Large language models (LLMs) have demonstrated remarkable performance across diverse tasks by encoding vast amounts of factual knowledge. However, they are still prone to hallucinations, generating incorrect or misleading information, often accompanied by high uncertainty. Existing methods for hallucination detection primarily focus on quantifying internal uncertainty, which arises from missing or conflicting knowledge within the model. However, hallucinations can also stem from external uncertainty, where ambiguous user queries lead to multiple possible interpretations. In this work, we introduce **Semantic Volume**, a novel mathematical measure for quantifying both external and internal uncertainty in LLMs. Our approach perturbs queries and responses, embeds them in a semantic space, and computes the Gram matrix determinant of the embedding vectors, capturing their dispersion as a measure of uncertainty. Our framework provides a generalizable and unsupervised uncertainty detection method without requiring internal access to LLMs. We conduct extensive experiments on both external and internal uncertainty detections, demonstrating that our Semantic Volume method consistently outperforms existing baselines in both tasks. Additionally, we provide theoretical insights linking our measure to differential entropy, unifying and extending previous sampling-based uncertainty measures such as the semantic entropy. Semantic Volume is shown to be a robust and interpretable approach to improving the reliability of LLMs by systematically detecting uncertainty in both user queries and model responses.

Reasoning-enhanced large language models (RLLMs), whether explicitly trained for reasoning or prompted via chain-of-thought (CoT), have achieved state-of-the-art performance on many complex reasoning tasks. However, we uncover a surprising and previously overlooked phenomenon: explicit CoT reasoning can significantly degrade instruction-following accuracy. Evaluating 20+ models on two benchmarks: IFEval (with simple, rule-verifiable constraints) and ComplexBench (with complex, compositional constraints), we consistently observe performance drops when CoT prompting is applied. Through large-scale case studies and an attention-based analysis, we identify common patterns where reasoning either helps (e.g., with formatting or lexical precision) or hurts (e.g., by neglecting simple constraints or introducing unnecessary content). We propose a metric, constraint attention, to quantify model focus during generation and show that CoT reasoning often diverts attention away from instruction-relevant tokens. To mitigate these effects, we introduce and evaluate four strategies: in-context learning, self-reflection, self-selective reasoning, and classifier-selective reasoning. Our results demonstrate that selective reasoning strategies, particularly classifier-selective reasoning, can substantially recover lost performance. To our knowledge, this is the first work to systematically expose reasoning-induced failures in instruction-following and offer practical mitigation strategies.

Learning an effective outfit-level representation is critical for predicting the compatibility of items in an outfit, and retrieving complementary items for a partial outfit. We present a framework, OutfitTransformer, that uses the pro-posed task-specific tokens and leverages the self-attention mechanism to learn effective outfit-level representations en-coding the compatibility relations between all items in the entire outfit for addressing both compatibility prediction and complementary item retrieval. For compatibility pre-diction, we design an outfit token to capture a global out-fit representation and train the framework using a classification loss. For complementary item retrieval, we design a target item token that additionally takes the target item specification (in the form of a category or text description) into consideration. We train our framework using a pro-posed set-wise outfit ranking loss to generate a target item embedding given an outfit, and a target item specification as inputs. The generated target item embedding is then used to retrieve compatible items that match the rest of the out-fit. Additionally, we adopt a pre-training approach and a curriculum learning strategy to improve retrieval performance. Experiments show that our approach outperforms state-of-the-art methods on compatibility prediction, fill-in-the-blank, and complementary item retrieval tasks.

Recommending sets of items that include both personalized and compatible items is crucial to personalized styling programs such as Amazon’s Personal Shopper. There is both an extensive literature on learning generic fashion compatibility and also on personalization in fashion. However, recommending pairs of items that the customer would like to wear together is still less studied as it involves learning a compatibility metric personalized to each customer. We propose a new framework (PSA-Net) to learn compatibility that is personalized to the customer - a customer dependent subspace learning framework where attention weights of subspaces are learnt using customer representations. We evaluate our approach on compatibility data provided directly by customers. Our approach outperforms the non-personalized approach in predicting compatibility preferences of customers. In other words, an approach that learns a common compatibility metric for all customers. In addition, we compare the significance of feedback collected directly from customers to that of data collected from human stylists in predicting compatibility for Amazon customers.