There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of (approximately) "navigable" graphs over high-dimensional point sets. A graph is navigable if we can successfully move from any starting node to any target node using a greedy routing strategy where we always move to the neighbor that is closest to the destination according to the given distance function. The complete graph is obviously navigable for any point set, but the important question for applications is if sparser graphs can be constructed. While this question is fairly well understood in low-dimensions, we establish some of the first upper and lower bounds for high-dimensional point sets. First, we give a simple and efficient way to construct a navigable graph with average degree O(\sqrt{n \log n }) for any set of n points, in any dimension, for any distance function.

We introduce Exemplar VAEs, a family of generative models that bridge the gap between parametric and non-parametric, exemplar based generative models. Exemplar VAE is a variant of VAE with a non-parametric latent prior based on a Parzen window estimator. To sample from it, one first draws a random exemplar from a training set, then stochastically transforms that exemplar into a latent code and a new observation. We propose retrieval augmented training (RAT) as a way to speed up Exemplar VAE training by using approximate nearest neighbor search in the latent space to define a lower bound on log marginal likelihood. To enhance generalization, model parameters are learned using exemplar leave-one-out and subsampling.

Considering the importance of detecting hateful language, labeled hate speech data is expensive and time-consuming to collect, particularly for low-resource languages. Prior work has demonstrated the effectiveness of cross-lingual transfer learning and data augmentation in improving performance on tasks with limited labeled data. To develop an efficient and scalable cross-lingual transfer learning approach, we leverage nearest-neighbor retrieval to augment minimal labeled data in the target language, thereby enhancing detection performance. Specifically, we assume access to a small set of labeled training instances in the target language and use these to retrieve the most relevant labeled examples from a large multilingual hate speech detection pool. We evaluate our approach on eight languages and demonstrate that it consistently outperforms models trained solely on the target language data. Furthermore, in most cases, our method surpasses the current state-of-the-art. Notably, our approach is highly data-efficient, retrieving as small as 200 instances in some cases while maintaining superior performance. Moreover, it is scalable, as the retrieval pool can be easily expanded, and the method can be readily adapted to new languages and tasks. We also apply maximum marginal relevance to mitigate redundancy and filter out highly similar retrieved instances, resulting in improvements in some languages.

We introduce Gradual Abstract Argumentation for Case-Based Reasoning (Gradual AA-CBR), a data-driven, neurosymbolic classification model in which the outcome is determined by an argumentation debate structure that is learned simultaneously with neural-based feature extractors. Each argument in the debate is an observed case from the training data, favouring their labelling. Cases attack or support those with opposing or agreeing labellings, with the strength of each argument and relationship learned through gradient-based methods. This argumentation debate structure provides human-aligned reasoning, improving model interpretability compared to traditional neural networks (NNs). Unlike the existing purely symbolic variant, Abstract Argumentation for Case-Based Reasoning (AA-CBR), Gradual AA-CBR is capable of multi-class classification, automatic learning of feature and data point importance, assigning uncertainty values to outcomes, using all available data points, and does not require binary features. We show that Gradual AA-CBR performs comparably to NNs whilst significantly outperforming existing AA-CBR formulations.

In this technical note, we introduce and analyze AWNN: an adaptively weighted nearest neighbor method for performing matrix completion. Nearest neighbor (NN) methods are widely used in missing data problems across multiple disciplines such as in recommender systems and for performing counterfactual inference in panel data settings. Prior works have shown that in addition to being very intuitive and easy to implement, NN methods enjoy nice theoretical guarantees. However, the performance of majority of the NN methods rely on the appropriate choice of the radii and the weights assigned to each member in the nearest neighbor set and despite several works on nearest neighbor methods in the past two decades, there does not exist a systematic approach of choosing the radii and the weights without relying on methods like cross-validation. AWNN addresses this challenge by judiciously balancing the bias variance trade off inherent in weighted nearest-neighbor regression. We provide theoretical guarantees for the proposed method under minimal assumptions and support the theory via synthetic experiments.

This report addresses the challenge of limited labeled datasets for developing legal recommender systems, particularly in specialized domains like labor disputes. We propose a new approach leveraging the co-citation of legal articles within cases to establish similarity and enable algorithmic annotation. This method draws a parallel to the concept of case co-citation, utilizing cited articles as indicators of shared legal issues. To evaluate the labeled results, we employ a system that recommends similar cases based on plaintiffs' accusations, defendants' rebuttals, and points of disputes. The evaluation demonstrates that the recommender, with finetuned text embedding models and a reasonable BiLSTM module can recommend labor cases whose similarity was measured by the co-citation of the legal articles. This research contributes to the development of automated annotation techniques for legal documents, particularly in areas with limited access to comprehensive legal databases.

Agents powered by Large Language Models (LLMs) have recently demonstrated impressive capabilities in various tasks. Still, they face limitations in tasks requiring specific, structured knowledge, flexibility, or accountable decision-making. While agents are capable of perceiving their environments, forming inferences, planning, and executing actions towards goals, they often face issues such as hallucinations and lack of contextual memory across interactions. This paper explores how Case-Based Reasoning (CBR), a strategy that solves new problems by referencing past experiences, can be integrated into LLM agent frameworks. This integration allows LLMs to leverage explicit knowledge, enhancing their effectiveness. We systematically review the theoretical foundations of these enhanced agents, identify critical framework components, and formulate a mathematical model for the CBR processes of case retrieval, adaptation, and learning. We also evaluate CBR-enhanced agents against other methods like Chain-of-Thought reasoning and standard Retrieval-Augmented Generation, analyzing their relative strengths. Moreover, we explore how leveraging CBR's cognitive dimensions (including self-reflection, introspection, and curiosity) via goal-driven autonomy mechanisms can further enhance the LLM agent capabilities. Contributing to the ongoing research on neuro-symbolic hybrid systems, this work posits CBR as a viable technique for enhancing the reasoning skills and cognitive aspects of autonomous LLM agents.

The era of foundation models has revolutionized AI research, yet Graph Foundation Models (GFMs) remain constrained by the scarcity of large-scale graph corpora. Traditional graph data synthesis techniques primarily focus on simplistic structural operations, lacking the capacity to generate semantically rich nodes with meaningful textual attributes: a critical limitation for real-world applications. While large language models (LLMs) demonstrate exceptional text generation capabilities, their direct application to graph synthesis is impeded by context window limitations, hallucination phenomena, and structural consistency challenges. To address these issues, we introduce GraphMaster, the first multi-agent framework specifically designed for graph data synthesis in data-limited environments. GraphMaster orchestrates four specialized LLM agents (Manager, Perception, Enhancement, and Evaluation) that collaboratively optimize the synthesis process through iterative refinement, ensuring both semantic coherence and structural integrity. To rigorously evaluate our approach, we create new data-limited "Sub" variants of six standard graph benchmarks, specifically designed to test synthesis capabilities under realistic constraints. Additionally, we develop a novel interpretability assessment framework that combines human evaluation with a principled Grassmannian manifold-based analysis, providing both qualitative and quantitative measures of semantic coherence. Experimental results demonstrate that GraphMaster significantly outperforms traditional synthesis methods across multiple datasets, establishing a strong foundation for advancing GFMs in data-scarce environments.

The $k$-nearest-neighbor language model ($k$NN-LM), one of the retrieval-augmented language models, improves the perplexity for given text by directly accessing a large datastore built from any text data during inference. A widely held hypothesis for the success of $k$NN-LM is that its explicit memory, i.e., the datastore, enhances predictions for long-tail phenomena. However, prior works have primarily shown its ability to retrieve long-tail contexts, leaving the model's performance remain underexplored in estimating the probabilities of long-tail target tokens during inference. In this paper, we investigate the behavior of $k$NN-LM on low-frequency tokens, examining prediction probability, retrieval accuracy, token distribution in the datastore, and approximation error of the product quantization. Our experimental results reveal that $k$NN-LM does not improve prediction performance for low-frequency tokens but mainly benefits high-frequency tokens regardless of long-tail contexts in the datastore.

In this work, we explore the potential of large language models (LLMs) for generating functional test scripts, which necessitates understanding the dynamically evolving code structure of the target software. To achieve this, we propose a case-based reasoning (CBR) system utilizing a 4R cycle (i.e., retrieve, reuse, revise, and retain), which maintains and leverages a case bank of test intent descriptions and corresponding test scripts to facilitate LLMs for test script generation. To improve user experience further, we introduce Re4, an optimization method for the CBR system, comprising reranking-based retrieval finetuning and reinforced reuse finetuning. Specifically, we first identify positive examples with high semantic and script similarity, providing reliable pseudo-labels for finetuning the retriever model without costly labeling. Then, we apply supervised finetuning, followed by a reinforcement learning finetuning stage, to align LLMs with our production scenarios, ensuring the faithful reuse of retrieved cases. Extensive experimental results on two product development units from Huawei Datacom demonstrate the superiority of the proposed CBR+Re4. Notably, we also show that the proposed Re4 method can help alleviate the repetitive generation issues with LLMs.