This paper explores the realm of infinite horizon average reward Constrained Markov Decision Processes (CMDPs).

Many articles in the literature solve the CMDP with an unknown environment.

For an example unit j, if it shows activity for input images having white pixels at 6 dva to 8 dva, we say the RF for the unit j is 2 dva and its eccentricity is 7 dva.

Industrial image anomaly detection is a challenging problem owing to extreme class imbalance and the scarcity of labeled defective samples, particularly in few-shot settings. We propose BayPrAnoMeta, a Bayesian generalization of Proto-MAML for few-shot industrial image anomaly detection. Unlike existing Proto-MAML approaches that rely on deterministic class prototypes and distance-based adaptation, BayPrAnoMeta replaces prototypes with task-specific probabilistic normality models and performs inner-loop adaptation via a Bayesian posterior predictive likelihood. We model normal support embeddings with a Normal-Inverse-Wishart (NIW) prior, producing a Student-$t$ predictive distribution that enables uncertainty-aware, heavy-tailed anomaly scoring and is essential for robustness in extreme few-shot settings. We further extend BayPrAnoMeta to a federated meta-learning framework with supervised contrastive regularization for heterogeneous industrial clients and prove convergence to stationary points of the resulting nonconvex objective. Experiments on the MVTec AD benchmark demonstrate consistent and significant AUROC improvements over MAML, Proto-MAML, and PatchCore-based methods in few-shot anomaly detection settings.

We show that while it is sensible to think of recall as simply retrieving items when probed with a cue - typically the item list itself - it is better to think of recognition as retrieving cues when probed with items.

In the landscape of Fact-based Judgment Prediction and Explanation (FJPE), reliance on factual data is essential for developing robust and realistic AI-driven decision-making tools. This paper introduces TathyaNyaya, the largest annotated dataset for FJPE tailored to the Indian legal context, encompassing judgments from the Supreme Court of India and various High Courts. Derived from the Hindi terms "Tathya" (fact) and "Nyaya" (justice), the TathyaNyaya dataset is uniquely designed to focus on factual statements rather than complete legal texts, reflecting real-world judicial processes where factual data drives outcomes. Complementing this dataset, we present FactLegalLlama, an instruction-tuned variant of the LLaMa-3-8B Large Language Model (LLM), optimized for generating high-quality explanations in FJPE tasks. Finetuned on the factual data in TathyaNyaya, FactLegalLlama integrates predictive accuracy with coherent, contextually relevant explanations, addressing the critical need for transparency and interpretability in AI-assisted legal systems. Our methodology combines transformers for binary judgment prediction with FactLegalLlama for explanation generation, creating a robust framework for advancing FJPE in the Indian legal domain. TathyaNyaya not only surpasses existing datasets in scale and diversity but also establishes a benchmark for building explainable AI systems in legal analysis. The findings underscore the importance of factual precision and domain-specific tuning in enhancing predictive performance and interpretability, positioning TathyaNyaya and FactLegalLlama as foundational resources for AI-assisted legal decision-making.

Legal Judgment Prediction (LJP) has emerged as a key area in AI for law, aiming to automate judicial outcome forecasting and enhance interpretability in legal reasoning. While previous approaches in the Indian context have relied on internal case content such as facts, issues, and reasoning, they often overlook a core element of common law systems, which is reliance on statutory provisions and judicial precedents. In this work, we propose NyayaRAG, a Retrieval-Augmented Generation (RAG) framework that simulates realistic courtroom scenarios by providing models with factual case descriptions, relevant legal statutes, and semantically retrieved prior cases. NyayaRAG evaluates the effectiveness of these combined inputs in predicting court decisions and generating legal explanations using a domain-specific pipeline tailored to the Indian legal system. We assess performance across various input configurations using both standard lexical and semantic metrics as well as LLM-based evaluators such as G-Eval. Our results show that augmenting factual inputs with structured legal knowledge significantly improves both predictive accuracy and explanation quality.