--With the rise of online learning, the demand for efficient and consistent assessment in mathematics has significantly increased over the past decade. Machine Learning (ML), particularly Natural Language Processing (NLP), has been widely used for autograding student responses, particularly those involving text and/or mathematical expressions. However, there has been limited research on autograding responses involving students' handwritten graphs, despite their prevalence in Science, T echnology, Engineering, and Mathematics (STEM) curricula. In this study, we implement multimodal meta-learning models for autograding images containing students' handwritten graphs and text. We further compare the performance of Vision Large Language Models (VLLMs) with these specially trained meta-learning models. Our results, evaluated on a real-world dataset collected from our institution, show that the best-performing meta-learning models outperform VLLMs in 2-way classification tasks. In contrast, in more complex 3-way classification tasks, the best-performing VLLMs slightly outperform the meta-learning models. While VLLMs show promising results, their reliability and practical applicability remain uncertain and require further investigation. S online education has gained popularity, the need for efficient and scalable methods of automatically grading and assessing student work has become increasingly important. Automated grading offers several advantages, including scalability, time efficiency, grading consistency, and immediate feedback. Early research on automated grading primarily focused on closed-ended questions, such as multiple-choice and fill-in-the-blank questions, where responses could be easily verified using rule-based systems [1], [2].

Recent advances have established a new machine learning paradigm based on scaling up compute at inference time as well as at training time. In that line of work, a combination of Supervised Fine-Tuning (SFT) on synthetic demonstrations and Reinforcement Learning with Verifiable Rewards (RLVR) is used for training Large Language Models to expend extra compute during inference in the form of "thoughts" expressed in natural language. In this paper, we propose to instead format these tokens as a multi-turn interaction trace with a stateful tool. At each turn, the new state of the tool is appended to the context of the model, whose job is to generate the tokens necessary to control the tool via a custom DSL. We benchmark this approach on the problem of repairing malfunctioning Python code, and show that this constrained setup allows for faster sampling of experience and a denser reward signal, allowing even models of size up to 3B parameters to learn how to proficiently expend additional compute on the task.

As machine learning models grow increasingly competent, their predictions can supplement scarce or expensive data in various important domains. In support of this paradigm, algorithms have emerged to combine a small amount of high-fidelity observed data with a much larger set of imputed model outputs to estimate some quantity of interest. Yet current hybrid-inference tools target only means or single quantiles, limiting their applicability for many critical domains and use cases. We present QuEst, a principled framework to merge observed and imputed data to deliver point estimates and rigorous confidence intervals for a wide family of quantile-based distributional measures. QuEst covers a range of measures, from tail risk (CVaR) to population segments such as quartiles, that are central to fields such as economics, sociology, education, medicine, and more. We extend QuEst to multidimensional metrics, and introduce an additional optimization technique to further reduce variance in this and other hybrid estimators. We demonstrate the utility of our framework through experiments in economic modeling, opinion polling, and language model auto-evaluation.

The rise of generative AI search engines is disrupting traditional SEO, with Gartner predicting 25% reduction in conventional search usage by 2026. This necessitates new approaches for web content visibility in AI-driven search environments. We present a domain-specific fine-tuning approach for Generative Engine Optimization (GEO) that transforms web content to improve discoverability in large language model outputs. Our method fine-tunes a BART-base transformer on synthetically generated training data comprising 1,905 cleaned travel website content pairs. Each pair consists of raw website text and its GEO-optimized counterpart incorporating credible citations, statistical evidence, and improved linguistic fluency. We evaluate using intrinsic metrics (ROUGE-L, BLEU) and extrinsic visibility assessments through controlled experiments with Llama-3.3-70B. The fine-tuned model achieves significant improvements over baseline BART: ROUGE-L scores of 0.249 (vs. 0.226) and BLEU scores of 0.200 (vs. 0.173). Most importantly, optimized content demonstrates substantial visibility gains in generative search responses with 15.63% improvement in absolute word count and 30.96% improvement in position-adjusted word count metrics. This work provides the first empirical demonstration that targeted transformer fine-tuning can effectively enhance web content visibility in generative search engines with modest computational resources. Our results suggest GEO represents a tractable approach for content optimization in the AI-driven search landscape, offering concrete evidence that small-scale, domain-focused fine-tuning yields meaningful improvements in content discoverability.

Large Language Models (LLMs) have demonstrated impressive generalization capabilities across various tasks, but their claim to practical relevance is still mired by concerns on their reliability. Recent works have proposed examining the activations produced by an LLM at inference time to assess whether its answer to a question is correct. Some works claim that a "geometry of truth" can be learned from examples, in the sense that the activations that generate correct answers can be distinguished from those leading to mistakes with a linear classifier. In this work, we underline a limitation of these approaches: we observe that these "geometries of truth" are intrinsically task-dependent and fail to transfer across tasks. More precisely, we show that linear classifiers trained across distinct tasks share little similarity and, when trained with sparsity-enforcing regularizers, have almost disjoint supports. We show that more sophisticated approaches (e.g., using mixtures of probes and tasks) fail to overcome this limitation, likely because activation vectors commonly used to classify answers form clearly separated clusters when examined across tasks.

LLM-based web agents have recently made significant progress, but much of it has occurred in closed-source systems, widening the gap with open-source alternatives. Progress has been held back by two key challenges: first, a narrow focus on single-step tasks that overlooks the complexity of multi-step web interactions; and second, the high compute costs required to post-train LLM-based web agents. To address this, we present the first statistically grounded study on compute allocation for LLM web-agent post-training. Our approach uses a two-stage pipeline, training a Llama 3.1 8B student to imitate a Llama 3.3 70B teacher via supervised fine-tuning (SFT), followed by on-policy reinforcement learning. We find this process highly sensitive to hyperparameter choices, making exhaustive sweeps impractical. To spare others from expensive trial-and-error, we sample 1,370 configurations and use bootstrapping to estimate effective hyperparameters. Our results show that combining SFT with on-policy RL consistently outperforms either approach alone on both WorkArena and MiniWob++. Further, this strategy requires only 55% of the compute to match the peak performance of pure SFT on MiniWob++, effectively pushing the compute-performance Pareto frontier, and is the only strategy that can close the gap with closed-source models.

W e present the Object-Based Sub-Environment Recognition (OBSER) framework, a novel Bayesian framework that infers three fundamental relationships between sub-environments and their constituent objects. In the OBSER framework, metric and self-supervised learning models estimate the object distributions of sub-environments on the latent space to compute these measures. Both theoretically and empirically, we validate the proposed framework by introducing the ( ϵ, δ) statistically separable (EDS) function which indicates the alignment of the representation. Our framework reliably performs inference in open-world and photorealistic environments and outperforms scene-based methods in chained retrieval tasks. The OBSER framework enables zero-shot recognition of environments to achieve autonomous environment understanding.

Large language models (LLMs) achieve strong performance across many domains but are difficult to deploy in resource-constrained settings due to their size. Low-rank weight matrix compression is a popular strategy for reducing model size, typically by minimizing weight reconstruction error under the assumption that weights are low-rank. However, this assumption often does not hold in LLMs. Instead, LLM activations exhibit stronger low-rank structure-prompting a shift toward minimizing activation reconstruction error. We show that this shift alone is insufficient: activation dimensions contribute unequally to model performance, and uniform reconstruction can harm performance. We propose IMPACT, a principled framework for importance-aware activation reconstruction that links model compression decisions to their impact on model behavior. IMPACT formulates an optimization problem that considers both activation structure and gradient sensitivity, and derives a closed-form solution where the optimal reconstruction bases are the eigenvectors of an importance-weighted activation covariance matrix. This enables low-rank approximations explicitly optimized to preserve accuracy. Experiments across diverse models and tasks show that IMPACT achieves up to 48.6% greater model size reduction with accuracy comparable to state-of-the-art baselines.

A significant use case of instruction-finetuned Large Language Models (LLMs) is to solve question-answering tasks interactively. In this setting, an LLM agent is tasked with making a prediction by sequentially querying relevant information from the user, as opposed to a single-turn conversation. This paper explores sequential querying strategies that aim to minimize the expected number of queries. One such strategy is Information Pursuit (IP), a greedy algorithm that at each iteration selects the query that maximizes information gain or equivalently minimizes uncertainty. However, obtaining accurate estimates of mutual information or conditional entropy for LLMs is very difficult in practice due to over- or under-confident LLM probabilities, which leads to suboptimal query selection and predictive performance. To better estimate the uncertainty at each iteration, we propose Conformal Information Pursuit (C-IP), an alternative approach to sequential information gain based on conformal prediction sets. More specifically, C-IP leverages a relationship between prediction sets and conditional entropy at each iteration to estimate uncertainty based on the average size of conformal prediction sets. In contrast to conditional entropy, we find that conformal prediction sets are a distribution-free and robust method of measuring uncertainty. Experiments with 20 Questions show that C-IP obtains better predictive performance and shorter query-answer chains compared to previous approaches to IP and uncertainty-based chain-of-thought methods. Furthermore, extending to an interactive medical setting between a doctor and a patient on the MediQ dataset, C-IP achieves competitive performance with direct single-turn prediction while offering greater interpretability.

In modern search systems, search engines often suggest relevant queries to users through various panels or components, helping refine their information needs. Traditionally, these recommendations heavily rely on historical search logs to build models, which suffer from cold-start or long-tail issues. Furthermore, tasks such as query suggestion, completion or clarification are studied separately by specific design, which lacks generalizability and hinders adaptation to novel applications. Despite recent attempts to explore the use of LLMs for query recommendation, these methods mainly rely on the inherent knowledge of LLMs or external sources like few-shot examples, retrieved documents, or knowledge bases, neglecting the importance of the calibration and alignment with user feedback, thus limiting their practical utility. To address these challenges, we first propose a general Generative Query Recommendation (GQR) framework that aligns LLM-based query generation with user preference. Specifically, we unify diverse query recommendation tasks by a universal prompt framework, leveraging the instruct-following capability of LLMs for effective generation. Secondly, we align LLMs with user feedback via presenting a CTR-alignment framework, which involves training a query-wise CTR predictor as a process reward model and employing list-wise preference alignment to maximize the click probability of the generated query list. Furthermore, recognizing the inconsistency between LLM knowledge and proactive search intents arising from the separation of user-initiated queries from models, we align LLMs with user initiative via retrieving co-occurrence queries as side information when historical logs are available.