Legal case retrieval (LCR) aims to automatically scour for comparable legal cases based on a given query, which is crucial for offering relevant precedents to support the judgment in intelligent legal systems. Due to similar goals, it is often associated with a similar case matching (LCM) task. To address them, a daunting challenge is assessing the uniquely defined legal-rational similarity within the judicial domain, which distinctly deviates from the semantic similarities in general text retrieval. Past works either tagged domain-specific factors or incorporated reference laws to capture legal-rational information. However, their heavy reliance on expert or unrealistic assumptions restricts their practical applicability in real-world scenarios. In this paper, we propose an end-to-end model named LCM-LAI to solve the above challenges. Through meticulous theoretical analysis, LCM-LAI employs a dependent multi-task learning framework to capture legal-rational information within legal cases by a law article prediction (LAP) sub-task, without any additional assumptions in inference. Besides, LCM-LAI proposes an article-aware attention mechanism to evaluate the legal-rational similarity between across-case sentences based on law distribution, which is more effective than conventional semantic similarity. Weperform a series of exhaustive experiments including two different tasks involving four real-world datasets. Results demonstrate that LCM-LAI achieves state-of-the-art performance.

Many modern methods for prediction leverage nearest neighbor search to find past training examples most similar to a test example, an idea that dates back in text to at least the 11th century and has stood the test of time. This monograph aims to explain the success of these methods, both in theory, for which we cover foundational nonasymptotic statistical guarantees on nearest-neighbor-based regression and classification, and in practice, for which we gather prominent methods for approximate nearest neighbor search that have been essential to scaling prediction systems reliant on nearest neighbor analysis to handle massive datasets. Furthermore, we discuss connections to learning distances for use with nearest neighbor methods, including how random decision trees and ensemble methods learn nearest neighbor structure, as well as recent developments in crowdsourcing and graphons. In terms of theory, our focus is on nonasymptotic statistical guarantees, which we state in the form of how many training data and what algorithm parameters ensure that a nearest neighbor prediction method achieves a user-specified error tolerance. We begin with the most general of such results for nearest neighbor and related kernel regression and classification in general metric spaces. In such settings in which we assume very little structure, what enables successful prediction is smoothness in the function being estimated for regression, and a low probability of landing near the decision boundary for classification. In practice, these conditions could be difficult to verify for a real dataset. We then cover recent guarantees on nearest neighbor prediction in the three case studies of time series forecasting, recommending products to people over time, and delineating human organs in medical images by looking at image patches. In these case studies, clustering structure enables successful prediction.

Given the rapid development of Legal AI, a lot of attention has been paid to one of the most important legal AI tasks--similar case retrieval, especially with language models to use. In our paper, however, we try to improve the ranking performance of current models from the perspective of learning to rank instead of language models. Specifically, we conduct experiments using a pairwise method--RankSVM as the classifier to substitute a fully connected layer, combined with commonly used language models on similar case retrieval datasets LeCaRDv1 and LeCaRDv2. We finally come to the conclusion that RankSVM could generally help improve the retrieval performance on the LeCaRDv1 and LeCaRDv2 datasets compared with original classifiers by optimizing the precise ranking. It could also help mitigate overfitting owing to class imbalance. Our code is available in https://github.com/liuyuqi123study/RankSVM_for_SLR

Therefore, the second property holds for any far away point y, i.e. y q cr. The first property holds for any close point x, i.e. x q r, since their projection value onto r Figure 1 shows the recall-speed comparison between Falconn++ and recent theoretical LSF frameworks [2, 3]. All 3 data sets use L = 100, α = {0.1, We use D = {128, 256, 256} for NYTimes, Glove200, and Glove300. Figure 1 shows superior performance of Falconn++ compared to the theoretical LSF with α = {0.1,

Falconn++ can filter out potential far away points in any hash bucket before querying, which results in higher quality candidates compared to other hashing-based solutions. Theoretically, Falconn++ asymptotically achieves lower query time complexity than Falconn, an optimal locality-sensitive hashing scheme on angular distance. Empirically, Falconn++ achieves higher recall-speed tradeoffs than Falconn on many real-world data sets. Falconn++ is also competitive with HNSW, an efficient representative of graphbased solutions on high search recall regimes.

We present the first sample compression algorithm for nearest neighbors with nontrivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly optimal. Our result yields new insight into margin-based nearest neighbor classification in metric spaces and allows us to significantly sharpen and simplify existing bounds. Some encouraging empirical results are also presented.

The paper attempts to scale nearest neighbor search using heterogenous memory hardware. In this regard, authors devised a practical trick on top of HNSW. It is a clean node promotion strategy along the memory hierarchy using the degree information. The method was evaluated on some common large datasets, but not necessarily difficult ones. Reviewers found the setup to leverage the memory hierarchy interesting and the benefits obtained from it appears promising.

Fast algorithms for nearest neighbor (NN) search have in large part focused on L2 distance. Here we develop an approach for L1 distance that begins with an explicit and exact embedding of the points into L2. We show how this embedding can efficiently be combined with random projection methods for L2 NN search, such as locality-sensitive hashing or random projection trees. We rigorously establish the correctness of the methodology and show by experimentation that it is competitive in practice with available alternatives.

We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires k as the sample size n) into the functional of interest, the estimators we consider fix k and perform a bias correction. This can be more efficient computationally, and, as we show, statistically, leading to faster convergence rates. Our framework unifies several previous estimators, for most of which ours are the first finite sample guarantees.

Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees. We study the worst-case performance of recent graph-based approximate nearest neighbor search algorithms, such as HNSW, NSG and DiskANN. For DiskANN, we show that its "slow preprocessing" version provably supports approximate nearest neighbor search query with constant approximation ratio and poly-logarithmic query time, on data sets with bounded "intrinsic" dimension. For the other data structure variants studied, including DiskANN with "fast preprocessing", HNSW and NSG, we present a family of instances on which the empirical query time required to achieve a "reasonable" accuracy is linear in instance size. For example, for DiskANN, we show that the query procedure can take at least 0.1n steps on instances of size n before it encounters any of the 5 nearest neighbors of the query.