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arXiv

Hybrid Mamba-Attention Neural Architecture for Channel Estimation

Dianxin Luan, Chengsi Liang, Jie Huang, Zheng Lin, Kaitao Meng, John Thompson, Cheng-Xiang Wang, Ozgur Akan

This paper proposes a hybrid Mamba-attention neural architecture to achieve improved channel estimation for orthogonal frequency-division multiplexing (OFDM) waveforms, particularly for configurations with a large number of subcarriers. By integrating a customized Mamba module, the proposed framework handles large-scale subcarrier channel estimation efficiently while capturing long-distance dependencies among these subcarriers effectively. Unlike the conventional Mamba structure, this paper implements a bidirectional selective scan to enable information propagation from both directions, because channel gains at different subcarriers are inherently non-causal. In addition, by integrating Mamba to reduce the reliance on quadratic-complexity self-attention, the proposed solution achieves lower space complexity than fully transformer architectures. Simulation results based on the 3GPP TS 36.101 channel demonstrate that compared to other baseline neural networks, the proposed method achieves superior channel estimation performance with fewer tunable parameters and exhibits good generalization across previously unseen channels.

arXiv

Fundamental Limitations of Favorable Privacy-Utility Guarantees for DP-SGD

Murat Bilgehan Ertan, Marten van Dijk

Differentially Private Stochastic Gradient Descent (DP-SGD) is the dominant paradigm for private training, but its fundamental limitations under worst-case adversarial privacy definitions remain poorly understood. We analyze DP-SGD in the $f$-differential privacy framework, which characterizes privacy via hypothesis-testing trade-off curves, and study shuffled sampling over a single epoch with $M$ gradient updates. We derive an explicit suboptimal upper bound on the achievable trade-off curve. This result induces a geometric lower bound on the separation $κ$, which is the maximum distance between the mechanism's trade-off curve and the ideal random-guessing line. Because a large separation implies significant adversarial advantage, meaningful privacy requires small $κ$. However, we prove that enforcing a small separation imposes a strict lower bound on the Gaussian noise multiplier $σ$, which directly limits the achievable utility. In particular, under the standard worst-case adversarial model, shuffled DP-SGD must satisfy $$σ\ge \frac{1}{\sqrt{2\ln M}} \quad\text{or}\quad κ\ge\ \frac{1}{\sqrt{8}}\!\left(1-\frac{1}{\sqrt{4π\ln M}}\right),$$ thus cannot simultaneously achieve strong privacy and high utility. Although the noise threshold vanishes asymptotically as $M \to \infty$, the convergence is extremely slow. Even for practically relevant numbers of updates the required noise magnitude remains substantial. We further show that the same limitation extends to Poisson subsampling up to constant factors. Our experiments confirm that the noise levels implied by this bound lead to significant accuracy degradation at realistic training settings, thus showing a bottleneck in DP-SGD under standard worst-case adversarial assumptions.

arXiv

Neuronal Attention Circuit (NAC) for Representation Learning

Waleed Razzaq, Yun-Bo Zhao

Attention improves representation learning over RNNs, but its discrete nature limits continuous-time (CT) modeling. We introduce Neuronal Attention Circuit (NAC), a novel, biologically inspired CT-attention mechanism that reformulates attention logit computation as the solution to a linear first-order ODE with nonlinear interlinked gates derived from repurposing the wiring of C. elegans Neuronal Circuit Policies (NCPs). NAC replaces dense projections with sparse sensory gates for query-key projections and introduces a sparse backbone network with two heads for computing content-target and learnable time-constant gates, enabling efficient adaptive dynamics. To improve efficiency and memory consumption, we implement an adaptable, sparse, subquadratic Top-K pairwise concatenation mechanism that selectively curates query-key interactions. We provide rigorous theoretical guarantees, including state stability and bounded approximation errors. Empirically, we implement NAC in diverse domains, including irregular time-series, long-range forecasting, lane-keeping for autonomous vehicles, and industrial prognostics. We observe that NAC matches or outperforms in accuracy against several CT state-of-the-art baselines, while being interpretable at the neuron cell level.

arXiv

Transformers for Multimodal Brain State Decoding: Integrating Functional Magnetic Resonance Imaging Data and Medical Metadata

Danial Jafarzadeh Jazi, Maryam Hajiesmaeili

Decoding brain states from functional magnetic resonance imaging (fMRI) data is vital for advancing neuroscience and clinical applications. While traditional machine learning and deep learning approaches have made strides in leveraging the high-dimensional and complex nature of fMRI data, they often fail to utilize the contextual richness provided by Digital Imaging and Communications in Medicine (DICOM) metadata. This paper presents a novel framework integrating transformer-based architectures with multimodal inputs, including fMRI data and DICOM metadata. By employing attention mechanisms, the proposed method captures intricate spatial-temporal patterns and contextual relationships, enhancing model accuracy, interpretability, and robustness. The potential of this framework spans applications in clinical diagnostics, cognitive neuroscience, and personalized medicine. Limitations, such as metadata variability and computational demands, are addressed, and future directions for optimizing scalability and generalizability are discussed.

arXiv

iLTM: Integrated Large Tabular Model

David Bonet, Marçal Comajoan Cara, Alvaro Calafell, Daniel Mas Montserrat, Alexander G Ioannidis

Tabular data underpins decisions across science, industry, and public services. Despite rapid progress, advances in deep learning have not fully carried over to the tabular domain, where gradient-boosted decision trees (GBDTs) remain a default choice in practice. We present iLTM, an integrated Large Tabular Model that unifies tree-derived embeddings, dimensionality-agnostic representations, a meta-trained hypernetwork, multilayer perceptrons (MLPs), and retrieval within a single architecture. Pre-trained on more than 1,800 heterogeneous classification datasets, iLTM achieves consistently superior performance across tabular classification and regression tasks, from small datasets to large and high-dimensional tasks. After light fine-tuning, the meta-trained hypernetwork transfers to regression targets, matching or surpassing strong baselines. Extensive experiments show that iLTM outperforms well-tuned GBDTs and leading deep tabular models while requiring less task-specific tuning. By bridging the gap between tree-based and neural methods, iLTM offers a new framework for tabular foundation models for robust, adaptable, and scalable tabular learning.

arXiv

Directional-Clamp PPO

Gilad Karpel, Ruida Zhou, Shoham Sabach, Mohammad Ghavamzadeh

Proximal Policy Optimization (PPO) is widely regarded as one of the most successful deep reinforcement learning algorithms, known for its robustness and effectiveness across a range of problems. The PPO objective encourages the importance ratio between the current and behavior policies to move to the "right" direction -- starting from importance sampling ratios equal to 1, increasing the ratios for actions with positive advantages and decreasing those with negative advantages. A clipping function is introduced to prevent over-optimization when updating the importance ratio in these "right" direction regions. Many PPO variants have been proposed to extend its success, most of which modify the objective's behavior by altering the clipping in the "right" direction regions. However, due to randomness in the rollouts and stochasticity of the policy optimization, we observe that the ratios frequently move to the "wrong" direction during the PPO optimization. This is a key factor hindering the improvement of PPO, but it has been largely overlooked. To address this, we propose the Directional-Clamp PPO algorithm (DClamp-PPO), which further penalizes the actions going to the strict "wrong" direction regions, where the advantage is positive (negative) and importance ratio falls below (above) $1 - β$ ($1+β$), for a tunable parameter $β\in (0, 1)$. The penalty is by enforcing a steeper loss slope, i.e., a clamp, in those regions. We demonstrate that DClamp-PPO consistently outperforms PPO, as well as its variants, by focusing on modifying the objective's behavior in the "right" direction, across various MuJoCo environments, using different random seeds. The proposed method is shown, both theoretically and empirically, to better avoid "wrong" direction updates while keeping the importance ratio closer to 1.

arXiv

flowengineR: A Modular and Extensible Framework for Fair and Reproducible Workflow Design in R

Maximilian Willer, Peter Ruckdeschel

flowengineR is an R package designed to provide a modular and extensible framework for building reproducible algorithmic workflows for general-purpose machine learning pipelines. It is motivated by the rapidly evolving field of algorithmic fairness, where new metrics, mitigation strategies, and methods continuously emerge. A central challenge in fairness, but also far beyond, is that existing toolkits either focus narrowly on single interventions or treat reproducibility and extensibility as secondary considerations rather than core design principles. flowengineR addresses this by introducing a unified architecture of standardized engines for data splitting, execution, preprocessing, training, inprocessing, postprocessing, evaluation, and reporting. Each engine encapsulates one methodological task yet communicates via a lightweight interface, ensuring workflows remain transparent, auditable, and easily extensible. Although implemented in R, flowengineR builds on ideas from workflow languages (CWL, YAWL), graph-oriented visual programming languages (KNIME), and R frameworks (BatchJobs, batchtools). Its emphasis, however, is less on orchestrating engines for resilient parallel execution than on the straightforward setup and management of distinct engines as data structures. This orthogonalization enables distributed responsibilities, independent development, and streamlined integration. In the context of fairness, by structuring fairness methods as interchangeable engines, flowengineR lets researchers integrate, compare, and evaluate interventions across the modeling pipeline. At the same time, the architecture generalizes to explainability, robustness, and compliance metrics without core modifications. While motivated by fairness, flowengineR ultimately provides a general infrastructure for any workflow context where reproducibility, transparency, and extensibility are essential.

arXiv

Self-Attention to Operator Learning-based 3D-IC Thermal Simulation

Zhen Huang, Hong Wang, Wenkai Yang, Muxi Tang, Depeng Xie, Ting-Jung Lin, Yu Zhang, Wei W. Xing, Lei He

Thermal management in 3D ICs is increasingly challenging due to higher power densities. Traditional PDE-solving-based methods, while accurate, are too slow for iterative design. Machine learning approaches like FNO provide faster alternatives but suffer from high-frequency information loss and high-fidelity data dependency. We introduce Self-Attention U-Net Fourier Neural Operator (SAU-FNO), a novel framework combining self-attention and U-Net with FNO to capture long-range dependencies and model local high-frequency features effectively. Transfer learning is employed to fine-tune low-fidelity data, minimizing the need for extensive high-fidelity datasets and speeding up training. Experiments demonstrate that SAU-FNO achieves state-of-the-art thermal prediction accuracy and provides an 842x speedup over traditional FEM methods, making it an efficient tool for advanced 3D IC thermal simulations.

arXiv

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory

Yixuan Sun, Srinivas Eswar, Yin Lin, William Detmold, Phiala Shanahan, Xiaoye Li, Yang Liu, Prasanna Balaprakash

Linear systems arise in generating samples and in calculating observables in lattice quantum chromodynamics~(QCD). Solving the Hermitian positive definite systems, which are sparse but ill-conditioned, involves using iterative methods, such as Conjugate Gradient (CG), which are time-consuming and computationally expensive. Preconditioners can effectively accelerate this process, with the state-of-the-art being multigrid preconditioners. However, constructing useful preconditioners can be challenging, adding additional computational overhead, especially in large linear systems. We propose a framework, leveraging operator learning techniques, to construct linear maps as effective preconditioners. The method in this work does \emph{not} rely on explicit matrices from either the original linear systems or the produced preconditioners, allowing efficient model training and application in the CG solver. In the context of the Schwinger model U(1) gauge theory in 1+1 spacetime dimensions with two degenerate-mass fermions), this preconditioning scheme effectively decreases the condition number of the linear systems and approximately halves the number of iterations required for convergence in relevant parameter ranges. We further demonstrate the framework learns a general mapping dependent on the lattice structure which leads to zero-shot learning ability for the Dirac operators constructed from gauge field configurations of different sizes.

arXiv

Scalable extensions to given-data Sobol' index estimators

Teresa Portone, Bert Debusschere, Samantha Yang, Emiliano Islas-Quinones, T. Patrick Xiao

Given-data methods for variance-based sensitivity analysis have significantly advanced the feasibility of Sobol' index computation for computationally expensive models and models with many inputs. However, the limitations of existing methods still preclude their application to models with an extremely large number of inputs. In this work, we present practical and theoretical extensions to the existing given-data Sobol' index method, which allow variance-based sensitivity analysis to be efficiently performed on large models such as neural networks, which have $>10^4$ inputs. For models of this size, holding all input-output evaluations simultaneously in memory---as required by existing methods---can quickly become impractical. Our extensions include a general definition of the given-data Sobol' index estimator with arbitrary partition, a streaming algorithm to process input-output samples in batches, and an asymptotic analysis of the new estimator that motivates a practical screening heuristic for small indices. We show that the equiprobable partition employed in existing given-data methods can introduce significant bias into Sobol' index estimates even at large sample sizes and provide numerical analyses that demonstrate why this can occur. We also show that the streaming algorithm can achieve comparable accuracy and runtime while substantially reducing memory requirements, enabling sensitivity analysis of models with much larger input dimension. We demonstrate our novel developments on two application problems in neural network modeling.

arXiv

Enhancing Knowledge Tracing through Leakage-Free and Recency-Aware Embeddings

Yahya Badran, Christine Preisach

Knowledge Tracing (KT) aims to predict a student's future performance based on their sequence of interactions with learning content. Many KT models rely on knowledge concepts (KCs), which represent the skills required for each item. However, some of these models are vulnerable to label leakage, a phenomenon in which the input data inadvertently reveal the correct answer, particularly in datasets with multiple KCs per question. We propose a straightforward yet effective solution to prevent label leakage by masking ground-truth labels during input embedding construction whenever such leakage could occur. To accomplish this, we introduce a dedicated \texttt{MASK} label, inspired by masked language modeling (e.g., BERT), to replace ground-truth labels. In addition, we introduce Recency Encoding, which encodes the step-wise distance between the current item and its most recent previous occurrence. This distance is important for modeling learning dynamics such as forgetting, which is a fundamental aspect of human learning, yet it is often overlooked in existing models. Recency Encoding demonstrates improved performance over traditional positional encodings on multiple KT benchmarks. We show that incorporating our embeddings into KT models such as DKT, DKT+, AKT, and SAKT consistently improves prediction accuracy across multiple benchmarks. The approach is both efficient and widely applicable.

arXiv

ML-PWS: Estimating the Mutual Information Between Experimental Time Series Using Neural Networks

Manuel Reinhardt, Gašper Tkačik, Pieter Rein ten Wolde

The ability to quantify information transmission is crucial for the analysis and design of both natural and engineered systems. For systems driven by time-varying signals, the fundamental measure is the information transmission rate. However, due to the high dimensionality of signal trajectory space, this rate cannot be obtained directly from time-series data without approximations. Path Weight Sampling (PWS) is a computational technique that enables the exact calculation of the information rate for any stochastic model, raising the question of how this rate can be determined from time-series data in the absence of a prior model. Here, we present a method that combines machine learning (ML) with PWS: a generative model is learned from time-series data, to which PWS is applied to yield a rigorous lower bound on the information rate. We demonstrate the accuracy of this technique, called ML-PWS, by comparing its results on synthetic time-series data generated from several non-linear models against ground-truth results obtained by applying PWS directly to the same models. We illustrate the utility of ML-PWS by applying it to neuronal time-series data.

arXiv

Physics-Informed Policy Iteration for High-Dimensional Hamilton--Jacobi--Bellman Equations: Interior Error Bounds without Boundary Data

Yeongjong Kim, Minseok Kim, Yeoneung Kim, Namkyeong Cho

We develop a physics-informed policy-iteration method for stationary second-order Hamilton--Jacobi--Bellman equations arising in continuous-time stochastic control. Each policy-evaluation step is a linear elliptic PDE and is approximated by a mesh-free neural residual solver; policy improvement is then performed pointwise from the surrogate gradient. The analysis addresses bounded-domain training without prescribed boundary data. We prove well-posedness of the PDE-defined evaluation for every Borel Markov policy, establish Lipschitz stability of the greedy map on bounded gradient ranges, and derive an exponential attenuation estimate for unresolved boundary information. These ingredients yield a closed finite-step interior error bound whose floors are determined by a continuous $L^p$ residual, with a finite exponent $p>d$, and an attenuated amplitude term. The experiments measure the quantities in the estimate. On a linear--quadratic testbed with an exact reference, the gradient-error floor scales nearly linearly with a fresh-sample $L^p$ residual estimate, and finite-difference probes identify when a training buffer is beneficial. At matched architecture and budget, linear fixed-policy training becomes markedly more reliable than direct minimization of the nonlinear HJB residual as the tested problems become more difficult. The method also produces effective feedback on an inverted pendulum, a planar quadrotor, and a 100-dimensional posterior-seeking problem. These nonlinear tests expose two limitations not visible from sampled residuals alone: the collocation distribution may miss the region visited by the learned closed loop, and evaluation without boundary data may leave undetermined the gradient component on which the greedy update depends. On-policy collocation, rollout-anchored evaluation, and rollout-based stopping provide effective model-only safeguards.

arXiv

Kolmogorov-Arnold Energy Models: Fast, Interpretable Generative Modeling

Prithvi Raj

Generative models typically rely on either simple latent priors (e.g., Variational Autoencoders, VAEs), which are efficient but limited, or expressive iterative samplers (e.g., Diffusion and Energy-based Models), which are costly and opaque. We introduce a new unsupervised model, the Kolmogorov-Arnold Energy Model (KAEM), to bridge this trade-off and provide new opportunities for interpretability. Based on a novel adaptation of the Kolmogorov-Arnold Representation Theorem, KAEM imposes a univariate latent prior, enabling fast and exact inference via the inverse transform method. On small datasets, we show that importance sampling becomes a tractable, unbiased, and single-pass posterior inference method. For settings requiring exploration, we propose a population-based strategy that decomposes the posterior into a sequence of annealed distributions, serving as a new remedy for poor mixing in Energy-based Models. KAEM attains competitive Fréchet Inception Distance among latent-prior models on SVHN, CIFAR10, and CelebA while sampling in a single forward pass at lower cost than iterative EBMs, and exposing an interpretable prior built from 1D densities.

arXiv

neuralGAM: An R Package for Fitting Generalized Additive Neural Networks

Ines Ortega-Fernandez, Marta Sestelo

Nowadays, Neural Networks are considered one of the most effective methods for various tasks such as anomaly detection, computer-aided disease detection, or natural language processing. However, these networks suffer from the ``black-box'' problem which makes it difficult to understand how they make decisions. In order to solve this issue, an R package called neuralGAM is introduced. This package implements a Neural Network topology based on Generalized Additive Models, allowing to fit an independent Neural Network to estimate the contribution of each feature to the output variable, yielding a highly accurate and interpretable Deep Learning model. The neuralGAM package provides a flexible framework for training Generalized Additive Neural Networks, which does not impose any restrictions on the Neural Network architecture. We illustrate the use of the neuralGAM package in both synthetic and real data examples.

arXiv

An Expectation-Maximization Perspective on Reinforcement Learning for LLM Reasoning

Tianbing Xu

Reinforcement learning has emerged as a powerful approach for improving the reasoning capabilities of large language models, as demonstrated by systems such as OpenAI's O1~\cite{o1} and DeepSeek-R1~\cite{r1}. However, widely used algorithms such as PPO~\cite{ppo} and GRPO~\cite{grpo} rely on likelihood-ratio correction and heuristic clipping, which increase algorithmic complexity and may introduce additional variance and optimization bias. We present \textbf{EM Policy Gradient (EMPG)}, a simple and principled framework that formulates reinforcement learning over reasoning trajectories as an Expectation-Maximization (EM) problem~\cite{em, dempster1977em}. The E-step constructs a reward-weighted distribution over rationale trajectories, while the M-step improves the language model by maximizing their weighted log-likelihood. This formulation leads to a practical off-policy policy-gradient algorithm that directly optimizes the EM surrogate objective without trajectory-level importance weighting or likelihood-ratio clipping. Moreover, under exact E- and improving M-steps, EMPG guarantees monotonic improvement of the expected-reward objective. Experiments on GSM8K and MATH Hard with multiple Qwen2.5 base models show that EMPG achieves performance comparable to or better than GRPO while using a substantially simpler optimization procedure. EMPG also produces more concise reasoning trajectories and exhibits structured reasoning behaviors, including subproblem decomposition, self-verification, reflection, and backtracking. These results suggest that the EM perspective provides an effective theoretical and algorithmic foundation for reinforcement learning of reasoning language models.

arXiv

Wasserstein Distributionally Robust Regret Optimization

Lukas-Benedikt Fiechtner, Jose Blanchet

Distributionally robust optimization (DRO) is widely used for decision-making under uncertainty, but its adversarial focus on worst-case loss can lead to overly conservative policies. To mitigate this, we study ex-ante Distributionally Robust Regret Optimization (DRRO) with Wasserstein ambiguity sets, designed to balance robustness with upside potential. We develop a theory of Wasserstein DRRO (WDRRO) paralleling Wasserstein DRO. Under smoothness and regularity, WDRRO selects among ERM optima by a first-order gradient-discrepancy rule. If the ERM optimizer is unique, first-order sensitivity vanishes and a second-order expansion governs deviations. For convex quadratics ERM and DRRO coincide for any radius. We then study regimes where these assumptions fail: nondifferentiable max-affine losses, discrete references, and larger radii, where WDRRO can differ from ERM and WDRO. We show that computing WDRRO regret is NP-hard even without bilinear terms. Nevertheless, we develop exact algorithms, a tractable convex relaxation with guarantees, and experiments showing tightness and loss-dependent behavior.

arXiv

ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks

Yuezhou Ma, Haixu Wu, Hang Zhou, Huikun Weng, Jianmin Wang, Mingsheng Long

Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function. By analyzing the loss distribution, previous research observed the propagation failure phenomenon of PINNs, intuitively described as the correct supervision for model outputs cannot ''propagate'' from initial states or boundaries to the interior domain. Going beyond intuitive understanding, this paper provides a formal and in-depth study of propagation failure and its root cause. Based on a detailed comparison with classical finite element methods, we ascribe the failure to the conventional single-point-processing architecture of PINNs and further prove that propagation failure is essentially caused by the lower gradient correlation of PINN models on nearby collocation points. Compared to superficial loss maps, this new perspective provides a more precise quantitative criterion to identify where and why PINN fails. The theoretical finding also inspires us to present a new PINN architecture, named ProPINN, which can effectively unite the gradients of region points for better propagation. ProPINN can reliably resolve PINN failure modes and significantly surpass advanced Transformer-based models with 46% relative promotion.

arXiv

Machine Learning for Inverse Problems and Data Assimilation

Eviatar Bach, Ricardo Baptista, Daniel Sanz-Alonso, Andrew Stuart

The aim of this book is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems and/or data assimilation who wish to see a mathematical presentation of machine learning as it pertains to their fields. As a by-product, we include a succinct mathematical treatment of various fundamental underpinning topics in machine learning, and adjacent areas of (computational) mathematics.

arXiv

Characteristic Learning for Provable One Step Generation

Zhao Ding, Chenguang Duan, Yuling Jiao, Ruoxuan Li, Jerry Zhijian Yang, Pingwen Zhang

We propose the characteristic generator, an one-step generative model that combines the sampling efficiency of generative adversarial networks (GANs) with the training stability of flow-based models. The proposed model is based on characteristics along which probability-density transport is governed by ordinary differential equations (ODEs). Specifically, we first estimate the underlying velocity field and numerically solve the probability-flow ODE using an exponential integrator, thereby obtaining discrete approximations of the characteristic trajectories. We then train a deep neural network to approximate these trajectories, yielding a one-step transport map from a Gaussian prior to the target distribution. Theoretically, we analyze the errors introduced by velocity-field estimation, numerical discretization, and characteristic approximation, and establish a nonasymptotic convergence rate in the Wasserstein-2 distance under mild assumptions on the data distribution. Moreover, under a low-dimensional linear-subspace assumption, we show that the convergence rate depends on the intrinsic data dimension rather than the potentially much larger ambient dimension, demonstrating the model's ability to alleviate the curse of dimensionality. Experiments on synthetic and real-world datasets show that the characteristic generator produces high-quality, high-resolution samples using only one or a few neural-network evaluations.

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