These profiles are fed back to the LLM, which then revises the code to reduce overhead.

Code generation models have increasingly become integral to aiding software development.

The U.S. State Department reissued its Russia travel warning as the Ukraine conflict intensifies, telling U.S. citizens to leave immediately due to detention risks and limited embassy help.

We develop a computational framework for classifying Galois groups of irreducible degree-7 polynomials over~$\mathbb{Q}$, combining explicit resolvent methods with machine learning techniques. A database of over one million normalized projective septics is constructed, each annotated with algebraic invariants~$J_0, \dots, J_4$ derived from binary transvections. For each polynomial, we compute resolvent factorizations to determine its Galois group among the seven transitive subgroups of~$S_7$ identified by Foulkes. Using this dataset, we train a neurosymbolic classifier that integrates invariant-theoretic features with supervised learning, yielding improved accuracy in detecting rare solvable groups compared to coefficient-based models. The resulting database provides a reproducible resource for constructive Galois theory and supports empirical investigations into group distribution under height constraints. The methodology extends to higher-degree cases and illustrates the utility of hybrid symbolic-numeric techniques in computational algebra.

These profiles are fed back to the LLM, which then revises the code to reduce overhead.

We introduce the Graded Transformer framework, a novel class of sequence models that embeds algebraic inductive biases through grading transformations on vector spaces. Extending the theory of Graded Neural Networks (GNNs), we propose two architectures: the Linearly Graded Transformer (LGT) and the Exponentially Graded Transformer (EGT). These models apply parameterized scaling operators-governed by fixed or learnable grading tuples and, for EGT, exponential factors to infuse hierarchical structure into attention and representation layers, enhancing efficiency for structured data. We derive rigorous theoretical guarantees, including universal approximation theorems for continuous and Sobolev functions, reduced sample complexity via effective VC dimension bounds, Lipschitz continuity of graded operations, and robustness to adversarial perturbations. A graded loss function ensures gradient stability and alignment with domain priors during optimization. By treating grades as differentiable parameters, the framework enables adaptive feature prioritization, overcoming limitations of fixed grades in prior work. The Graded Transformer holds transformative potential for hierarchical learning and neurosymbolic reasoning, with applications spanning algebraic geometry (e.g., moduli spaces and zeta functions), physics (e.g., multiscale simulations), natural language processing (e.g., syntactic parsing), biological sequence analysis (e.g., variant prediction), and emerging areas like graph neural networks and financial modeling. This work advances structured deep learning by fusing geometric and algebraic principles with attention mechanisms, offering a mathematically grounded alternative to data-driven models and paving the way for interpretable, efficient systems in complex domains.

Vertical Federated Learning (VFL) is a distributed AI software deployment mechanism for cross-silo collaboration without accessing participants' data. However, existing VFL work lacks a mechanism to audit the execution correctness of the inference software of the data party. To address this problem, we design a Vertical Federated Inference Auditing (VeFIA) framework. VeFIA helps the task party to audit whether the data party's inference software is executed as expected during large-scale inference without leaking the data privacy of the data party or introducing additional latency to the inference system. The core of VeFIA is that the task party can use the inference results from a framework with Trusted Execution Environments (TEE) and the coordinator to validate the correctness of the data party's computation results. VeFIA guarantees that, as long as the abnormal inference exceeds 5.4%, the task party can detect execution anomalies in the inference software with a probability of 99.99%, without incurring any additional online inference latency. VeFIA's random sampling validation achieves 100% positive predictive value, negative predictive value, and true positive rate in detecting abnormal inference. To the best of our knowledge, this is the first paper to discuss the correctness of inference software execution in VFL.

Vulnerability datasets used for ML testing implicitly contain retrospective information. When tested on the field, one can only use the labels available at the time of training and testing (e.g. seen and assumed negatives). As vulnerabilities are discovered across calendar time, labels change and past performance is not necessarily aligned with future performance. Past works only considered the slices of the whole history (e.g. DiverseVUl) or individual differences between releases (e.g. Jimenez et al. ESEC/FSE 2019). Such approaches are either too optimistic in training (e.g. the whole history) or too conservative (e.g. consecutive releases). We propose a method to restructure a dataset into a series of datasets in which both training and testing labels change to account for the knowledge available at the time. If the model is actually learning, it should improve its performance over time as more data becomes available and data becomes more stable, an effect that can be checked with the Mann-Kendall test. We validate our methodology for vulnerability detection with 4 time-based datasets (3 projects from BigVul dataset + Vuldeepecker's NVD) and 5 ML models (Code2Vec, CodeBERT, LineVul, ReGVD, and Vuldeepecker). In contrast to the intuitive expectation (more retrospective information, better performance), the trend results show that performance changes inconsistently across the years, showing that most models are not learning.