In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values are then applied to several conditional testing problems to illustrate their practicality. Firstly, we propose a conditional outlier detection procedure to test for outliers in the conditional distribution with finite-sample false discovery rate (FDR) control. We also introduce a novel conditional label screening problem with the goal of screening multivariate response variables and propose a screening procedure to control the family-wise error rate (FWER). Finally, we consider the two-sample conditional distribution test and define a weighted U-statistic through the aggregation of localized p-values. Numerical simulations and real-data examples validate the superior performance of our proposed strategies.
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Text embeddings enable various applications, but their performance deteriorates on longer texts. In this paper, we find that the performance degradation is due to a phenomenon called Length Collapse, where longer text embeddings collapse into a narrow space. This collapse results in a distributional inconsistency between embeddings of different text lengths, ultimately hurting the performance of downstream tasks. Theoretically, by considering the self-attention mechanism inherently functions as a low-pass filter, we prove that long sequences increase the attenuation rate of the low-pass filter effect of the self-attention mechanism. With layers going deeper, excessive low-pass filtering causes the token signals to retain only their Direct-Current (DC) component, which means the input token feature maps will collapse into a narrow space, especially in long texts. Based on the above analysis, we propose to mitigate the undesirable length collapse limitation by introducing a temperature in softmax(), which achieves a higher low-filter attenuation rate. The tuning-free method, called TempScale, can be plugged into multiple transformer-based embedding models. Empirically, we demonstrate that TempScale can improve existing embedding models, especially on long text inputs, bringing up to 0.53% performance gains on 40 datasets from Massive Text Embedding Benchmark (MTEB) and 0.82% performance gains on 4 datasets from LongEmbed, which specifically focuses on long context retrieval.
Unit derived schemes applied to Hadamard matrices are used to construct and analyse linear block and convolutional codes. Codes are constructed to prescribed types, lengths and rates and multiple series of self-dual, dual-containing, linear complementary dual and quantum error-correcting of both linear block {\em and} convolutional codes are derived.
In this paper, we construct and compare algorithmic approaches to solve the Preference Consistency Problem for preference statements based on hierarchical models. Instances of this problem contain a set of preference statements that are direct comparisons (strict and non-strict) between some alternatives, and a set of evaluation functions by which all alternatives can be rated. An instance is consistent based on hierarchical preference models, if there exists an hierarchical model on the evaluation functions that induces an order relation on the alternatives by which all relations given by the preference statements are satisfied. Deciding if an instance is consistent is known to be NP-complete for hierarchical models. We develop three approaches to solve this decision problem. The first involves a Mixed Integer Linear Programming (MILP) formulation, the other two are recursive algorithms that are based on properties of the problem by which the search space can be pruned. Our experiments on synthetic data show that the recursive algorithms are faster than solving the MILP formulation and that the ratio between the running times increases extremely quickly.
In this paper, we investigate the existence of parameterized algorithms running in subexponential time for two fundamental cycle-hitting problems: Feedback Vertex Set (FVS) and Triangle Hitting (TH). We focus on the class of pseudo-disk graphs, which forms a common generalization of several graph classes where such results exist, like disk graphs and square graphs. In these graphs, we show that TH can be solved in time $2^{O(k^{3/4}\log k)}n^{O(1)}$, and given a geometric representation FVS can be solved in time $2^{O(k^{6/7}\log k)}n^{O(1)}$.
We develop denotational and operational semantics designed with continuations for process calculi based on CCS extended with mechanisms offering support for multiparty interactions. We investigate the abstractness of this continuation semantics. We show that our continuation-based denotational models are weakly abstract with respect to the corresponding operational models.
In this paper, we propose a flexible SLAM framework, XRDSLAM. It adopts a modular code design and a multi-process running mechanism, providing highly reusable foundational modules such as unified dataset management, 3d visualization, algorithm configuration, and metrics evaluation. It can help developers quickly build a complete SLAM system, flexibly combine different algorithm modules, and conduct standardized benchmarking for accuracy and efficiency comparison. Within this framework, we integrate several state-of-the-art SLAM algorithms with different types, including NeRF and 3DGS based SLAM, and even odometry or reconstruction algorithms, which demonstrates the flexibility and extensibility. We also conduct a comprehensive comparison and evaluation of these integrated algorithms, analyzing the characteristics of each. Finally, we contribute all the code, configuration and data to the open-source community, which aims to promote the widespread research and development of SLAM technology within the open-source ecosystem.
This book is written to offer a humble, but unified, treatment of e-values in hypothesis testing. The book is organized into three parts: Fundamental Concepts, Core Ideas, and Advanced Topics. The first part includes three chapters that introduce the basic concepts. The second part includes five chapters of core ideas such as universal inference, log-optimality, e-processes, operations on e-values, and e-values in multiple testing. The third part contains five chapters of advanced topics. We hope that, by putting the materials together in this book, the concept of e-values becomes more accessible for educational, research, and practical use.
There exists an extremely wide array of LLM benchmarking tasks, whereas oftentimes a single number is the most actionable for decision-making, especially by non-experts. No such aggregation schema exists that is not Elo-based, which could be costly or time-consuming. Here we propose a method to aggregate performance across a general space of benchmarks, nicknamed Project "MPG," dubbed Model Performance and Goodness, additionally referencing a metric widely understood to be an important yet inaccurate and crude measure of car performance. Here, we create two numbers: a "Goodness" number (answer accuracy) and a "Fastness" number (cost or QPS). We compare models against each other and present a ranking according to our general metric as well as subdomains. We find significant agreement between the raw Pearson correlation of our scores and those of Chatbot Arena, even improving on the correlation of the MMLU leaderboard to Chatbot Arena.
To retrieve more relevant, appropriate and useful documents given a query, finding clues about that query through the text is crucial. Recent deep learning models regard the task as a term-level matching problem, which seeks exact or similar query patterns in the document. However, we argue that they are inherently based on local interactions and do not generalise to ubiquitous, non-consecutive contextual relationships.In this work, we propose a novel relevance matching model based on graph neural networks to leverage the document-level word relationships for ad-hoc retrieval. In addition to the local interactions, we explicitly incorporate all contexts of a term through the graph-of-word text format. Matching patterns can be revealed accordingly to provide a more accurate relevance score. Our approach significantly outperforms strong baselines on two ad-hoc benchmarks. We also experimentally compare our model with BERT and show our ad-vantages on long documents.
Many real-world problems can be represented as graph-based learning problems. In this paper, we propose a novel framework for learning spatial and attentional convolution neural networks on arbitrary graphs. Different from previous convolutional neural networks on graphs, we first design a motif-matching guided subgraph normalization method to capture neighborhood information. Then we implement subgraph-level self-attentional layers to learn different importances from different subgraphs to solve graph classification problems. Analogous to image-based attentional convolution networks that operate on locally connected and weighted regions of the input, we also extend graph normalization from one-dimensional node sequence to two-dimensional node grid by leveraging motif-matching, and design self-attentional layers without requiring any kinds of cost depending on prior knowledge of the graph structure. Our results on both bioinformatics and social network datasets show that we can significantly improve graph classification benchmarks over traditional graph kernel and existing deep models.
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