Papers

Backpropagation is the computational engine of deep learning, yet its mathematical structure is typically treated as a procedural traversal of computational graphs. We present a global operator theory of the F-adjoint framework, which reformulates the layerwise backward recursion of an $L$-depth feedforward network into a single linear system $(I-\cB)\Xs=\bG$, where $\bG$ is a source vector. We prove that the global backward operator $\cB$ is strictly block upper-triangular and nilpotent of index at most $L$. This nilpotency guarantees the exact termination of the Neumann series solution after at most $L$ terms, revealing classical backpropagation to be mathematically equivalent to block back-substitution on an upper bidiagonal system. We formalise F-symmetry – the condition in which the backward pass perfectly mirrors the forward pass – identifying orthogonal weight matrices as canonical examples. Through worked numerical examples, we demonstrate how this operator perspective exposes the single-path collapse of strictly feedforward networks and its breakdown in residual architectures. Finally, we leverage this compositional structure to rigorously derive the mechanics of residual networks (gradient highways) and transfer learning (gradient truncation). This framework elevates backpropagation from an algorithmic recipe to a global nilpotent-operator formulation.

Quantum state tomography is sample-starved, and the states one prepares live on a narrow, learnable manifold. A $k{=}0$ prior-only control shows that on concentrated families a prior estimate is already near-optimal, so “high fidelity at few measurements” can be family memorization rather than tomography; genuine measurement-efficiency needs a model that conditions on the measurements and demonstrably uses them. On a shared matrix-product-state (MPS) core parameterization we study two routes. Approach~A learns a generative prior over MPS cores with measurement-guided posterior inference (gold-standard-validated, but whose few-measurement accuracy the control shows is largely the prior). Approach~B, our main proposal, is a fixed-protocol amortized MPS estimator trained once with a gauge-invariant fidelity loss; we deliberately do not rest it on a permutation-invariant set encoder (a plain MLP matches it). The decisive lever is the measurement design: motivated by the fact that local reduced density matrices determine a $\chi$-MPS, conditioning on an informative local Pauli set rather than random strings turns a modest, memorization-prone estimator into a high-fidelity one ($\approx\!0.95$, up to $+0.59$ over prior-only, decisively passing a shuffled-measurement control). A dropout ensemble, conformally recalibrated, gives $\approx\!90\%$-coverage intervals – including for observables never measured, where a shot-based interval does not exist. Quality holds as the system grows (fidelity $0.90$ at $n{=}10$, gain growing in $n$; $0.88$ at bond dimension $\chi{=}4$), the parameterization is polynomial (native contraction to $20$ qubits), and we close the loop on IBM hardware ($5$ states at $0.97$ from hardware-measured Paulis).

Accurate dengue forecasting is crucial for public health planning, but remains challenging because incidence series are often short, noisy, non-stationary, nonlinear, and often affected by long-range temporal dependence. Fractional differencing in Autoregressive Fractionally Integrated Moving Average (ARFIMA) helps balance non-stationarity and persistence, but its linear structure limits its ability to capture nonlinear dynamics. Deep neural networks can model nonlinear patterns, but usually require large training samples and do not explicitly encode statistical long memory. Echo State Networks (ESNs), a widely used reservoir computing framework, are attractive in this setting because they retain nonlinear recurrent dynamics while training only a simple readout, making them suitable for data-scarce scenarios. However, standard ESNs lack long-term memory from a time-series perspective. This study proposes a long-memory reservoir computing framework that integrates dedicated long-memory and short-memory ESN reservoirs with a ridge-regression readout. We introduce two variants: Fractional ESN (fESN), which incorporates fractional-differencing dynamics into the reservoir to encode long-range dependence directly, and Wavelet ESN (wESN), which extracts stable low-frequency components through wavelet smoothing before modeling them with a memory-aware reservoir. We establish theoretical guarantees for closed-loop reservoir dynamics, showing that standard ESNs induce short-memory processes under mild conditions, whereas the proposed long-memory reservoirs generate polynomially decaying dependence consistent with statistical long memory. Across multiple dengue datasets and forecasting horizons, fESN and wESN outperform statistical and deep learning baselines. Combining conformal prediction with fESN and wESN provides distribution-free calibrated uncertainty intervals.

Decision support systems (DSS) increasingly run retention what-if analysis on synthetic customer populations, because privacy constraints preclude unrestricted use of real data. Such a system is trustworthy only if the synthetic data lead managers to the same decisions as the real data would; yet prevailing criteria certify distributional similarity, not decision alignment, so a synthetic population can match every marginal distribution while still steering a marketing team toward the wrong campaigns. We close this decision-alignment gap with three contributions: strategy simulation fidelity (SSF), a criterion measuring how often the synthetic population yields the same go/no-go campaign decision as the real population; PolicySynth, a DSS framework whose generator is conditioned on the production churn scorer to align decision-relevant structure; and a three-axis reporting standard of decision alignment, membership-inference resistance, and novel-record rate as the minimum deployment quality gate. On a telecommunications churn corpus and a banking acquisition corpus, PolicySynth attains a mean SSF of 0.923 and 0.960, with seed-to-seed variance roughly ten times tighter than CTGAN on telecommunications and 2.5 times on banking. This stability is the deployable property: go/no-go recommendations shift by at most 1.2 percentage points between monthly retraining cycles, against 11.5 for CTGAN, a reversed recommendation on one campaign in nine. A bootstrap baseline matches PolicySynth on SSF yet copies real records verbatim and fails membership inference, evidence that no single axis suffices. PolicySynth reliably supports directional go/no-go screening; its ROI estimates diverge from real outcomes by 70 to 78% and require the volume correction we document.

Two competing perspectives on fluid intelligence (gf) measures propose that performance is primarily constrained either by working memory capacity or by the ability to induce novel relations. The first perspective is currently dominant in measurement, as evident from the use of a limited set of recurring rules, whereas the second perspective is reflected in many definitions but rarely present in measurement. The ARC-AGI benchmark predominantly requires rule induction and was proposed as a measure of gf for both humans and artificial systems. However, its psychometric properties have not yet been examined in human samples. We therefore investigated the psychometric characteristics and nomological network of ARC-AGI in a first study with 100 participants. A compilation of ARC-AGI items showed good psychometric properties and correlated substantially with figural fluid intelligence as measured by a figural reasoning test ($\rho$ = .63). Associations with figural originality were weak. These findings provide initial support for the validity of ARC-AGI as a measure of human fluid intelligence. Future research should include more rule induction tasks as well as additional multivariate covariates. This study is unusual by studying a task in humans that was initially designed for machines. We suggest systematically embedding AI benchmarks into the nomological network of human cognitive abilities to enable more systematic evaluation and interdisciplinary cooperation.

Pathology Foundation Models (PFMs) offer powerful Whole Slide Image (WSI) representations but suffer from massive computational costs. While Knowledge Distillation (KD) can create efficient student models, existing multi-teacher methods often use suboptimal uniform weighting that ignores tissue heterogeneity. We propose LaGuadia (Language-Guided Adaptive DistillAtion), a framework that develops a compact pathology image encoder by dynamically integrating expertise from multiple PFMs under clinical linguistic guidance. Our approach utilizes a multi-stage pipeline: first, extracting visually observable clinical keywords from pathology reports; second, aligning visual features with these keywords via a Vision-Language meta-teacher (MedSigLIP) to provide dense semantic guidance; and finally, performing adaptive KD where teacher contributions are weighted based on their semantic alignment with the clinical narrative. Experiments on WSI captioning, visual question answering, and slide-level classification tasks demonstrate that an 87M parameter LaGuadia student model matches or exceeds foundation-scale models such as GigaPath and UNI, achieving strong factual consistency and robust generalization. These results highlight clinical language as an effective semantic anchor for building efficient and reliable digital pathology systems. Code is available at https://github.com/hvcl/LaGuadia.

Relational fraud detection can exploit both label-free graph context and label-derived neighborhood evidence, but these two information sources obey different validity conditions. In particular, neighborhood risk becomes invalid when a queried node's own label, or any validation or test label, enters its construction. We formulate this issue as provenance-constrained relational evidence use and present PREF-Gate, an auditable decision framework with two fixed experts and a finite validation gate. The context expert uses attributes, one-hop means, feature residuals, and degree descriptors without labels. The evidence expert adds self-excluded, training-label-only neighborhood risk and empirical-Bayes summaries that expose support, uncertainty, availability, and shrinkage. Before test inference, the gate selects either expert or one of three pre-specified probability mixtures and fixes the decision threshold. On Amazon, YelpChi, and TFinance, using five identical stratified splits and 14 same-protocol methods, PREF-Gate obtains mean AUPRC values of 0.9085, 0.8104, and 0.8913. It selects the label-free expert on all Amazon and YelpChi splits and an evidence mixture on all TFinance splits. Thus, the main result is conditional rather than universal: label-derived relational evidence is useful only where held-out validation supports it. The framework couples competitive ranking performance with an explicit label-provenance contract, finite selection policy, failure accounting, and review-budget evaluation, providing an auditable knowledge-based decision pipeline for graph fraud detection.

The popularity of large language models (LLMs) escalates an ongoing demand for effective inference. However, due to the sequential processing of tokens during the token phase in decoder-only LLMs inference, the inherent low parallelism leads to reduced throughput and suboptimal utilization of the computing units on artificial intelligence (AI) accelerators, particularly when handling long-sequence inputs that impose significant memory overhead. Recently, many reported methods have been developed as potential solutions, since they emerge with numeric deviation. This paper presents FastTPS, a high performance and low-precision loss method for accelerating the token-phase in LLM inference on general AI accelerators which includes three key components: (1) AI accelerator-enabled reloading-free KV Cache concatenation which decreases memory access overhead as well as enables full fusion of Attention, (2) high-efficiency and high-accuracy 'RoPE' attention based on the tiling optimized FLAT, and (3) highly-fused MLP with fine-grain pipeline scheduling. Our results confirm that FastTPS significantly alleviates memory bottlenecks in the token phase, delivering a 6x speed improvement (compared to none-fusion) on an AMD Ryzen AI 300 series NPU with BF16 precision while sustaining 93% peak memory bandwidth utilization during Phi3-mini-4k-instruct inference.

We study amplitude-only rescaling of feed-forward network (FFN) activations to repair tool calls and other structured outputs, using multiplicative coordinate masks rather than additive steering vectors. Amplitude Gating (AG) keeps pretrained weights fixed and applies magnitude/entropy-based masks at six SwiGLU sites, with a Newton-Schulz windowed ranking variant. Across three Qwen checkpoints and six text/tool endpoints, effects are task dependent. Under frozen local scorers, Qwen3.5-9B non-NS configurations improve two function-call endpoints by +2.61/+2.67 percentage points (pp) and static ToolBench in/out-domain by +1.64/+2.82 pp; JSON gains are small. These gains survive comparing the weaker of two observed AG runs with the stronger baseline, supporting observed-run robustness rather than population significance. Scores measure lexical or answer/action-name agreement, not executed-tool success. Under the current experimental conditions, the six-task random-forest refit improves native score by +0.46 pp with a positive conditional paired interval; transfer to other settings requires further evaluation. The results support task-specific interventions; causal mechanisms, equal-budget advantages, repeated-run uncertainty, and serving cost require further evaluation. Code and experimental data: https://doi.org/10.5281/zenodo.23654706.

In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range dependence through a fractional Mittag-Leffler excitation kernel. Two neural architectures, namely a Long Short-Term Memory (LSTM) network and a Transformer, are developed to estimate the model parameters $(\mu,\gamma,\alpha,\beta)$ directly from sequences of inter-arrival times without requiring computationally intensive likelihood optimization. Experiments on synthetic data that both neural models significantly outperform the classical Maximum Likelihood Estimation (MLE) method, with the Transformer achieving the highest estimation accuracy (MSE = $0.1634$), followed by the LSTM (MSE = $0.1752$), compared to MLE (MSE = $2.8032$). An ablation study further examines the effects of key hyperparameters on model performance. The proposed framework is also on two real-world high-frequency datasets, namely AAPL NBBO transaction data and Montgomery County 911 emergency call records. Using a predictive validation approach, event sequences simulated from the estimated parameters closely reproduce the empirical distribution, tail behavior, and temporal dependence structure of the observed data. These results demonstrate that Transformer-based parameter estimation provides an accurate and efficient alternative to conventional estimation techniques for FHP and offers a promising framework for modeling event-driven systems with long-memory dynamics.

Reinforcement learning for deep-search agents has largely focused on trajectory-level scoring – outcome correctness, citation-aware rewards, and evidence coverage. Yet the actions that expose supporting documents receive no targeted credit, a gap we call the reward-credit mismatch. We propose STAMP, in which a reference-based verifier judges whether each cited document supports an entity or relation in a training-time evidence graph, and first-exposure attribution traces each supported citation back to the action that first surfaced it. This step credit is injected through sign-preserving advantage modulation, which redistributes advantage across steps without changing the trajectory-level reward or the relative ranking of trajectories within each group. On BrowseComp, BrowseComp-ZH, and xbench-DS, STAMP improves the GRPO baseline by +2.0/+5.5/+3.0 points under matched SFT initialization, training data, and search tools, and composes with both outcome-only and citation-rubric base rewards. Component ablations confirm that the provenance-based credit signal and the sign-preserving advantage modulation each contribute to the gains.

Representing manipulation actions as 2D trajectories in the camera plane provides a compact and interpretable basis for learning complex 3D manipulation policies. However, it also creates challenges from out-of-frame trajectories and limited precision. We propose Pix2Act, an imitation learning method that addresses these challenges by generating continuous image-space keypoint trajectories in each camera plane and losslessly recovering end-effector poses via triangulation. This reformulates high-dimensional 3D control as a simpler, more learnable 2D prediction problem. Crucially, it aligns observations and actions in the same coordinate space, enabling equivariant transformations to jointly rotate individual camera images together with their image-space actions. We analyze the symmetry properties of this augmentation and design a network architecture that can fuse multiple camera views while respecting their per-view rotations. As a result, Pix2Act implicitly enlarges the support of the data distribution and learns invariant action structures across transformations, yielding improved generalization and overall performance. Across diverse simulated and real-world manipulation tasks, Pix2Act outperforms state-of-the-art baselines and remains robust under camera perturbations.

We study the coupled objective J_K^WOR = E_{S ~ PL-WOR_K}[max_{i in S} R_i]: the expected maximum reward of a size-K Plackett-Luce draw without replacement, the law of Gumbel-Top-K / Stochastic Beam Search decoding. This estimand differs from the conventional i.i.d. objective J_K^iid = E[max_{i<=K} R_i] targeted by existing sample-reuse Max@K estimators, and reusing their i.i.d. weights under the coupled sampler is provably biased (a closed-form three-item instance gives E[g_iid] = (4/5) grad J_K^WOR exactly; pass@K under the coupled sampler is the binary-reward special case). Generic joint-score REINFORCE is already unbiased for J_K^WOR; what it lacks is sample reuse. Our contribution is to instantiate standard rank-conditioned Horvitz-Thompson estimation for the J_K^WOR subset total: from one Gumbel-Top-n pool (n>K) and its observed priority threshold we build an estimator that reuses all C(n,K) embedded K-subsets, unbiased with an unbiased exact score-function surrogate gradient, plus a reward-sorted Max-specific dynamic program that collapses the C(n,K)-term subset sum (with K!-cost set probabilities) exactly to a one-dimensional integral. A fixed-Q quadrature evaluation costs O(n log n + nKQ) arithmetic and is numerically, not algebraically, exact; no epsilon-approximation rate is certified. Each nonzero degree-K Horvitz-Thompson term has finite second moment exactly when n >= 2K; under the same assumptions the full surrogate gradient has finite second moment whenever n >= 2K (sharpness there is open). At K=1 the construction recovers classical priority sampling. All quantities require only the values and differentiable computation graphs of the n+1 drawn items' probabilities, so finite structured sequence policies sampled by exact SBS are covered. A certified finite-Q quadrature bound and countably infinite support remain open. Validation code is included as ancillary files.

Determining whether one finite group is isomorphic to a subgroup of another is a fundamental problem in computational group theory. In this work, we propose a Siamese Graph Neural Network (Siamese GNN) for subgroup prediction using Cayley graph representations of finite groups. Each input group is represented by its undirected Cayley graph and encoded by one branch of a Siamese GNN to produce a graph embedding. The resulting graph embeddings are combined with algebraic features derived directly from the input groups to construct a joint feature vector, which is processed by a fully connected classifier to predict subgroup relations between finite groups. By integrating graph-based structural representations with algebraic features, the proposed framework provides a unified approach for learning subgroup relations from finite groups. Experimental results on an expanded and more diverse dataset of 308 finite-group pairs drawn from 11 group families demonstrate the effectiveness of the proposed architecture, achieving a test BA of 91.67% on an independent test set. Additional experiments evaluate generalization to unseen groups, robustness to different Cayley graph generating sets, the contribution of GNN message passing, performance relative to non-neural baselines, and comparison with exact computational methods. These results illustrate the potential of geometric deep learning for subgroup prediction.

The rapid expansion of capabilities in Large Language Model (LLM) agents has exposed a critical architectural bottleneck: when agents are given access to a flat, monolithic registry of tools, the model must evaluate hundreds or thousands of options simultaneously. This leads to decision-space explosion, context window saturation, and degraded routing accuracy. To address these limitations, this paper presents a hierarchical, skill-based architecture for agentic orchestration. Capabilities are organized as a rooted tree where internal nodes make routing decisions and leaf nodes execute deterministic tasks. The runtime enforces a single-step execution loop governed by a Last-In-First-Out (LIFO) stack, giving the agent a form of memory akin to a Pushdown Automaton, therefore enabling it to track nested execution contexts and resume deterministically from any depth. Capability discovery follows a manifest-driven, lazy-loading protocol: only the immediate children of the active node are loaded, so memory and prompt costs scale with the explored path rather than the global registry. By replacing global memory with localized stack frames, the architecture prevents outputs from one execution branch from leaking into another, establishing the isolation guarantees required for deployment in regulated enterprise environments. We also discuss UPI Help, an AI-powered digital payments support product, as a motivating production deployment context. We provide a mathematical formalization of the orchestration state, detailed algorithmic analysis of the execution loop, and controlled benchmarks comparing flat and hierarchical routing under increasing tool catalogs, multi-step workflow pressure, and visible schema-token exposure per LLM call.

Real-time driving risk assessment provides an essential basis for proactive safety by identifying and quantifying the danger of ongoing road interactions before adverse outcomes occur. However, due to the scarcity of collision data and frame-level risk labels, existing driving risk assessment methods often rely on surrogate objectives, which may imperfectly align with true collision risk and not faithfully reflect the relative danger of driving interaction. This paper proposes a comparison-based ordinal risk learning framework that learns collision-relevant risk scores from pairwise supervision in driving data, directly modeling relative risk ordering without requiring numerical frame-level risk labels. We derive pairwise comparisons from three sources of event-structured driving data for such ordinal risk learning: temporal progression within safety-critical sequences, event-level contrast between dangerous and normal interactions, and physics-based counterfactual perturbations. On this basis, instantiations with three risk-scoring function parameterizations are implemented, including directly learning risk scores from comparison data, and aligning existing single or multiple surrogate-based risk models. The proposed framework is evaluated on the 100-Car and SHRP2 naturalistic driving datasets using a proactive collision warning task. Results show that the proposed framework improves high-recall risk discrimination, warning precision, and warning lead time over representative surrogate-based baselines across both in-distribution and out-of-distribution evaluations. These results suggest that the proposed framework can contribute to proactive safety research by providing more reliable risk assessment for automated driving systems and safety-critical driving interactions.

Large language model (LLM) agents increasingly rely on external tools served by shared providers and accessed by heterogeneous downstream agents. Existing approaches improve tool use on the agent side through parameter updates, prompt refinement, or agent-side memory, making tool knowledge difficult to share and limited to behaviors observed in past tasks. We argue that reusable tool knowledge should instead be maintained by the tool provider. We introduce ToolAtlas, a graph-based framework that builds a persistent provider-side tool memory of tool capabilities, failure boundaries, and cross-tool compositions through execution-verified probing. At inference time, agents query the tool memory via adaptive graph traversal. Across two MCP-based benchmarks spanning eight services, ToolAtlas outperforms existing tool-side optimization and agent-side memory baselines by up to 21.61% in pass@1 and 18.61% in pass@4. The same tool memory also transfers across environment instances and agent frameworks without retraining or task-time exploration, yielding up to 24.16%/16.22% and 17.49%/14.27% relative gains in pass@1/pass@4, respectively. Ablation studies show that these gains arise from combining tool-centered memory organization with capability-guided execution probing. These results establish provider-side tool memory as an effective and reusable paradigm for tool servers. Our code is in: https://github.com/PuppyKnightUniversity/ToolAtlas.

Implicit neural controllers (INCs) are static feedback laws that are evaluated through an algebraic fixed point {equation}; they include as special cases neural network controllers. We propose a so-called implicit representation of neural networks as a key enabling device that exposes the controller as a trainable linear interconnection closed through a known static activation map, thereby making well-posedness and Lyapunov/IQC analysis mathematically easy to handle. For finite-dimensional LTI plants, we first develop a rigorous analysis theory for a given INC, including Perron–Frobenius and norm conditions for well posedness, LMI/IQC certificates for exponential stability, and LMIs for discounted infinite-horizon quadratic performance. We then formulate synthesis as a certification-compatible heuristic search: training is carried out under explicit well-posedness constraints, implicit-differentiation formulas provide gradients, and the resulting controller is accepted only after independent post-training LMIs or regional admissibility checks are feasible. Finally, we establish constrained-control separation results: for a specific scalar unstable plant with hard actuator bounds, an INC achieves a strictly smaller discounted infinite-horizon cost than any admissible finite-order dynamic linear controller. Additional results cover quadratic state-input costs, comparison with linear static output feedback, and computable upper/lower-bound certificates. Numerical examples illustrate the mechanism and the resulting certified performance.

Deep equilibrium models promise input-adaptive implicit computation: harder problems should demand more solver iterations, and the solved equilibrium should encode the result of genuine iterative inference. We report a cautionary study of a port-Hamiltonian DEQ with a learned initialization on two reasoning tasks – ProofWriter entailment over frozen DeBERTa embeddings and a BFS-verified graph-reachability benchmark – in which the implicit computation is a silent no-op. Across tasks, seeds, and controlled ablation arms, the solved equilibrium equals the solver's start point to numerical precision, and bypassing the solver entirely changes test accuracy by +0.00 percentage points in 18 of 19 training runs. Controlled interventions falsify the tempting explanation: removing the anchoring term reproduces every result, and retraining with noise-decoupled starts yields a solver that converges to the noisy start while the decoder learns to ignore it. The single escaping run diverges instead ($\|h^{*}-z_0\|=171$), producing a co-adapted noise channel whose removal improves accuracy. Iteration counts are uncorrelated with ground-truth difficulty ($r=0.009$), and the full apparatus never outperforms a two-layer MLP on either task. We trace the mechanism to gradient starvation along two distinct routes, show that the standard zeroing ablation is confounded and gives wildly seed-dependent answers where the correct substitution test gives a stable zero, and distill a four-test diagnostic protocol for auditing claimed implicit computation. All experiments run on a single free Colab GPU; code, raw logs, and analysis scripts are released.

Dynamic graph continual learning (DGCL) is an effective manner for handling catastrophic forgetting in dynamic graphs. However, existing DGCL methods underutilize temporal information across graph snapshots. To address this critical issue, we propose a novel framework for Dynamic Graph Continual Learning via Condensation and Attachment (CA-DGCL). Specifically, CA-DGCL first condenses historical graph snapshots into compact semantic representations efficiently. Further, a cross-timestamp node chains is built to construct a third-order tensor and Tucker decomposition is applied to this tensor for obtaining stable node features, which encapsulate historical knowledge. Finally, these node features are used to generate new nodes and attached to the current graph for replaying of past information without compromising the new patterns. In addtion, a refined forgetting measure is introduced to make it more suitable for dynamic graph settings. Extensive experiments demonstrate that CA-DGCL outperforms baselines in forgetting suppression as well as maintain competitive accuracy, proving its efficacy for dynamic graph continual learning.

Discovering the memory or nonlocal kernel governing an integro-differential equation (IDE) from sparse and noisy observations is an ill-posed inverse problem. Existing identification methods often rely on problem-specific analytical derivations, specialized observation requirements, or restrictive assumptions about the kernel, limiting their applicability across different classes of IDEs. In this work, we propose a differentiable-solver-based framework for discovering memory and nonlocal kernels directly from spatiotemporal observations. Within the solver, the unknown kernel is represented using a constrained Kolmogorov–Arnold Network (KAN) parameterization, with the physical constraints imposed through two different approaches: a Bernstein-polynomial-based Monotone–Convex KAN (MC-KAN), whose coefficient constraints enforce positivity, monotonic decrease, and convexity by construction, and a Chebyshev-based KAN (Cheb-KAN), in which the same properties are encouraged through soft penalty terms. After training, symbolic regression is applied to the learned kernels to obtain interpretable closed-form representations. We evaluate both methods on benchmarks spanning a one-dimensional Volterra equation, a one-dimensional viscoelastic wave partial integro-differential equation, and a two-dimensional nonlocal reaction-diffusion equation with an anisotropic coupled kernel. For the 1D problems, both methods recover the correct kernel functional form and achieve comparable solution-reconstruction accuracy. In contrast, for the sparse and noisy 2D nonlocal problem, the hard-constrained MC-KAN consistently achieves lower kernel reconstruction errors than the soft-constrained Cheb-KAN. Our results demonstrate that enforcing physically motivated shape constraints by construction provides greater robustness than soft penalties for multidimensional kernel discovery from sparse and noisy observations.

Graph fraud detection plays a pivotal role in safeguarding the security and integrity of modern digital ecosystems. Graph Neural Networks (GNNs) are commonly adopted for graph fraud detection. However, the practical performance of existing GNN-based detectors is severely hindered by incomplete node attributes and extreme class imbalance within graphs. To mitigate these limitations, this paper proposes a novel framework for Graph Fraud Detection with Grouped attribute completion and Confidence-aware Contrastive learning, named GFD-GC. Specifically, it first imitates heterogeneous neighborhood structures to implement group-wise aggregation, which obtains informative complete node features by capturing fine-grained graph contextual patterns. Further, it introduces a confidence-aware supervised contrastive learning strategy to augment scarce labeled fraud nodes with high confidence pseudo-fraud nodes, which enhances the compactness of fraud representations and their separability from non-fraud nodes. Extensive experiments demonstrate the superiority of the proposed GFD-GC over state-of-the-art baselines on the graph fraud detection task, thereby providing an effective solution for real-world fraud scenarios.

Adversarial perturbations threaten machine learning classifiers, including variational quantum classifiers. We show that finite quantum measurement statistics (shot noise) act as a built-in defense against gradient-based test-time attacks whose cost scales unfavorably for the attacker. Because every gradient component must be inferred from repeated circuit executions under any unbiased gradient-estimation rule, white-box extraction consumes a dimension-dependent measurement budget that measurement grouping cannot remove in expressive circuits. Under stated assumptions, single-step attacks need at least quadratically many shots in the input dimension $d$, growing as $d^{5/2}$ under norm-concentration scaling, with a sufficient-budget analysis for iterative attacks via stochastic gradient Langevin dynamics. Simulations up to 784 input dimensions validate the law: the realized total budget is the $d^{5/2}$ geometric floor for plateau-mitigated models and grows as $d^{3.00}$ for the tested deep circuits, whose gradient norms decay with dimension absent barren-plateau mitigation; folding the measured gradient norm back in recovers the parameter-free $d^{3/2}$ shot-noise geometry. Against a matched classical baseline whose attack overhead is dimension-independent (the cheap-gradient principle of automatic differentiation), the quantum gradient cost ratio grows empirically as $d^{3.00}$, so the attacker's relative cost diverges as the model scales. Experiments on a 156-qubit IBM processor (ibm_boston, 4-qubit circuits, $d=12$) reproduce the effect: at matched budgets the device attack tracks the ideal within a few percent, with the high-shot gradient faithful to the exact one. The defense operates precisely when the forward map is classically hard to simulate: only then is a white-box attacker denied the simulate-and-backpropagate shortcut and must pay the measurement cost we quantify.

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs); however, their synchronous optimization treats residuals of different regions and constraints equally, which is inconsistent with the progressive "from source to response" physical information propagation path, degrading training stability and accuracy. Existing causal training methods focus mainly on the temporal dimension, lacking a unified characterization of spatial and boundary dimensions. To address this, we define a unified class of training priorities according to the physical information propagation path: premise regions should be learned before dependent regions; temporal, spatial, and boundary priorities are instances of this principle. Using neural tangent kernel (NTK) dynamics, we theoretically analyze why standard PINNs do not obey this priority: their residual convergence order is governed by the NTK spectrum and is independent of the propagation path. Accordingly, we propose a unified multi-dimensional priority-constraint framework that partitions the domain along the propagation path and constructs negative-exponential residual weights, converting the physical propagation order into a training priority. For cases with coexisting priorities, we introduce a directional compatibility coefficient to clarify that "orthogonal directions can be coupled multiplicatively in synergy, whereas coaxial opposite directions cannot." Benchmark cases show that this method consistently improves the convergence behavior and prediction accuracy of PINNs on problems with clear propagation paths or constraint-dominated structures, without modifying the network architecture and with controllable additional computational cost.

A trained molecular property model can be refined at test time by correcting each prediction with the measured labels of the most similar training molecules, a retraining-free procedure we call neighbor fusion; evidential neural networks make it principled by using their aleatoric and epistemic uncertainty to parameterize a Bayesian update. Our main contribution, PG-EVIKAL, learns a property-distance metric to re-rank structurally similar neighbors by their property relevance before fusion, building on EVIKAL (scalar Kalman filter) and GP-EVIKAL (Gaussian process variant handling correlated neighbors). Evaluated on 16 molecular datasets, PG-EVIKAL reduces RMSE relative to the evidential model baseline on 14 of them, with a median reduction of 19.4%, and improves calibration; in sequential-assay scenarios it further incorporates newly measured molecules, refining predictions as they arrive without retraining. This work demonstrates that evidential uncertainty decomposition is not merely a calibration objective but an actionable inference resource that enables test-time refinement of molecular property predictions.

The choice of Modulation and Coding (MCS) type for a particular channel condition is made through link adaptation (LA) algorithms that operate at the MAC layer. These algorithms rely on the ACK/NACK statistics and the channel quality index (CQI) feedback. Several existing works model LA as a multi-armed bandit (MAB) problem across cellular and Wi-Fi links. In the MAB formulation, each available MCS is a Bernoulli arm parameterized by its transmission success probability, and the goal is to design a selection strategy that accrues maximum reward. Several popular MAB algorithms, such as upper confidence bound (UCB) and Thompson Sampling (TS), have been proposed in the literature. Using the fact that MCS success probabilities are ordered, we propose the Joint-Thompson Sampling (Joint-TS) algorithm. Unlike classical TS, which assumes independent Beta distributions for each arm, Joint-TS utilizes a multivariate ordered Beta distribution as the prior to preserve the inherent monotonicity of success probabilities. Our simulation results show that while existing MAB algorithms fail in specific scenarios, Joint-TS delivers competitive throughput with robust, consistent performance in all scenarios.

Accurately representing atmospheric aerosol populations is essential for simulating aerosol-cloud interactions, radiative forcing, and ice nucleation, yet existing reduced schemes impose structural assumptions that limit their ability to capture composition diversity and mixing state. Machine-learning approaches offer more flexible representations, but standard autoencoders do not preserve the mathematical structure of aerosol populations and therefore cannot support physically meaningful process operators. We introduce AeroMELD (Aerosol Measure Embedding for Latent Dynamics), a mathematically grounded framework for constructing low-dimensional latent variables that retain this structure. We show that any permutation-invariant linear encoder must take a scale-shape decomposition, with total number concentration represented explicitly and latent shape given by a barycentric combination of per-particle embeddings. This aggregated latent state retains the diagnostic expressiveness of a Deep Sets model by moving the nonlinear post-aggregation stage into the learned diagnostic map while preserving latent linearity. Using particle-resolved data as ground truth, we encode weighted particle populations directly rather than binned aerosol states; size-resolved mass and number distributions serve only as diagnostic targets and visual summaries. The latent space accurately reconstructs these distributions, CCN spectra, optical coefficients, and immersion-freezing behavior while preserving the linear population structure needed for hybrid ML-physics models. Although the experiments focus on diagnostic reconstruction, the embedding is designed so that emissions and mixing can be represented exactly and nonlinear microphysical processes learned in a controlled latent space. This work establishes a foundation for learning aerosol-process evolution directly in latent space.

Machine learning progress is often attributed to scaling model size and dataset volume, yet the composition of data can be just as consequential. Empirical findings repeatedly show that combining datasets from different domains yields nontrivial interactions. For instance, adding code improves mathematical reasoning, while certain mixtures introduce interference that reduces model performance. We refer to these effects collectively as data synergy, where the contribution of multiple domains exceeds or falls short of the sum of their isolated contributions. In this work, we formalize and quantify data synergy in language model pretraining. Leveraging observational variation across open-weight LLMs with diverse pretraining mixtures, we estimate both direct domain-to-benchmark synergy (how one domain contributes to performance on another) and a second-order domain-domain synergy (capabilities that require co-occurrence of multiple domains). Our framework improves predictive accuracy over domain-agnostic scaling laws and recovers stable synergy estimates. We validate these estimates by training models on predicted optimal and predicted anti-optimal mixtures and confirm that our synergy estimates correctly predict performance rankings.

Multimodal information is pivotal for e-commerce search ranking. Existing works leverage multimodal data typically by fine-tuning general Multimodal Large Language Models (MLLMs) via collaborative signals, subsequently integrating the derived representations into ranking models as item features. Despite their efficacy, these methods face two primary limitations: (1) they rely on a single collaborative signal for MLLM fine-tuning, failing to exploit the heterogeneous signals essential for multitask ranking; and (2) they treat multimodal representations as regular item features in ranking models, underutilizing their latent potential for user behavior modeling. To address these challenges, we propose the Multiplex Multimodal Representation Model (MMRM), a unified framework that aligns MLLMs with diverse collaborative signals. By employing a shared backbone with task-specific tokens and projection layers, MMRM simultaneously learns from multiple signals and generates comprehensive multiplex item representations in a single inference pass. Furthermore, we introduce a multiplex user representation strategy in ranking models, which derives task-specific user representations via search-based behavior sequence modeling leveraging multiplex item representations. Extensive experiments demonstrate MMRM's superior efficiency and effectiveness. Notably, MMRM has been successfully deployed in the JD e-commerce search engine, yielding significant performance gains for millions of daily users.

Face super-resolution is the task of increasing the resolution of an image containing a face thereby adding finer detail. It is a ubiquitous task in many computer vision applications and quite often the user isn't even aware that it is being performed. However, doing it with high fidelity is challenging as it is an ill-posed problem. In this paper we present a reference-based solution for face super-resolution that uses higher resolution reference images to aid in the task. We show an alignment module based on the spatial transformer that is considerably more stable than the popular deformable convolutions. We also show an aggregation function that can take good quality information from the reference images when available or suppress the function when such information is unavailable. Finally, we show that our relatively smaller model can achieve state of the art results on multiple datasets. The source code is available at https://github.com/varun-jois/FSRST.