In recent years, various software supply chain (SSC) attacks have posed significant risks to the global community. Severe consequences may arise if developers integrate insecure code snippets that are vulnerable to SSC attacks into their products. Particularly, code generation techniques, such as large language models (LLMs), have been widely utilized in the developer community. However, LLMs are known to suffer from inherent issues when generating code, including fabrication, misinformation, and reliance on outdated training data, all of which can result in serious software supply chain threats. In this paper, we investigate the security threats to the SSC that arise from these inherent issues. We examine three categories of threats, including eleven potential SSC-related threats, related to external components in source code, and continuous integration configuration files. We find some threats in LLM-generated code could enable attackers to hijack software and workflows, while some others might cause potential hidden threats that compromise the security of the software over time. To understand these security impacts and severity, we design a tool, SSCGuard, to generate 439,138 prompts based on SSC-related questions collected online, and analyze the responses of four popular LLMs from GPT and Llama. Our results show that all identified SSC-related threats persistently exist. To mitigate these risks, we propose a novel prompt-based defense mechanism, namely Chain-of-Confirmation, to reduce fabrication, and a middleware-based defense that informs users of various SSC threats.

We propose a randomized neural network approach called RaNNDy for learning transfer operators and their spectral decompositions from data. The weights of the hidden layers of the neural network are randomly selected and only the output layer is trained. The main advantage is that without a noticeable reduction in accuracy, this approach significantly reduces the training time and resources while avoiding common problems associated with deep learning such as sensitivity to hyperparameters and slow convergence. Additionally, the proposed framework allows us to compute a closed-form solution for the output layer which directly represents the eigenfunctions of the operator. Moreover, it is possible to estimate uncertainties associated with the computed spectral properties via ensemble learning. We present results for different dynamical operators, including Koopman and Perron-Frobenius operators, which have important applications in analyzing the behavior of complex dynamical systems, and the Schrödinger operator. The numerical examples, which highlight the strengths but also weaknesses of the proposed framework, include several stochastic dynamical systems, protein folding processes, and the quantum harmonic oscillator.

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic regression. However, existing approaches are dominated by heuristic algorithms or data-hungry black-box methods, which often demand low-noise settings and lack principled uncertainty quantification. Motivated by interpretable Statistical Artificial Intelligence, we develop a hierarchical Bayesian framework for symbolic regression that represents scientific laws as ensembles of tree-structured symbolic expressions endowed with a regularized tree prior. This coherent probabilistic formulation enables full posterior inference via an efficient Markov chain Monte Carlo algorithm, yielding a balance between predictive accuracy and structural parsimony. To guide symbolic model selection, we develop a marginal posterior-based criterion adhering to the Occam's window principle and further quantify structural fidelity to ground truth through a tailored expression-distance metric. On the theoretical front, we establish near-minimax rate of Bayesian posterior concentration, providing the first rigorous guarantee in context of symbolic regression. Empirical evaluation demonstrates robust performance of our proposed methodology against state-of-the-art competing modules on a simulated example, a suite of canonical Feynman equations, and single-atom catalysis dataset.

The quadratic complexity of the attention mechanism in Transformer models has motivated the development of alternative architectures with sub-quadratic scaling, such as state-space models. Among these, Mamba has emerged as a leading architecture, achieving state-of-the-art results across a range of language modeling tasks. However, Mamba's performance significantly deteriorates when applied to contexts longer than those seen during pre-training, revealing a sharp sensitivity to context length extension. Through detailed analysis, we attribute this limitation to the out-of-distribution behaviour of its state-space dynamics, particularly within the parameterization of the state transition matrix $\mathbf{A}$. Unlike recent works which attribute this sensitivity to the vanished accumulation of discretization time steps, $\exp(-\sum_{t=1}^NΔ_t)$, we establish a connection between state convergence behavior as the input length approaches infinity and the spectrum of the transition matrix $\mathbf{A}$, offering a well-founded explanation of its role in length extension. Next, to overcome this challenge, we propose an approach that applies spectrum scaling to pre-trained Mamba models to enable robust long-context generalization by selectively modulating the spectrum of $\mathbf{A}$ matrices in each layer. We show that this can significantly improve performance in settings where simply modulating $Δ_t$ fails, validating our insights and providing avenues for better length generalization of state-space models with structured transition matrices.

We present a sensor-fusion framework for rapid, non-destructive classification and quality control of organic substances, built on a standard Arduino Mega 2560 microcontroller platform equipped with three commercial environmental and gas sensors. All data used in this study were generated in-house: sensor outputs for ten distinct classes - including fresh and expired samples of apple juice, onion, garlic, and ginger, as well as cinnamon and cardamom - were systematically collected and labeled using this hardware setup, resulting in a unique, application-specific dataset. Correlation analysis was employed as part of the preprocessing pipeline for feature selection. After preprocessing and dimensionality reduction (PCA/LDA), multiple supervised learning models - including Support Vector Machine (SVM), Decision Tree (DT), and Random Forest (RF), each with hyperparameter tuning, as well as an Artificial Neural Network (ANN) and an ensemble voting classifier - were trained and cross-validated on the collected dataset. The best-performing models, including tuned Random Forest, ensemble, and ANN, achieved test accuracies in the 93 to 94 percent range. These results demonstrate that low-cost, multisensory platforms based on the Arduino Mega 2560, combined with advanced machine learning and correlation-driven feature engineering, enable reliable identification and quality control of organic compounds.

Scaling laws have played a cornerstone role in guiding the training of large language models (LLMs). However, most existing works on scaling laws primarily focus on the final-step loss, overlooking the loss dynamics during the training process and, crucially, the impact of learning rate schedule (LRS). In this paper, we aim to bridge this gap by studying a teacher-student kernel regression setup trained via online stochastic gradient descent (SGD). Leveraging a novel intrinsic time viewpoint and stochastic differential equation (SDE) modeling of SGD, we introduce the Functional Scaling Law (FSL), which characterizes the evolution of population risk during the training process for general LRSs. Remarkably, the impact of the LRSs is captured through an explicit convolution-type functional term, making their effects fully tractable. To illustrate the utility of FSL, we analyze three widely used LRSs -- constant, exponential decay, and warmup-stable-decay (WSD) -- under both data-limited and compute-limited regimes. We provide theoretical justification for widely adopted empirical practices in LLMs pre-training such as (i) higher-capacity models are more data- and compute-efficient; (ii) learning rate decay can improve training efficiency; (iii) WSD-like schedules can outperform direct-decay schedules. Lastly, we explore the practical relevance of FSL as a surrogate model for fitting, predicting and optimizing the loss curves in LLM pre-training, with experiments conducted across model sizes ranging from 0.1B to 1B parameters. We hope our FSL framework can deepen the understanding of LLM pre-training dynamics and provide insights for improving large-scale model training.

Accurate time-series forecasting for complex physical systems is the backbone of modern industrial monitoring and control. While deep learning models excel at capturing complex dynamics, currently, their deployment is limited due to physical inconsistency and robustness, hence constraining their reliability in regulated environments. We introduce process-informed forecasting (PIF) models for temperature in pharmaceutical lyophilization. We investigate a wide range of models, from classical ones such as Autoregressive Integrated Moving Average Model (ARIMA) and Exponential Smoothing Model (ETS), to modern deep learning architectures, including Kolmogorov-Arnold Networks (KANs). We compare three different loss function formulations that integrate a process-informed trajectory prior: a fixed-weight loss, a dynamic uncertainty-based loss, and a Residual-Based Attention (RBA) mechanism. We evaluate all models not only for accuracy and physical consistency but also for robustness to sensor noise. Furthermore, we test the practical generalizability of the best model in a transfer learning scenario on a new process. Our results show that PIF models outperform their data-driven counterparts in terms of accuracy, physical plausibility and noise resilience. This work provides a roadmap for developing reliable and generalizable forecasting solutions for critical applications in the pharmaceutical manufacturing landscape.

Account Takeover (ATO) fraud poses a significant challenge in consumer banking, requiring high recall under strict latency while minimizing friction for legitimate users. Production systems typically rely on tabular gradient-boosted decision trees (e.g., XGBoost) that score sessions independently, overlooking the relational and temporal structure of online activity that characterizes coordinated attacks and "fraud rings." We introduce ATLAS (Account Takeover Learning Across Spatio-Temporal Directed Graph), a framework that reformulates ATO detection as spatio-temporal node classification on a time-respecting directed session graph. ATLAS links entities via shared identifiers (account, device, IP) and regulates connectivity with time-window and recency constraints, enabling causal, time-respecting message passing and latency-aware label propagation that uses only labels available at scoring time, non-anticipative and leakage-free. We operationalize ATLAS with inductive GraphSAGE variants trained via neighbor sampling, at scale on a sessions graph with more than 100M nodes and around 1B edges. On a high-risk digital product at Capital One, ATLAS delivers 6.38 percent AUC improvement and more than 50 percent reduction in customer friction, improving fraud capture while reducing user friction.

Transformer-based LLMs demonstrate strong performance on graph reasoning tasks, yet their internal mechanisms remain underexplored. To uncover these reasoning process mechanisms in a fundamental and unified view, we set the basic decoder-only transformers and explain them using the circuit-tracer framework. Through this lens, we visualize reasoning traces and identify two core mechanisms in graph reasoning: token merging and structural memorization, which underlie both path reasoning and substructure extraction tasks. We further quantify these behaviors and analyze how they are influenced by graph density and model size. Our study provides a unified interpretability framework for understanding structural reasoning in decoder-only Transformers.