Papers

Unique and rapid classification of knots and links is an open mathematical problem that is relevant to a range of (bio)physical systems, including polymer melts, DNA, and proteins. In this paper, we explore a data-driven approach to the classification problem of link topology. Extending the framework introduced in Ref. 1 (Sleiman et al, 2024 Soft Matter, 20(1), pp.71-78), we show that a feedforward neural network trained on the writhe density matrix classifies thermally equilibrated configurations of the first six prime links with 97% accuracy. We demonstrate that this accuracy remains high across a range of temperatures and lengths of link components, while rapidly deteriorating with the addition of topology-altering Gaussian noise; a result consistent with the writhe density matrix containing features sensitive to topology. Our results show that neural networks based on the writhe density matrix efficiently classify two-component links, establishing machine learning as a promising tool for rapid classification of more complex link topologies, e.g. Borromean rings and multi-component links, as the computational cost of exact numerical calculation of topological invariants becomes prohibitive.

Effective decision-making in complex and changing environments requires balancing short-term and long-term consequences. In reinforcement learning (RL), this trade-off is typically controlled through a fixed discount factor, which imposes a single exponentially discounted temporal horizon. However, biological agents exhibit flexible and adaptive temporal discounting, suggesting that effective planning requires multiple timescales. Here, we propose a multi-horizon approach that adaptively selects and combines temporal horizons, enabling robust adaptation to changes in reward structure without manual discount-factor tuning. This flexibility makes the method particularly suitable for continual learning scenarios involving task switches and varying environmental configurations. Empirically, we demonstrate that our approach identifies effective discount factors across a range of MiniGrid environments, including continual settings composed of three sequentially changing tasks. These results suggest that adaptive temporal discounting can improve parameter efficiency and enhance adaptability in both artificial and biologically inspired learning systems.

Lead ranking in Customer Relationship Management (CRM) systems faces a persistent challenge: models achieving high offline accuracy often underperform in production. We identify three fundamental gaps responsible for this disconnect: offline-online metric mismatch, pointwise-listwise objective misalignment, and temporal distribution drift. To address these gaps, we propose SalesLoop, a reinforcement learning framework that establishes a closed feedback loop between model predictions and real-world business outcomes. Our approach introduces (1) a performance-aware reward that encodes conversion outcomes weighted by ranking position and conversion velocity, and (2) Discriminative GRPO, a listwise optimization objective that adapts Group Relative Policy Optimization to discriminative ranking models. SalesLoop improves NDCG@K by +7.9% and P@K by +15.8% over the strongest static baseline. A 160-day production A/B test at a New Energy Vehicle manufacturer, spanning 16.5M leads and 280 sales specialists across two provincial markets, validates statistically significant cumulative lift of +4.7% ($p=0.047$) and +8.7% ($p=0.002$). In production, the ranking backbone achieves Top-10% recall of 44.1% and surfaces high-intent leads at $2.3\times$ the conversion rate of specialist baselines.

Predicting how deformable objects evolve under robotic manipulation is a longstanding challenge. Existing approaches typically rely on per-object optimization to fit material parameters, which can be slow and cannot generalize, while end-to-end learned alternatives extrapolate poorly and often violate basic physical structure. We present PhysCoRe, a physics-corrected residual world model that couples a differentiable Material Point Method (MPM) simulator with two feed-forward neural networks. A material refinement module, Material from Motion (MfM), infers per-particle elasticity from visual observations, grounding the simulator in object-specific physics. A residual correction module, Residual from Dynamics (RfD), learns the discrepancy and predicts corrections to the simulator's internal dynamics, absorbing systematic biases that the analytical model cannot capture. This design also supports online material identification on novel objects. MfM adapts from limited interactions, and its predictive uncertainty steers further exploration toward the regions where its estimate is least confident. Experiments on real deformable-object manipulation sequences show that PhysCoRe outperforms state-of-the-art baselines in prediction accuracy, and that its predicted confidence forms a reliable distribution across the object's geometry, providing a natural signal for future confidence-guided exploration.

Language models are thought to exhibit the phenomenon of superposition, representing many more features than dimensions in their residual streams. Sparse autoencoders (SAEs) are designed to recover such features post-hoc, but training models that are interpretable by construction has remained impractical, as a per-layer over-complete bottleneck is prohibitively expensive in both memory and compute. To overcome this issue, we introduce the ParityTransformer, a GPT-2-scale architecture whose intermediate representations are efficient and wide / sparse by design. At each layer, a Deep Parity Bottleneck (DPB) replaces a learned over-complete basis with a parameter-free algebraic dictionary, providing a deterministic incoherence guarantee and eliminating the memory requirements that have prevented per-layer interpretable bottlenecks at scale. A DPB is a hierarchically structured sparse bottleneck which efficiently enforces sparsity using a multi-level mixture-of-experts approach: a hardware-aware implementation that closes the cost gap between activation sparse and dense training to a manageable interpretability tax. Empirically, ParityTransformers perform at least as well as post-hoc SAEs on sparse probing tasks, while out-performing on measures of feature absorption, steering effectiveness, and fine-grained causal interventions. Because subsequent computation acts only on features that survive the sparse bottleneck, the ParityTransformer's features are native to the model's forwards pass by construction, addressing the question of whether SAEs probe features the model actually uses during computation. We see this as a step toward training models whose internal representations are interpretable by design rather than recovered post hoc.

We introduce Frontier Financial Judgement, a challenging new benchmark developed in collaboration with professional equity analysts to assess agents' ability to replicate expert human judgements. Rapidly identifying new information, evaluating its implications and determining its valuation impact is one of the most time-consuming and challenging aspects of real-world equity coverage. This is becoming ever more difficult and important as AI rapidly increases the quantity of new information to process. The strongest agent we evaluate on Frontier Financial Judgement matches all expert labels in only 52.4% of cases. We also find significant divergence in estimated false-positive rates among frontier agents, ranging from ~1% for GPT-5.6 Sol to ~32% for Claude Sonnet 4.6. To construct the benchmark and make it representative of real-world settings, we combine human-designed and labelled synthetic articles with live news articles and historical documents, creating 656 items for assessment. The resulting task requires agents to distinguish genuinely new, valuation-relevant financial information from stale, immaterial or misleading news under realistic conditions. We find substantial trade-offs among agent accuracy, cost, false positives and reliability that continue to hinder the reliable deployment of news-flow filtering in practice.

Computer aided design (CAD) is ubiquitous: virtually any modern object was designed using editable CAD tools. However, with the shortage of available CAD datasets in its native editable and parametric format, boundary representation (B-Rep), it is ever more important to develop data-efficient methods for this domain. We present a new self-supervised pretraining task, Masked Topology Modeling (MTM), that leverages the face-adjacency graph, an induced structure unique to B-reps that the encoder can be asked to reconstruct. MTM masks a fraction of edges and trains a small head to predict each masked edge's convexity and curve type from the encoder's post-message-passing face features. We combine MTM with a MoCo-style momentum-queue contrastive learning over B-rep-aware augmentations, a BFS-connected face-region masked-reconstruction objective, and pretraining on the ABC dataset and our new procedurally generated dataset to show strong performance on a number of benchmarks.

Federated learning (FL) enables multiple clinical institutions to collaboratively train a shared disease classifier without centralizing patient data. In practice, however, each institution annotates only the pathologies within its area of expertise, so the federation operates under task heterogeneity: each client holds labels for a strict subset of the target disease categories while the remaining classes are entirely unobserved at that site. Existing gradient-based FL methods fail under this setting because they require hundreds of communication rounds to converge and because missing class labels introduce systematic false-negative bias that the model cannot correct without a principled mechanism. We propose an analytic federated learning framework for multi-label medical image classification under task heterogeneity. The proposed method replaces iterative gradient optimization with three closed-form operations: a balanced label projection that neutralizes class-imbalance bias by normalizing positive and negative contributions to equal total mass; a per-class absolute aggregation law that independently assembles the optimal ridge-regression classifier for each disease category from the sufficient statistics uploaded by its annotating clients; and an optional analytic pseudo-label refinement round that propagates missing-class knowledge from a confidence-filtered teacher classifier to non-annotating clients. The entire procedure requires at most two communication rounds, irrespective of the degree of task heterogeneity or the number of participating clients. Experiments on ChestXray14 under four progressively severe missing-class configurations demonstrate that the proposed method consistently outperforms the state-of-the-art federated multi-label method FedMLP by up to 18.44 BACC points and 13.24 AUC points, while reducing the communication.

As humans, we face many decisions that require us to choose between sticking to something and giving up. This thesis uses algorithmic tools to derive insights about such decision-making problems in theoretical models, studying both near-optimal methods and outcomes of social and behavioral influences. Along the way, this thesis sheds light on what we gain and what we lose as we move from a messy and complex real world setting to a very general abstract model by studying various points along this spectrum. In Part I, we study algorithms for sequential decision-making in the improving multi-armed bandits problem. We provide nearly matching upper and lower bounds in the general case. Then, we then ask what is possible if we have access to similar instances to the one we wish to deploy our algorithm on. To that end, we provide guarantees in the data-driven algorithm design framework, showing that a polynomial number of samples is sufficient for learning good algorithms from a class of algorithms. In Part II, we study algorithmic approaches for problems in social epistemology. We start by analyzing what role theoretical models can play in the study of social problems. We then study social and behavioral influences in decision-making requiring investment. First, we provide mathematical formalism in which to study the formation of pessimism traps, a phenomenon identified by philosophers in which agents are influenced by their predecessors to engage in less-ambitious goals. We develop financial interventions to sustainably shift communities out of these traps. The second problem we study is the influence of grit as a behavioral trait in ambitious decision-making. Overall, these works seek to theoretically model phenomena in social epistemology and provide a framework for intervening algorithmically.

Sparse autoencoder (SAE) features are used to interpret and steer large language models, yet nobody has tested whether a feature's causal role is stable across SAE families. Single-token features fire on one vocabulary item, so ground truth permits direct comparison. We analyze 3.9M features across six models and three SAE families and zero-ablate at full layer depth: they sit 4.7x tighter in decoder space and concentrate in early layers. Deleting one lowers the model's logit for that token in 178 of 208 layer conditions, significant after multiple-comparison correction. And depth decides how the damage lands: early-layer deletions disrupt the layers that follow, late-layer deletions change the output directly. Cross-family causal differences exceed within-family scale effects: on the same base model, GemmaScope and BatchTopK features are causally anchored, LlamaScope features locally redundant. Under LlamaScope the token returns to within 2x its pre-ablation rank 96-98% of the time. Changing only the activation function reverses the sign of that difference, so the training recipe is the remaining candidate: cross-family claims are sensitive to training methodology, not just activation function or scale.

When does a weight-tied looped transformer – one block applied T times – implement an actual algorithm? We answer with four findings from controlled populations on group word problems. (1) The budget law: free training installs a linear computation frontier, a mechanism that solves v positions per loop, whose speed is priced by the training contract: v ~ n_train/T_train (exponent 0.98 +/- 0.04, R^2=0.99), exactly unity under T=n training. SGD selects a frontier matching the minimum the contract demands; granting more test-time loops than ever trained rescues late positions at fixed input length, yielding a principled halting rule T* = ceil(n / v-hat). (2) Architecture prior, not expressivity, picks the algorithm: standard-depth transformers learn parallel scans on this family; weight tying flips the selection to the serial frontier, even when positional addressing for a log-depth scan is supplied. At matched depth and parameters, untied models extrapolate worst and fail to learn A5 at all. (3) The walls are not where circuit complexity says: NC1-completeness costs nothing (A5 generalizes fully), while group order does (S5's 120x120 operator deadlocks joint learning) – and an operator-first curriculum dissolves the wall in every seed. (4) Mechanisms are portable, not mandatable: warm-starting across budget contracts transfers the algorithm in every seed, re-pricing its speed, while imposing seriality through the input schedule fails where free training succeeds. These results are invisible to standard instruments, which provably saturate at the fixed points trained loops converge to. We introduce a head instrument, the convergence-time scaling tau(n,i), validate it causally via damage cones whose slope reproduces v, and show in-distribution head measurements predict out-of-distribution fate where tail metrics do not. Results replicate on the public easy-to-hard benchmark.

Spatio-temporal machine-learning modelling is an important tool in environmental research. However, machine-learning models are highly sensitive to both the characteristics of the training data, such as its distribution, and methodological choices, including the cross-validation strategy. Each decision has impact and implications on the model itself as well as the estimation of the model quality and applicability for certain purposes. Taking into account the large role of machine-learning based maps of the environment in science and their transfer into practice, transparent reporting of spatio-temporal models, ideally using standardized model protocols, is essential to enable trust, transparency and comparability. However, such protocols are currently lacking for spatio-temporal modelling. We propose STeMP (Spatio-Temporal Modelling Protocol) to fill this gap by serving two purposes: standardized reporting to understand the model functioning as well as providing guidance during the modelling process by pointing at critical decisions and parameters. The protocol is structured in three sections: Overview, Model and Prediction. The Overview section contains metadata, while the Model and Prediction sections go into detail, describing predictors, evaluation and software, and further relevant elements of the modelling workflow. The protocol definition is hosted on GitHub and accompanied by an R-package (https://github.com/LOEK-RS/STeMP). The R-package contains a web application that can be used to fill the protocol either manually or in a semi-automated way from provided modelling objects. Warnings are returned from the protocol when common pitfalls are encountered, which may help authors as a guide through the modelling process but also support reviewers in the assessment of modelling studies. Via GitHub, incorporation of contributions and feedback from the community is encouraged.

Neural network misclassifications exhibit characteristic spectral instability in internal activations that is invisible at the output layer. This phenomenon is identified and formalized as Spectral Drift – the frequency-domain distance between consecutive layer activations – with empirical validation showing that failures exhibit significantly higher drift than correct predictions (1.9% increase, p<0.001). This spectral signature emerges during internal processing but becomes masked in final outputs, explaining why confidence-based detection methods struggle. This work introduces Self-Detecting Neural Networks (SDNN), a framework that monitors spectral dynamics across network depth using Short-Time Fourier Transform, wavelet decomposition, and statistical moments to capture multi-scale spectral features. A lightweight detector network (5% parameter overhead) learns to identify failure-indicative patterns via curriculum learning on progressively challenging distributions: natural misclassifications, distribution shifts, and adversarial perturbations. Experiments on CIFAR-10 demonstrate that SDNN achieves 79.0 +/- 25.3% AUROC across three seeds, substantially outperforming confidence-based baselines including MaxSoftmax (50.5%) and Energy Score (52.9%) by approximately 25-30 percentage points. Ablation studies reveal that wavelet decomposition and statistical features make consistent contributions, while STFT's role remains unclear. This work establishes spectral analysis of internal activations as a promising direction for neural network reliability, revealing diagnostic information inaccessible to output-based approaches.

Modern power systems increasingly require probabilistic forecasts amid interacting uncertainties from renewable intermittency, flexible demand, market volatility, and weather-dependent generation. However, existing methods often treat multi-scale decomposition, exogenous-variable alignment, and probabilistic output as separate steps, obscuring how predictable structures and uncertainty-bearing fluctuations jointly shape the forecast distribution. This paper proposes a state-space exogenous-context and temporal-frequency resolution architecture for general probabilistic energy forecasting. Its central premise is that trend-periodic components primarily determine the baseline trajectory, whereas high-frequency residuals and external perturbations govern the spread and asymmetry of forecast uncertainty. Accordingly, the architecture adaptively separates deterministic and residual streams, aligns exogenous context with both, refines the deterministic backbone through multi-resolution spectral-temporal state-space modeling, and estimates ordered quantile boundaries from their complementary representations. Experiments on load, price, solar, and wind forecasting achieve the best continuous ranked probability score in 14 of 18 settings, reducing average CRPS by 5.74% and upper-tail quantile risk by 7.27% over the strongest baselines. These results support deterministic-stochastic separation as an effective design principle for general probabilistic energy forecasting.

We study vector-valued affine refinement operators of the form [ (W\gamma)(t)=\sum_{j\in\mathbb{Z}} A_j\gamma(Mt-j)+B(t), ] with finitely supported matrix mask and compactly supported continuous piecewise linear input and forcing data. Building on the homogeneous realization theorem for (B\equiv 0), we prove that, for (M\ge 3), every finite affine iterate (W^n\gamma) admits an exact fixed-width ReLU realization whose depth is (O(n)). The main new ingredient is a residual memory controller. It replaces the noninvertible residual dynamics by an injective skew-product and permits exact backward replay of the residual states required by a Horner-type evaluation of the affine forcing sum. Offset frames align the forcing atoms away from residual seams, allowing complementary loop readouts to recover their values exactly. The remaining branch-selection ambiguity occurs only where the accumulated affine state has already vanished. For (M\ge 3), the result applies to arbitrary compactly supported continuous piecewise linear forcing terms. For (M=2), the same construction applies to ordinary-frame seam-separated forcing. We also prove a stage-dependent extension for forcing terms in a fixed finite-dimensional continuous piecewise linear span and record the resulting linear-depth upgrade for open-curve, finite-state, and Hilbert- and Morton-type recursive constructions.

Sample-based quantum diagonalization (SQD), an extension of quantum selected configuration interaction (QSCI), is a promising hybrid quantum-classical paradigm for molecular ground-state energies. By replacing variational optimization with quantum sampling, QSCI avoids barren plateaus and directly reconstructs correlated wavefunctions. However, existing configuration recovery mainly enforces symmetry constraints without targeting the most physically relevant configurations, often yielding oversized subspaces and costly classical diagonalization. We introduce QSCI-RBM, a compact subspace generation protocol based on Restricted Boltzmann Machines (RBMs), and integrate it within Density Matrix Embedding Theory (DMET). The RBM learns the distribution of dominant determinants from hardware samples, generating high-probability configurations. Sampling was performed on IBM Heron R1 (ibm\_torino) for CH$_5$NO, R2 (ibm\_fez) for C$_2$H$_4$, and R3 (ibm\_boston) for the larger H$_2$O benchmark and the protein-ligand system. After validating on these benchmarks of increasing active-space size, we simulate the inhibitor Carmofur bound to the SARS-CoV-2 main protease (M\textsuperscript{pro}), fragmented into ten DMET impurities. Both DMET-QSCI-RBM and a DMET-SQD baseline reach chemical-potential self-consistency within four $\mu$-iterations. At the converged chemical potential, DMET-QSCI-RBM lies within $0.05\,\mathrm{mHa}$ of DMET-FCI while accessing on average only $0.22\%$ of the symmetry-preserving configuration space, versus $0.55\,\mathrm{mHa}$ at $33.0\%$ for DMET-SQD, leading to a $\sim$153-fold subspace reduction. RBM-assisted expansion thus yields far more compact hardware-derived determinant spaces at equal or better accuracy, reducing classical overhead for scalable quantum embedding of biological systems on real hardware.

Machine learning models for medical image analysis typically lack a reliable measure of confidence, limiting their use in ambiguous or atypical cases. Here we show that Monte Carlo dropout, applied to a multi-task chest-radiograph classifier (eight thoracic findings, 137,593 training images), provides an epistemic uncertainty signal that tracks generalisation across training-set scales and flags confident yet error-prone predictions. Adding this signal to the point prediction raised error-detection AUROC from 0.74 to 0.77 ($\Delta$AUROC +0.023, 95% CI [+0.014, +0.033]). In a controlled 2x2 factorial experiment, a clinical-decision-support agent exploited this uncertainty only when it was delivered as a binary error-risk flag rather than as raw scores, cutting confident misdiagnoses on unreliable findings from 8.5% to 2.7%. Epistemic uncertainty estimation thus carries decision-relevant information beyond point predictions, but its value for downstream agents depends on how it is communicated.

We study Gaussian-width complexity on statistical manifolds through a pair of functionals: the primal Fisher width $w_G(T) = w(G^{1/2}T)$, induced by the Fisher metric, and the inverse-Fisher width $w_{G^{-1}}(T) = w(G^{-1/2}T)$, induced by the inverse Fisher metric. The two widths play complementary statistical roles. On the learning side, the Fisher width measures the size of local parameter fluctuations in the geometry induced by the Fisher information. For Fisher-regular losses, we prove that the scale \(w_G(H_r)/\sqrt n\) is attained on sufficiently small Fisher balls. On the recovery side, the inverse-Fisher width captures the effect of anisotropic Gaussian measurements whose covariance is determined by the inverse Fisher information. For sparse recovery, the resulting geometry depends not only on sparsity but also on the position of the active coordinates in the Fisher spectrum. We obtain a two-sided estimate for the corresponding statistical dimension, together with support-sensitive recovery estimates and a natural ordering of supports with different curvature profiles. Finally, we establish a sharp relation between the primal and inverse-Fisher widths. On any common compact coordinate set $T$, they satisfy \[ w_G(T)w_{G^{-1}}(T)\geq w(T)^2. \] Thus, Fisher anisotropy may transfer complexity from one geometry to the other, but cannot reduce both widths relative to the Euclidean scale.

Physics-based simulations are essential for understanding the electrode-scale discharge behavior of lithium-ion batteries (LIBs) but suffer from prohibitive computational costs. To address this, we introduce a novel deep learning surrogate pipeline based on the Swin3D Transformer to predict spatiotemporal discharge dynamics directly from volumetric data. Our approach integrates two key innovations: Gaussian Positional Encoding (GPE), which enhances spatial feature representation by adapting to the complex geometry of electrode microstructures, and a specialized Temporal Encoding module to capture non-linear timeseries evolution. Experimental validation on an Electrochemical Simulation (ES) dataset demonstrates that our pipeline significantly outperforms state-of-the-art point cloud baselines in prediction accuracy. Furthermore, the proposed method reduces the computational overhead by orders of magnitude, providing a scalable and efficient framework for high-throughput battery design and optimization.

We prove strong laws of large numbers for random functions in the Lipschitz pseudometric. Our results hold under either a topological or a model-theoretic condition, with the latter encompassing functions jointly definable in o-minimal structures but extending substantially beyond this class. Applications include uniform convergence of limiting and Clarke subdifferentials and finite-sample identification of solutions. Consequently, we identify broad classes of functions for which the failure phenomena revealed by our previous negative results [Tian and Royset, arXiv:2511.16568, 2025] do not occur.

Full-sized humanoid robot capabilities have grown exponentially in recent years, aiming towards general-purpose deployment in human environments. A popular control method used by manufacturers utilizes Virtual Reality for upper-body teleoperation and Reinforcement Learning for lower-body balance and locomotion control. As a result, a single remote operator can see, manipulate, and navigate about a real, distant physical environment. This powerful control stack is often relegated to expensive full-sized robots, many of which are inaccessible to the research community. Miniature humanoids are more prevalent, but employ less biomimicry in their design (e.g. fewer sensors, Degrees of Freedom, etc) and lack similar developments. This paper describes a compliant full-body telepresence control stack developed from the ground up for miniature humanoids. Framework experimentation on ROBOTIS OP3 hardware showcases walking at speeds up to 0.45 m/s independent of arm motions. Tele-loco-manipulation is demonstrated via a cube relocation experiment with an expert human operator. On average, the teleoperated system moved 2 different 40 g cubes within 10 mins, walking a total distance of 5 m. Overall, the developed system shows potential for miniature humanoid tele-loco-manipulation.

Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability. Kolmogorov Arnold Networks (KANs) mitigate these limitations because their learnable spline activations are structurally aligned with the piecewise-polynomial bases of classical discretizations. However, the way a PDE is cast into a loss functional is as decisive as the choice of approximator: strong-form residual minimization requires high-order derivatives and heavily weighted losses, the energy (Bubnov-Galerkin) form is restricted to self-adjoint operators and, as we show, collapses to a trivial solution for parameter-identification problems, and boundary integral forms require a known fundamental solution. We propose PG-KINN, a physics-informed KAN built on a Petrov-Galerkin formulation in which the trial space is a KAN and the test space is an independent, compactly supported, piecewise-polynomial space evaluated with Gauss-Legendre quadrature. Integration by parts lowers the differentiation order while retaining applicability to general non-self-adjoint, nonlinear, and inverse problems; the localized test functions turn the global residual into a set of element-wise weak residuals with favorable conditioning. On a suite of benchmarks spanning crack singularities, stress concentration, Neo-Hookean hyperelasticity, inverse parameter identification in heterogeneous media, and complex geometries, PG-KINN consistently outperforms legacy MLP baselines and state-of-the-art KAN-based strong/energy/inverse formulations (PIKAN). These results position the Petrov-Galerkin coupling of KAN trial spaces and polynomial test spaces as a robust and accurate route for AI-based computational mechanics.

Hardware noise and finite sampling perturb the fidelity estimates forming a quantum-kernel Gram matrix. We measured how far three hardware-reconstructed Gram matrices depart from an exact statevector reference for one frozen four-qubit ZZ feature map on N=24 indoor air-quality windows, executed on ibm_fez at 1024 shots per circuit in three single, non-interleaved jobs: baseline, dynamical decoupling alone, and gate twirling alone. All were complete, finite, and positive-semidefinite. Off-diagonal root-mean-squared error (RMSE) against the reference was 0.0878, 0.0864, and 0.0427; full-matrix centered kernel alignment (CKA) ranged 0.933-0.989 and the post hoc diagonal-excluded (U-centered) CKA 0.816-0.986. The gate-twirled job deviated least on every reported geometry axis; its baseline contrasts are deletion-stable for the Spearman, mean-absolute-error, RMSE, and full-matrix CKA diagnostics, while the Pearson and diagonal-excluded contrasts fall just below that convention. Dynamical decoupling was not separated from the baseline. The observed error exceeded both finite-shot reference scales, so, under those sampling-only models, sampling does not explain it. Centered kernel-target alignment did not track reconstruction fidelity and stayed at or below each label-permutation reference: implementation fidelity and task relevance are distinct diagnostic axes. All configuration-level statements describe three realized jobs on one backend; no mitigation-efficacy, classifier-superiority, forecasting, or quantum-advantage claim is made.

This paper studies the problem of stochastic variance reduction (SVR) for the maximum mean discrepancy (MMD) and correlation alignment (CORAL) loss functions. Although various offline SVR algorithms for these losses have been proposed, these are incompatible with online, distributed, or incremental learning settings. This paper presents Adaptive vaRiance Reduction via Online reWeighting (ARROW), the first online SVR algorithm for the MMD and CORAL for streamed data. The method maintains moving average references of the alignment statistics, and adaptively reweights incoming minibatches so that the minibatch and reference statistics are aligned. Further, we propose a relaxed reweighting scheme so that the ensuing weight-optimisation problem is tractable. In experiments and simulations, we show that ARROW performs competitively with offline algorithms in terms of runtime, degree of variance reduction achieved, and target domain accuracy.

Correlation alignment and the maximum mean discrepancy are two widely used distribution-matching frameworks for unsupervised domain adaptation (UDA). However, high variance in these losses has been shown to undermine their effectiveness in minibatch optimisation settings. Furthermore, the losses lack finite-sum structure, which renders them incompatible with classical stochastic variance reduction (SVR) methods. This paper proposes Paired Sampling for Domain Adaptation (PSDA), a novel SVR technique tailored to such objectives. PSDA pairs observations both within and across domains, to form quadruplets that are always sampled together during training. The pairings are designed to minimise expected gradient variance, and reduce to solving a set of linear assignment problems. Our simulations demonstrate reduced variance compared to related methods, and experiments on three domain shift datasets show improved target domain accuracy.

Constitutive modeling under uncertainty remains a central challenge for reliable mechanics simulations, particularly when the available stress-deformation data are sparse, noisy, or heterogeneous. We propose interval and fuzzy physics-augmented neural networks (iPANNs and fPANNs) for uncertainty-aware hyperelastic constitutive modeling. iPANNs learn sparse lower, mean, and upper free energy density branches whose stresses, obtained by automatic differentiation, ultimately enclose noisy stress observations. In contrast to this deterministic interval description, fPANNs embed the learned iPANN branches into a fuzzy-set representation through membership-level (alpha-cut) interpolation, yielding a nested family of admissible responses. iPANNs and fPANNs encode mechanistic constraints by preserving objectivity, consistency and promoting polyconvexity and, smoothed L0 regularization promoting interpretable energy representations. The bound models are trained through a two-stage transfer-learning procedure in which a sparse mean constitutive response is learned first and then fine-tuned into lower and upper energy branches. We evaluate the framework on synthetic isotropic hyperelastic data with heteroscedastic noise, varying random realizations, shifted noise means, and varying noise magnitudes. The results show that the learned bounds enclose noisy stress observations while generalizing to the test set. Further, we examine the propagation of uncertainty through the mean, upper and lower bound predictions of the learned iPANN models in a finite element setting. The proposed framework provides a compact, physics-consistent route for distribution-free aleatoric uncertainty quantification in hyperelastic constitutive modeling, and propagation in downstream finite element simulations.

Nanopore devices have emerged as powerful tools for single-molecule sensing, with potential for rapid, portable diagnostics. They detect changes in ionic current as analytes enter nanometer-scale pores, providing a means of identifying diverse biomarkers from their characteristic signal patterns. However, these signals are highly complex, and reliably assigning them to specific molecules remains a major challenge. Here, we address this by introducing a multi-modal deep learning architecture that jointly processes multiple signal representations, including raw time-series data, wavelet-based images, and static feature vectors. Our approach surpasses existing methods by more than 10 percentage points on a 42-peptide benchmark and transfers to a 20-amino-acid dataset with near-perfect accuracy. The model integrates complementary information from these representations, with attention analysis showing that the time-series and wavelet-image inputs emphasize different features of the same event. Together, these results demonstrate the potential of machine learning to enable robust, high-accuracy molecular identification with nanopore sensors.

Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations. These residuals are evaluated directly on the mesh, requiring no labeled data. We evaluate the trained surrogates against computational fluid dynamics (CFD) references and a data-supervised baseline across four scenarios. On the two steady-state benchmarks, each solved on the same mesh as its CFD reference, the FVM-loss model reproduces the reference flow and temperature fields with mean field-averaged normalized root-mean-square errors (nRMSEs) near 3%, including the buoyancy-energy coupling. On the two parametric transient cases, the FVM-loss model attains lower rollout errors than the supervised baseline in almost every field, while avoiding the data-generation cost entirely. These results indicate that the FVM loss can provide a practical training signal for neural surrogates and reduce the model development cost.

We study decentralized online optimization for strongly geodesically convex (strongly g-convex) losses on Riemannian manifolds with bounded sectional curvature, including positively curved manifolds. In centralized Riemannian optimization, strong g-convexity tightens the optimal regret from $O(\sqrt{T})$ to $O(\log T)$, where $T$ is the time horizon; in the decentralized Riemannian setting, however, existing methods address only g-convex losses, leaving the strongly g-convex regime unexplored. One challenge is that the required decaying step size in the centralized regime is incompatible with existing network-error analyses, which typically assume a fixed step size. First, we provide a general network-error analysis for time-varying schedules. Next, we build on this analysis to establish the first $O(\log T)$ static regret bound for decentralized online Riemannian gradient descent, matching the minimax-optimal rate for strongly-convex Euclidean online optimization. Finally, we prove the same $O(\log T)$ regret bound for the two-point bandit feedback setting using novel strong subconvexity arguments for the smoothed versions of the loss functions.

Covariate shift often occurs because, in many real applications, the source and the target observations may be generated from different distributions. In this case, the standard metric under the source distribution is not appropriate. This paper considers deep neural network estimators for nonparametric quantile and Huber regression under covariate shift and from dependent observations. We deal with a generalized Bernstein-type inequality that is satisfied by many classical models, including i.i.d. observations, $\phi$-mixing, strong mixing, and $\mathcal{C}$-mixing processes. To perform the covariate shift phenomenon, we propose a sparse-penalized deep neural network (SPDNN) estimator that takes into account the discrepancy between the source and target distributions of the data. When the density ratio (between the source and target distributions of the covariate) is unknown, a two steps pre-training procedure is carried out: the first step is devoted to the construction of a least squares SPDNN estimator of the density ratio; which is used in the second step to perform a pre-training reweighted SPDNN estimator of the regression function. For both the quantile and the Huber regression, non-asymptotic error bounds of the proposed SPDNN estimators are established in the class of Hölder smooth functions. These estimators can adaptively attain (up to a logarithmic factor) the minimax optimal convergence rate from i.i.d. data as well as from several classical time series models.