Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized algorithms. However, despite its widespread use, TD procedures are generally sensitive to step size specification. A poor choice of step size can dramatically increase variance and slow convergence in both on-policy and off-policy evaluation tasks. In practice, researchers use trial and error to identify stable step sizes, but these approaches tend to be ad hoc and inefficient. As an alternative, we propose implicit TD algorithms that reformulate TD updates into fixed point equations. Such updates are more stable and less sensitive to step size without sacrificing computational efficiency. Moreover, we derive asymptotic convergence guarantees and finite-time error bounds for our proposed implicit TD algorithms, which include implicit TD(0), TD($λ$), and TD with gradient correction (TDC). Our results show that implicit TD algorithms are applicable to a much broader range of step sizes, and thus provide a robust and versatile framework for policy evaluation and value approximation in modern RL tasks. We demonstrate these benefits empirically through extensive numerical examples spanning both on-policy and off-policy tasks.

We consider optimal resource allocation for restless multi-armed bandits (RMABs) in unknown, non-stationary settings. RMABs are PSPACE-hard to solve optimally, even when all parameters are known. The Whittle index policy is known to achieve asymptotic optimality for a large class of such problems, while remaining computationally efficient. In many practical settings, however, the transition kernels required to compute the Whittle index are unknown and non-stationary. In this work, we propose an online learning algorithm for Whittle indices in this setting. Our algorithm first predicts current transition kernels by solving a linear optimization problem based on upper confidence bounds and empirical transition probabilities calculated from data over a sliding window. Then, it computes the Whittle index associated with the predicted transition kernels. We design these sliding windows and upper confidence bounds to guarantee sub-linear dynamic regret on the number of episodes $T$, under the condition that transition kernels change slowly over time (rate upper bounded by $ε=1/T^k$ with $k>0$). Furthermore, our proposed algorithm and regret analysis are designed to exploit prior domain knowledge and structural information of the RMABs to accelerate the learning process. Numerical results validate that our algorithm achieves superior performance in terms of lowest cumulative regret relative to baselines in non-stationary environments.

We investigate language generation in the limit - a model by Kleinberg and Mullainathan [NeurIPS 2024] and extended by Li, Raman, and Tewari [COLT 2025]. While Kleinberg and Mullainathan proved generation is possible for all countable collections, Li et al. defined a hierarchy of generation notions (uniform, non-uniform, and generatable) and explored their feasibility for uncountable collections. Our first set of results resolve two open questions of Li et al. by proving finite unions of generatable or non-uniformly generatable classes need not be generatable. These follow from a stronger result: there is a non-uniformly generatable class and a uniformly generatable class whose union is non-generatable. This adds to the aspects along which language generation in the limit is different from traditional tasks in statistical learning theory like classification, which are closed under finite unions. In particular, it implies that given two generators for different collections, one cannot combine them to obtain a single "more powerful" generator, prohibiting this notion of boosting. Our construction also addresses a third open question of Li et al. on whether there are uncountable classes that are non-uniformly generatable and do not satisfy the eventually unbounded closure (EUC) condition introduced by Li, Raman, and Tewari. Our approach utilizes carefully constructed classes along with a novel diagonalization argument that could be of independent interest in the growing area of language generation.

Knowledge erasure in large language models (LLMs) is important for ensuring compliance with data and AI regulations, safeguarding user privacy, mitigating bias, and misinformation. Existing unlearning methods aim to make the process of knowledge erasure more efficient and effective by removing specific knowledge while preserving overall model performance, especially for retained information. However, it has been observed that the unlearning techniques tend to suppress and leave the knowledge beneath the surface, thus making it retrievable with the right prompts. In this work, we demonstrate that \textit{step-by-step reasoning} can serve as a backdoor to recover this hidden information. We introduce a step-by-step reasoning-based black-box attack, Sleek, that systematically exposes unlearning failures. We employ a structured attack framework with three core components: (1) an adversarial prompt generation strategy leveraging step-by-step reasoning built from LLM-generated queries, (2) an attack mechanism that successfully recalls erased content, and exposes unfair suppression of knowledge intended for retention and (3) a categorization of prompts as direct, indirect, and implied, to identify which query types most effectively exploit unlearning weaknesses. Through extensive evaluations on four state-of-the-art unlearning techniques and two widely used LLMs, we show that existing approaches fail to ensure reliable knowledge removal. Of the generated adversarial prompts, 62.5% successfully retrieved forgotten Harry Potter facts from WHP-unlearned Llama, while 50% exposed unfair suppression of retained knowledge. Our work highlights the persistent risks of information leakage, emphasizing the need for more robust unlearning strategies for erasure.

Outcome-Based Education (OBE) emphasizes the development of specific competencies through student-centered learning. In this study, we reviewed the importance of OBE and implemented transformer-based models, particularly DistilBERT, to analyze an NLP dataset that includes student feedback. Our objective is to assess and improve educational outcomes. Our approach is better than other machine learning models because it uses the transformer's deep understanding of language context to classify sentiment better, giving better results across a wider range of matrices. Our work directly contributes to OBE's goal of achieving measurable outcomes by facilitating the identification of patterns in student learning experiences. We have also applied LIME (local interpretable model-agnostic explanations) to make sure that model predictions are clear. This gives us understandable information about how key terms affect sentiment. Our findings indicate that the combination of transformer models and LIME explanations results in a strong and straightforward framework for analyzing student feedback. This aligns more closely with the principles of OBE and ensures the improvement of educational practices through data-driven insights.

Semi-supervised semantic segmentation (SSSS) faces persistent challenges in effectively leveraging unlabeled data, such as ineffective utilization of pseudo-labels, exacerbation of class imbalance biases, and neglect of prediction uncertainty. Current approaches often discard uncertain regions through strict thresholding favouring dominant classes. To address these limitations, we introduce a holistic framework that transforms uncertainty into a learning asset through four principal components: (1) fuzzy pseudo-labeling, which preserves soft class distributions from top-K predictions to enrich supervision; (2) uncertainty-aware dynamic weighting, that modulate pixel-wise contributions via entropy-based reliability scores; (3) adaptive class rebalancing, which dynamically adjust losses to counteract long-tailed class distributions; and (4) lightweight contrastive regularization, that encourage compact and discriminative feature embeddings. Extensive experiments on benchmarks demonstrate that our method outperforms current state-of-the-art approaches, achieving significant improvements in the segmentation of under-represented classes and ambiguous regions.

This report presents a unified instruction-based framework for learning generalized text embeddings optimized for both information retrieval (IR) and non-IR tasks. Built upon a decoder-only large language model (Mistral-7B), our approach combines in-context learning, soft supervision, and adaptive hard-negative mining to generate context-aware embeddings without task-specific fine-tuning. Structured instructions and few-shot examples are used to guide the model across diverse tasks, enabling strong performance on classification, semantic similarity, clustering, and reranking benchmarks. To improve semantic discrimination, we employ a soft labeling framework where continuous relevance scores, distilled from a high-performance dense retriever and reranker, serve as fine-grained supervision signals. In addition, we introduce adaptive margin-based hard-negative mining, which filters out semantically ambiguous negatives based on their similarity to positive examples, thereby enhancing training stability and retrieval robustness. Our model is evaluated on the newly introduced MTEB (English, v2) benchmark, covering 41 tasks across seven categories. Results show that our method achieves strong generalization and ranks among the top-performing models by Borda score, outperforming several larger or fully fine-tuned baselines. These findings highlight the effectiveness of combining in-context prompting, soft supervision, and adaptive sampling for scalable, high-quality embedding generation.

Large Language Models (LLMs) define probability measures on text. By considering the implicit knowledge question of what it means for an LLM to know such a measure and what it entails algorithmically, we are naturally led to formulate a series of tasks that go beyond generative sampling, involving forms of summarization, counterfactual thinking, anomaly detection, originality search, reverse prompting, debating, creative solving, etc. These tasks can be formulated as games based on LLM measures, which we call Cross-Entropy (Xent) Games . Xent Games can be single-player or multi-player. They involve cross-entropy scores and cross-entropy constraints, and can be expressed as simple computational graphs and programs. We show the Xent Game space is large enough to contain a wealth of interesting examples, while being constructible from basic game-theoretic consistency axioms. We then discuss how the Xent Game space can be used to measure the abilities of LLMs. This leads to the construction of Xent Game measures: finite families of Xent Games that can be used as capability benchmarks, built from a given scope, by extracting a covering measure. To address the unbounded scope problem associated with the challenge of measuring general abilities, we propose to explore the space of Xent Games in a coherent fashion, using ideas inspired by evolutionary dynamics.

Large language models (LLMs) have demonstrated exceptional performance across a wide range of natural language tasks. However, selecting the optimal LLM to respond to a user query often necessitates a delicate balance between performance and cost. While powerful models deliver better results, they come at a high cost, whereas smaller models are more cost-effective but less capable. To address this trade-off, we propose IRT-Router, a multi-LLM routing framework that efficiently routes user queries to the most suitable LLM. Inspired by Item Response Theory (IRT), a psychological measurement methodology, IRT-Router explicitly models the relationship between LLM capabilities and user query attributes. This not only enables accurate prediction of response performance but also provides interpretable insights, such as LLM abilities and query difficulty. Additionally, we design an online query warm-up technique based on semantic similarity, further enhancing the online generalization capability of IRT-Router. Extensive experiments on 20 LLMs and 12 datasets demonstrate that IRT-Router outperforms most baseline methods in terms of effectiveness and interpretability. Its superior performance in cold-start scenarios further confirms the reliability and practicality of IRT-Router in real-world applications. Code is available at https://github.com/Mercidaiha/IRT-Router.

System prompts in Large Language Models (LLMs) are predefined directives that guide model behaviour, taking precedence over user inputs in text processing and generation. LLM deployers increasingly use them to ensure consistent responses across contexts. While model providers set a foundation of system prompts, deployers and third-party developers can append additional prompts without visibility into others' additions, while this layered implementation remains entirely hidden from end-users. As system prompts become more complex, they can directly or indirectly introduce unaccounted for side effects. This lack of transparency raises fundamental questions about how the position of information in different directives shapes model outputs. As such, this work examines how the placement of information affects model behaviour. To this end, we compare how models process demographic information in system versus user prompts across six commercially available LLMs and 50 demographic groups. Our analysis reveals significant biases, manifesting in differences in user representation and decision-making scenarios. Since these variations stem from inaccessible and opaque system-level configurations, they risk representational, allocative and potential other biases and downstream harms beyond the user's ability to detect or correct. Our findings draw attention to these critical issues, which have the potential to perpetuate harms if left unexamined. Further, we argue that system prompt analysis must be incorporated into AI auditing processes, particularly as customisable system prompts become increasingly prevalent in commercial AI deployments.