Tensil NN accelerator deployed on a Zynq UltraScale+ SoC executing ResNet-20 inference. Under 20 to 58 MeV proton irradiation, we delivered $4.29 \times 10^{10}$ p/cm$^{2}$ within monitored operational windows. Seven workload interruptions required two restarts of the notebook process, four reboots or board resets, and one power-cycle sequence. Two output-corruption events returned incorrect CIFAR-10 classes without loss of service. In the longer event, the accelerator returned a class absent from the ten-image CIFAR-10 pool for 39 consecutive inputs at normal cadence. The process remained alive, while the kernel log, limited memory test, and sampled power showed no anomaly. Observation of the stuck-class sequence ended with scheduled bitstream reconfiguration. All nine onsets occurred under the nominal 4 cm beam, which exposed the SoC, LPDDR4, and additional board circuitry; none occurred under the 2 cm SoC-centered field. This pattern shows a field association but does not establish LPDDR4 as the cause because field size was confounded with run order and dose. Linux-managed accelerators require end-to-end content checks and recovery that reaches the state in which corruption can persist. This baseline documents availability loss and silent output corruption, supporting future software hardening of COTS FPGA-SoCs for neural-network inference in space systems.

Cryptocurrency markets exhibit extreme volatility and non-stationary dynamics that challenge conventional forecasting methods. Although Large Language Models (LLMs) have shown promise for time series forecasting, the combined effects of adaptation choices remain largely unexplored in financial settings. This study introduces PRICE, a structured approach for adapting LLMs to short-term Bitcoin price forecasting. Built on a 4-bit quantized LLaMA-3 8B model, PRICE investigates how fine-tuning, numerical representation, prompting, inference, and decoding jointly influence forecasting performance. PRICE integrates Parameter-efficient fine-tuning with Low-Rank Adaptation (LoRA), Recursive multi-step inference, Integer-rounded numerical representation, Context-Task-Format (CTF) prompting, and Exact zero-temperature decoding. Ablation studies show that each component contributes to forecasting accuracy and reliability. LoRA enables efficient training on limited hardware, recursive inference improves accuracy, integer-rounded values reduce errors, CTF prompting outperforms Chain-of-Thought, Implicit Chain-of-Thought (iCoT), and few-shot prompting, and zero-temperature decoding improves stability during recursive forecasting. Comparative evaluation against eight transformer-based and time-series foundation models shows that PRICE achieves the lowest forecasting errors on both validation and test sets while maintaining robust performance across evaluation periods. Despite being based on a model primarily pretrained on text rather than time-series data, PRICE achieves competitive or superior performance relative to specialized foundation models. These findings demonstrate that adaptation choices critically determine the accuracy and robustness of LLMs for numerical time-series forecasting.

While machine-learning interatomic potentials (MLIPs) have successfully learned potential energy surfaces (PES) and atomic forces, many practical applications, such as vibrational analysis and transition state search, rely heavily on the PES Hessian. Yet standard MLIPs are trained on energy and forces only, and using the Hessian as an additional training objective requires backpropagation whose memory cost grows quadratically with the number of atoms. To address these limitations, we propose two Hessian-derived data augmentation schemes: isotropic Gaussian displacement (UniAug) and normal mode-weighted displacement (ModeAug). Both methods utilize simple Taylor expansions, generating physically grounded molecular structures with highly accurate energy and force labels. By preserving the underlying MLIP architecture and training procedure, this approach contributes to improving energy and force predictions in various benchmarks. Comprehensive evaluations across non-equilibrium and equilibrium datasets demonstrate that our approach enhances model accuracy where reference forces are large and training data are limited.

Artificial intelligence models are promising for medical diagnosis, but they require large numbers of unbiased data, which in medicine are distributed across hospitals and cannot be centralized to protect patient privacy. Federated Learning (FL) addresses this, since hospitals train one shared diagnostic model while patient data remain local. Training proceeds in communication rounds, in which each hospital trains the shared model locally and returns it to the server for merging by weighted average. This aggregation weight determines whose institutional knowledge shapes the result. Federated averaging (FedAvg) sets it in proportion to local sample count, so a small but informative hospital is permanently assigned a small influence, andl argest clients could dominate the global model even when they are less informative. We propose Federated Dual Reputation Annealing Weighting (FedDRAW), a server-side aggregation method that combines a data-size prior with the cosine similarity between client and global parameters under two coupled annealing schedules. An inner schedule shifts client reputation from the size prior towards similarity. An outer, deferred annealing schedule on the softmax inverse temperature keeps the weighting selective in the early and middle rounds and relaxes it to uniformity at convergence. We evaluate FedDRAW on 12 simulated client-partition scenarios of two chest radiograph datasets (CheXpert and ChestMNIST), against seven federated baselines under identical local training settings. FedDRAW achieved the highest average rank among all eight methods under both AUC and the geometric mean (GM) of sensitivity and specificity, which a Friedman test with Nemenyi post-hoc analysis confirmed to be a statistically significant difference between the methods. Scheduling two signals, rather than fixing the weights by sample count alone, could enable less biased diagnostic models.

Large language models (LLMs) show strong reasoning ability, but their explanations can remain inconsistent, weakly grounded, or difficult to verify. We propose a verifier-guided explainable reasoning framework for transparent educational question answering that combines gold-anchored QLoRA, task-aware symbolic routing, and group-relative RLVR. Qwen2.5-3B-Instruct is first adapted with field-weighted QLoRA supervision anchored to authoritative answers. A lightweight router then assigns logic problems to a FOL/Z3 verifier and physics problems to a formula- and unit aware symbolic solver. Verifier feedback is further used to support candidate evaluation, self-revision, and reward construction during RLVR. Candidate responses are evaluated along three complementary dimensions: P1 for answer correctness, P2 for evidence or unit consistency, and P3 for reasoning depth and explainability. At inference, gold-free self-consistency aggregates multiple candidate responses before an optional question-only physics verifier performs conservative system-level correction. On 438 held-out examples, RLVR increases P3 from 50.68% to 72.20%, while hybrid P1 remains approximately stable at 55.94%. Self-consistency improves model only P1 from 48.86% to 50.23%, with symbolic verification providing the remaining hybrid gain. These results indicate that RLVR primarily strengthens explicit reasoning structure, while symbolic verification complements the neural policy by improving answer reliability at the system level.

The Appropriately Combined Edge-length (ACE) sequence in A-BLiN depends on the zooming dimension $d_z$. This note removes that dependence. The next edge length is selected from the number of cubes that survive the preceding elimination. The resulting Count-Adaptive BLiN algorithm does not use $d_z$ or the zooming constant $C_z$, yet it attains $\widetilde{\mathcal O}_d(T^{(d_z+1)/(d_z+2)})$ regret with $\mathcal O_d(\log\log T)$ batches. Together with the adaptive-grid lower bound in Theorem 10 of the original paper, the optimal batch complexity remains $\Theta_d(\log\log T)$ when $d_z$ is unknown.

Forecasting time series accurately is critical for applications with complex data ranging from energy systems to healthcare and finance. Among current state of the art models, generative latent variable models are increasingly implemented; yet principled generalisation guarantees for modern latent variable models remain limited. In particular, while Variational AutoEncoders are widely used for sequential data, their theoretical analysis is largely restricted to i.i.d. settings. In this work, we develop a PAC-Bayesian framework for latent variables models applied to time series. Building on reconstruction-based bounds, we extend PAC-Bayesian guarantees to Markovian latent structures, capturing temporal dependencies through a sequential generative process. These guarantees do not grow with the length of the trajectory. Our bounds depend on assumptions which are common in the literature; we provide an example framework where they would be verified to show that they are not as restrictive as they may seem.

Dynamical symbolic regression methods identify governing differential equations from noisy data, balancing interpretability and predictive accuracy. However, standard methods often produce expressions that violate known physical laws. To address this, we propose FluxDisco, a physics-informed framework tailored for flux-based, stoichiometric ODE systems. By leveraging a known stoichiometry, we reduce the expression search space and ensure physical adherence. Our framework adapts the Monte Carlo Graph Search algorithm for the unique challenges associated with joint flux discovery of stoichiometric systems. We evaluate our method across a range of physical and biological systems, demonstrating its ability to accurately recover governing dynamics through interpretable equations.

The number of discrete class-separability jumps observed during ResNet finetuning is examined empirically as a predictor of final test accuracy. Across 75 experiments spanning four benchmarks (CIFAR-10, CIFAR-100, TinyImageNet, and CIFAR-10-C) and three architectures (ResNet-18, ResNet-50, and ResNet-101), with five to ten seeds per configuration, a strong within-dataset negative correlation is obtained on standard i.i.d. classification benchmarks: \(r = -0.84\) on CIFAR-10 (\(p < 10^{-8}\), \(n = 30\)) and \(r = -0.87\) on CIFAR-100 (\(p < 10^{-5}\), \(n = 15\)). Under distributional stress, the relationship attenuates: TinyImageNet yields \(r = -0.45\), and the CIFAR-10-C corruption benchmark yields \(r = -0.19\). Two additional analyses discipline the empirical claim. A partial correlation controlling for architecture depth, treated as a linear covariate, shows that on CIFAR-100 the transition count retains statistically significant predictive power (\(r_{\mathrm{partial}} = -0.69\), \(p = 0.007\)); the corresponding result under the stricter categorical conditioning is not established at \(n = 15\). A comparison against six alternative training-curve signals shows that transition count achieved the strongest correlation among the evaluated signals on CIFAR-100 and one of the strongest on CIFAR-10, but is dominated by other signals on the two stressed benchmarks. The comparison is restricted to training-curve-level signals; comparisons against effective rank, Hessian sharpness, Fisher information, margin, and neural-collapse measures, which are the strongest competitors in the current literature, are not part of the present study and remain open. The observation is presented as an in-distribution training-quality probe among a family of candidate probes, and an inexpensive detection procedure suitable for logging alongside a standard training loop is provided.

Explainability is increasingly seen as a crucial requirement in AI-based medical diagnosis, particularly in safety-critical clinical decision-making. Most existing explainability methods in healthcare operate in a post-hoc manner and are predominantly designed for unimodal data, which limits their applicability in increasingly prevalent multimodal diagnostic settings. This paper addresses the problem of self-explainable multimodal diagnosis by formulating it within the information bottleneck (IB) framework. We propose a unified learning paradigm that jointly optimizes predictive performance and modality-specific explainability by identifying the most informative elements inside each modality that contribute to diagnostic decisions. To enable tractable and stable optimization, we employ a matrix-based Renyi's $\alpha$-order entropy functional under the assumption of sufficiently expressive encoders. Extensive experiments on representative medical datasets spanning heterogeneous modalities demonstrate that the proposed method consistently achieves strong diagnostic performance, including an absolute accuracy improvement of 9.1 percentage points on the iCTCF dataset. Moreover, the learned explanations provide transparent and modality-aware insights into feature relevance, thereby improving both the explainability and generalization.

Despite its introduction more than a quarter century ago, Conformal Prediction (CP) has seen surprisingly few applications to the cyber security world thus far. In particular, we observe that, while CP has been employed as a defensive measure in many recent works, its use for carrying out attacks (i.e., for offensive security) is hard to trace in the literature. We explore this gap, by presenting initial findings in two key areas of offensive security: Privacy-Preserving Machine Learning, and network traffic analysis.

This paper introduces Regime-aware Constraint-Based and Noise-Based causal discovery with Markov Blankets (RCBNB-MB), a novel causal discovery algorithm for time series that relaxes the common assumption of a single, time-consistent causal structure. Time series are typically observed at discrete time points and often exhibit regime changes that challenge the assumption of a static causal structure, a limitation in many real-world dynamic systems. To address this challenge, RCBNB-MB identifies latent causal regimes, defined as subsets of time points within which a stable causal structure holds. The algorithm follows an iterative strategy that segments the time series into regimes and discovers the causal graph within each regime. By leveraging the Markov blanket rather than direct parents, RCBNB-MB gains robustness to errors in causal discovery and preserves predictive information. We provide theoretical guarantees for RCBNB-MB's ability to recover both regime transitions and causal graphs under reasonable assumptions. Furthermore, we validate its effectiveness through extensive experiments on simulated datasets with known ground truth and real-world IT monitoring data, where taking into account regime shifts is critical. Empirical results show that RCBNB-MB systematically outperforms baseline approaches in accurately detecting regime changes and their associated causal graphs, positioning it as a robust and versatile framework for non-stationary time series analysis.

This study introduces an intelligent framework that integrates machine learning and deep neural network ensemble techniques for early detection and prognosis of cardiovascular diseases. The system utilizes real-time physiological data collected from Internet of Medical Things (IoMT) devices, including ECG sensors, heart rate monitors, and blood pressure trackers. To ensure the accuracy and reliability of input data, preprocessing steps such as noise reduction, normalization, and missing value imputation are employed. The most significant health indicators are identified through effective feature selection methods and then processed using optimized classifiers such as Support Vector Machines (SVM), Random Forests, and eXtreme Gradient Boosting (XGBoost), which are combined in an ensemble architecture to improve diagnostic precision. The framework demonstrates remarkable performance in predicting cardiovascular disease risk, achieving higher accuracy, reduced false positives, and enhanced consistency compared to conventional methods. It is designed on a cloud-based infrastructure that ensures scalability and real-time processing for continuous patient monitoring. Experimental evaluation on real-world cardiovascular datasets confirms the framework's efficiency in early-stage risk assessment and clinical decision support. The results highlight the potential of combining traditional machine learning and deep learning paradigms to achieve proactive healthcare management and improve patient outcomes.

Comparisons between GPU implementations are usually asymmetric: one side is tuned by its author, the other is run as found. I report a programme that tuned both a novel SOM algorithm (SparseBin) and the baseline algorithm it was being compared to (cuSPARSE). The best-matching-unit search that dominates self-organizing map training was tuned through four levers - tile size, tile-membership clustering, neuron-axis chunking and vectorised loads - reaching 5.6-10.1x per epoch over the previously published configuration at map sizes from 32x32 to 512x512, and lifting the margin over the CUDA implementation behind our earlier MEDLINE atlases from ~80x to ~385x. cuSPARSE, the implementation SparseBin is compared against, received every lever with an analogue on its side, and became 2-3x faster in the process. The tuned kernel pressed the L2 bandwidth roof at 77% of peak with every other unit at 40-65%, bounding any further lever at ~1.3x - a terminal result rather than a waypoint, and every untested lever was either capped by that bound by construction or measured null.

Time series data is very common in many real-world applications and in numerous domains, with increasing interest for automated information extraction using machine learning. One of these subfields is time series classification, which consists in assigning a label to each new, unseen time series. Many algorithms have been developed over the past decades, with the trade-off between predictive performance and computational cost being consistently discussed. Quant, an interval-based algorithm extracting quantiles from recursive, fixed, dyadic intervals, was shown to achieve high accuracy, while being very fast. We propose two changes to make this algorithm even faster. The first one is a better optimized implementation of the exact same algorithm. The second one is to derive approximate quantiles, using the Cornish-Fisher expansion, instead of exact quantiles. This change removes the necessity to sort the time series, leading to a smaller computational complexity. We call this novel algorithm MomentQuant. We provide evidence that our implementation of Quant is faster than the original one, and that MomentQuant is even faster than our implementation of Quant, at the cost of a tiny decrease in predictive performance. These improvements are especially relevant for real-life applications, where inference is performed much more often than training.

Overparameterized neural networks carry far more hidden units than a task nominally requires, raising the question of which neurons are essential and whether that distinction is legible in the representation itself, without labels or gradients. We cast neuron selection as the problem of coarse-graining the hidden layer by retaining a subset of its neurons, and score each putative selection by the mapping entropy (ME). This quantity measures the loss of discriminatory power inherent in discarding part of the network neurons, and the selection that minimises the ME is taken as particularly informative. This criterion is fully unsupervised, in that it depends only on hidden-activation statistics. In teacher-student networks, ME optimisation recovers the minimal teacher-consistent representation and retains extra units in proportion to the hidden layer's residual variability; in a non-linear Gaussian process task, it selects coherent functional-class mappings whose preferred class shifts across training. On this task and on translation-augmented MNIST, ME-selected subnetworks outperform random subsets of equal size, most clearly under strong compression - linking configurational distinguishability to predictive performance.

Standard calibration evaluation and recalibration methods assume access to predicted probabilities. We study one-bit threshold access, a setting in which probabilities are hidden and the evaluator observes only whether the predicted probability exceeds a single chosen threshold per sample. Under this restriction, we show that classifiers can nevertheless be evaluated and recalibrated without reconstructing their hidden scores. We derive a consistent estimator of True Calibration Error, unbiased estimators of strictly proper scoring rules, and a one-bit objective for Temperature Scaling whose expectation matches the standard log-loss objective. Across these settings, we quantify the statistical cost incurred by replacing standard probability-access procedures by our one-bit estimators. Finally, we instantiate the framework for black-box LLMs, where the logit_bias API parameter allows us to realize the required threshold queries in zero-shot binary question answering.

Counterfactual explanations for graph-structured data seek to determine minimal and realistic modifications required in an input graph to alter a model's prediction to a predefined output. Although counterfactual explainers that support modifying the graph by both adding and removing edges have recently emerged, there is still a lack of general and efficient methods, especially when considering the quality of the generated explanations. Moreover, the problem remains far from solved, as existing methods exhibit different strengths and weaknesses, often trading off between explanation size, coverage and quality. For this reason, it is important to identify where each method performs well and where it falls short, so as to guide future research in the field. Thus, our study compares six state-of-the-art (SOTA) models on a diverse set of real-world and synthetic datasets, covering both binary and multi-class graph and node classification tasks, and evaluates their performance using diverse quantitative and qualitative metrics.

AI-driven de novo molecular design offers a promising route to accelerate early-stage drug discovery by generating novel ligands directly within target protein binding pockets. We present NEAT-POCKET, a pocket-conditioned extension of the autoregressive NEAT model for 3D molecular generation. NEAT-POCKET generates molecules atom by atom in protein pocket environments while preserving atom permutation invariance and explicitly modeling hydrogen atoms. Benchmarks on the CrossDocked and SPINDR datasets show that NEAT-POCKET achieves competitive structure-based generation performance while sampling substantially faster than existing baselines. Beyond full-molecule generation, NEAT-POCKET naturally enables pocket-conditioned fragment completion, a task directly relevant to lead optimization and scaffold elaboration. These results position NEAT-POCKET as a fast, flexible, and practical framework for structure-based drug design.

This paper introduces Deep Microcompression (DMC), a hardware-aware pipeline for deep learning inference on bare-metal microcontrollers. DMC integrates structured pruning, quantization-aware training, and fixed-length bit-packing to achieve a 55.8$\times$ weight compression ratio on LeNet-5 (98.77% accuracy), generating a dependency-free C library with deterministic latency. On the RP2040 (Cortex-M0+), DMC reduces binary size by 3$\times$ versus TensorFlow Lite while matching its accuracy. Critically, DMC enables the first documented deployment of a standard CNN on the ATmega328P, a device constrained to 2KB SRAM, previously considered infeasible for CNN inference.

Conformal counterfactual inference enables network operators to use logged telemetry to reliably answer 'what-if' questions about network operation. These answers typically take the form of prediction sets that contain, with a user-defined probability, the key performance indicators (KPIs) that would have been observed under alternative control actions. A key challenge is that logged telemetry may omit variables used by the controller, resulting in hidden confounding and invalidating the statistical guarantees of counterfactual analysis. In principle, this issue can be addressed using randomized telemetry, collected by assigning control actions independently of the network state. However, because such randomization may disrupt normal operation, randomized telemetry is typically scarce, causing counterfactual analysis based solely on it to produce uninformative prediction sets. To address these challenges, we propose Confounding-Valid Counterfactual Conformal Inference (CV-CCI), which combines abundant, potentially confounded observational telemetry with limited randomized data through the General Synthetic-Powered Inference (GESPI) principle. CV-CCI leverages observational data to improve efficiency while using randomized data to retain finite-sample coverage guarantees under arbitrary hidden confounding. Experiments on two representative radio access network (RAN) control tasks show that CV-CCI remains valid under hidden confounding while producing more efficient prediction sets than state-of-the-art confounding-valid baselines.

When a customer adds a professional camera to their cart, should the system suggest a matching lens, a generic tripod, or another camera body? Complementary Product Recommendation is vital for comprehensive basket building, yet standard models often fail to distinguish between items that are merely bought together and those that truly work together. In this paper, we present AlleCompanion: a production-scale retrieval framework deployed at Allegro.com that transforms noisy behavioural signals into precise semantic compatibility. We mitigate the intrinsic noise in large-scale co-purchase traffic by combining data-level filtering heuristics with a category-constrained Two Tower architecture. Within this framework, the Category Adapter guides the model in the embedding space, constraining candidates within logically complementary boundaries. Since modelling authentic user behaviour at scale is inherently difficult, we introduce ComCat, a multi-source Complementary Categories Mapping. ComCat acts as a translational layer that distils meaningful patterns from noisy traffic into a maintainable and controllable solution, integrating expert rules, human-in-the-loop feedback, LLM-based reasoning, and statistical mining. Our experimental results demonstrate that combining explicit category-level constraints with neural architectures effectively filters out co-purchase noise to surface recommendations that satisfy real-world user needs. Serving over 20 million active users monthly, the framework delivers significant uplifts in attributed GMV for organic discovery and drives substantial revenue growth in sponsored placements.

As quantum hardware scales to larger devices, the classical software layers that interface with it must evolve in step. Postprocessing routines developed and tested primarily in simulator settings can encode assumptions that no longer hold on utility-scale devices, leading to data loss that can be difficult to detect from high-level model outputs alone. We present a case study of SamplerQNN, the sampling-based quantum neural network class in the Qiskit Machine Learning library. Here, the postprocessing method applies a filter that assumes measurement bit-strings are in virtual qubit space. On our quantum hardware runs, where bit-strings span over 100 physical qubits, this filter led to the loss of 85 to 99.6% of valid measurement shots, depending on the transpiler's qubit placement. The resulting probability vector is unnormalised, allowing distorted prediction and loss values to propagate through the model without an API-level warning. We demonstrate the impact across five experiments on two IBM backends: for inference, accuracy drops from 0.94 to 0.39 on the same raw measurements; for training, the loss signal is compressed by 22 to 27$\times$, substantially reducing the sensitivity of the optimiser to the objective landscape. The behaviour arises in all released versions of the library (0.8.4 to 0.9.0). We implemented a layout-based marginalisation fix, merged into the GitHub codebase as Pull Request \#1041, that makes SamplerQNN postprocessing forward-compatible with current and upcoming hardware.

Self-supervised learning relies on so-called data augmentations $\phi(x)$ of unlabeled datapoints $x$ — for example, masking random pixels in an image $x$ — that should leave the label of $x$ invariant and are often used to learn a lower-complexity invariant subspace $\cal V$ for downstream tasks. In practice, such augmentations $\{ \phi_l(x_i) \}$ are pooled together to learn $\cal V$, despite obvious inter-dependencies between different augmentations $\phi_l(x), \phi_k(x)$ of the same datapoint $x$. However, theoretical works on the subject typically consider procedures that avoid such dependencies, and are therefore limited to operate on smaller subsets of independent data. We show in this work that pooling augmentations together, despite inter-dependencies, is a better alternative than the baseline of partitioning the data into subsets of independent data. More precisely, in the context of estimating $\cal V$, the statistical estimation error bounds for pooling are never worse than the partitioning baseline, and in some cases — such as masking or noise injection-based augmentations over a shallow neural network — naive pooling leads to faster rates in terms of the number of augmentations. The benefits of pooling are particularly prominent when the correlations between different augmentations $\phi_l(x), \phi_k(x)$ have mild effects on estimation or help decrease the estimation variance. The analysis, therefore, yields new insights into the success of pooling augmented samples in self-supervised pre-training, and provides an intuition behind the practical preference towards using many augmentations.

Scaling laws guide the design choices for training large foundation models, but deriving them involves training an exhaustive grid over hyperparameters, token budgets, and parameter counts, which is computationally expensive. Fitting a scaling law, however, only requires the best-loss frontier across compute scales, discarding most of the trained configurations. We propose a framework for efficient scaling law construction that formulates data collection as a Bayesian optimization problem, and introduce metrics for comparing scaling law fitting methods under constrained compute budgets. We find that progressively expanding the compute budget during acquisition, mirroring the compute-ordered evaluation of configurations in practice, substantially improves recovery efficiency. Augmenting the observed configurations with surrogate-fantasized evaluations then recovers the broader experimental grid, allowing accurate scaling law fitting without training every configuration. Together, these can closely match scaling law fits over a full dense grid at computational savings of up to $10\text{--}100\times$.

Federated scientific machine learning enables institutions to train neural surrogates without centralizing local physical data, yet studies of partial differential equations (PDEs) lack a transferable definition of non-independent and identically distributed data. Existing protocols partition coordinates, coefficients, boundary conditions, or geometries according to equation-specific rules. Here, we introduce solution-space PDE-Dirichlet, a protocol that converts continuous supervised responses into reusable solution bins and quantifies the realized separation between clients through optimal transport over the geometry of these bins. We derive an exact inverse relation between population allocation heterogeneity and the Dirichlet concentration, and we establish conditions under which response heterogeneity induces gradient disagreement, local-update dispersion, and parameter divergence. Across seven controlled and public PDE tasks, three neural-operator families, and five random seeds, a lower concentration consistently increases the realized solution distance and optimization heterogeneity. The degradation in final error is task dependent: the largest effect occurs for low-viscosity Burgers, reaching 4.157 percentage points under the most heterogeneous setting, whereas additional communication or smoother dynamics can reduce the final gap despite persistent parameter separation. These results distinguish a reproducible geometric mechanism from task-dependent generalization outcomes and provide a common basis for evaluating non-IID federated PDE learning.

Deep Imbalanced Regression (DIR) is pervasive in continuous prediction tasks across diverse modalities, such as age estimation, depth prediction, and protein mutation activity prediction, where label-scarce tail samples often carry higher practical value. However, most existing methods still learn deterministic point mappings under mean squared error or its simple variants, implicitly assuming a uniform uncertainty level across all samples and thereby overlooking the instance-wise heteroscedasticity that is widespread in long-tailed data. We further point out that even heteroscedastic negative log-likelihood suffers from a gradient coupling issue, which, under DIR scenarios, weakens the learning signal of hard tail samples and leads to optimization inertia as well as tail underfitting. To address this, we propose DUO, an uncertainty-aware long-tailed regression framework. Specifically, the proposed method models the regression target as a conditional Gaussian distribution to explicitly characterize instance-level predictive uncertainty, and transforms uncertainty into a dynamic enhancement signal for tail samples through decoupled mean-variance optimization. Furthermore, we design a distribution-guided contrastive learning mechanism that adaptively constructs positive and negative pairs based on the overlap between sample distributions, thereby alleviating feature looseness and cross-label semantic entanglement. Across visual and biological DIR benchmarks, DUO achieves the best few-shot bMAE and GM on IMDB-WIKI-DIR, AgeDB-DIR, and AAV2-DIR while remaining competitive on few-shot MAE.

Large Reasoning Models (LRMs) achieve superior problem-solving through extended Chain-of-Thought (CoT) generation, but the resulting key-value (KV) cache grows linearly with sequence length and creates severe memory bottlenecks, often exceeding GPU capacity for long reasoning traces. Existing KV cache compression methods rely on recent queries to estimate future token importance, implicitly assuming these serve as reliable proxies for future attention patterns. We demonstrate that this assumption fails in long-horizon reasoning: certain decoding steps generate Thought Revisiting Tokens (TRT) that re-attend to distant previous context, such as task-solving plans formulated early in the trace. Through systematic analysis, we discover that queries corresponding to the TRT cluster into a small number of similarity groups in the embedding space. Based on this insight, we propose BeaconKV, a training-free KV cache compression method that maintains beacon queries, compact representatives for each global query cluster, to anticipate which KV pairs will be revisited without storing the entire query history. Across four open-source LRMs and diverse reasoning benchmarks, BeaconKV generally outperforms existing compression methods, achieving up to $5.8\times$ memory reduction while nearly preserving full cache accuracy and improving throughput by over $4.3\times$.