In the current paper we relax the information structure of these classical frameworks by allowing arbitrary information arrivalprocesses.

Variational autoencoders (VAE)areapowerful andwidely-used classofmodels to learn complex data distributions in an unsupervised fashion.

It is commonplace to encounter heterogeneous data, of which some aspects of the data distribution may vary but the underlying causal mechanisms remain constant. When data are divided into distinct environments according to the heterogeneity, recent invariant learning methods have proposed to learn robust and invariant models using this environment partition.

Tothis end, anumber ofbenchmarks for measuring OOC performance have been recently introduced.

Evaluating mathematical reasoning in LLMs is constrained by limited benchmark sizes and inherent model stochasticity, yielding high-variance accuracy estimates and unstable rankings across platforms. On difficult problems, an LLM may fail to produce a correct final answer, yet still provide reliable pairwise comparison signals indicating which of two candidate solutions is better. We leverage this observation to design a statistically efficient evaluation framework that combines standard labeled outcomes with pairwise comparison signals obtained by having models judge auxiliary reasoning chains. Treating these comparison signals as control variates, we develop a semiparametric estimator based on the efficient influence function (EIF) for the setting where auxiliary reasoning chains are observed. This yields a one-step estimator that achieves the semiparametric efficiency bound, guarantees strict variance reduction over naive sample averaging, and admits asymptotic normality for principled uncertainty quantification. Across simulations, our one-step estimator substantially improves ranking accuracy, with gains increasing as model output noise grows. Experiments on GPQA Diamond, AIME 2025, and GSM8K further demonstrate more precise performance estimation and more reliable model rankings, especially in small-sample regimes where conventional evaluation is pretty unstable.

Knowledge tracing (KT) is a task that predicts students' future performance based on their historical learning interactions. With the rapid development of deep learning techniques, existing KT approaches follow a data-driven paradigm that uses massive problem-solving records to model students' learning processes. However, although the educational contexts contain various factors that may have an influence on student learning outcomes, existing public KT datasets mainly consist of anonymized ID-like features, which may hinder the research advances towards this field. Therefore, in this work, we present, \emph{XES3G5M}, a large-scale dataset with rich auxiliary information about questions and their associated knowledge components (KCs)\footnote{\label{ft:kc}A KC is a generalization of everyday terms like concept, principle, fact, or skill.}. The XES3G5M dataset is collected from a real-world online math learning platform, which contains 7,652 questions, and 865 KCs with 5,549,635 interactions from 18,066 students. To the best of our knowledge, the XES3G5M dataset not only has the largest number of KCs in math domain but contains the richest contextual information including tree structured KC relations, question types, textual contents and analysis and student response timestamps. Furthermore, we build a comprehensive benchmark on 19 state-of-the-art deep learning based knowledge tracing (DLKT) models. Extensive experiments demonstrate the effectiveness of leveraging the auxiliary information in our XES3G5M with DLKT models. We hope the proposed dataset can effectively facilitate the KT research work.

We prove identifiability of a broad class of deep latent variable models that (a) have universal approximation capabilities and (b) are the decoders of variational autoencoders that are commonly used in practice. Unlike existing work, our analysis does not require weak supervision, auxiliary information, or conditioning in the latent space. Specifically, we show that for a broad class of generative (i.e.

Software languages evolve over time for various reasons, such as the addition of new features. When the language's grammar definition evolves, textual instances that originally conformed to the grammar become outdated. For DSLs in a model-driven engineering context, there exists a plethora of techniques to co-evolve models with the evolving metamodel. However, these techniques are not geared to support DSLs with a textual syntax -- applying them to textual language definitions and instances may lead to the loss of information from the original instances, such as comments and layout information, which are valuable for software comprehension and maintenance. This study explores the potential of Large Language Model (LLM)-based solutions in achieving grammar and instance co-evolution, with attention to their ability to preserve auxiliary information when directly processing textual instances. By applying two advanced language models, Claude-3.5 and GPT-4o, and conducting experiments across seven case languages, we evaluated the feasibility and limitations of this approach. Our results indicate a good ability of the considered LLMs for migrating textual instances in small-scale cases with limited instance size, which are representative of a subset of cases encountered in practice. In addition, we observe significant challenges with the scalability of LLM-based solutions to larger instances, leading to insights that are useful for informing future research.