Structured prediction methods have been remarkably successful in learning mappings between input observations and output configurations [1; 2; 3]. The central guiding formulation involves learning a scoring function that recovers the configuration as the highest scoring assignment. In contrast, in a game theoretic setting, myopic strategic interactions among players lead to a Nash equilibrium or locally optimal configuration rather than highest scoring global configuration. Learning games therefore involves, at best, enforcement of local consistency constraints as recently advocated [4].

We provide novel theoretical insights on structured prediction in the context of efficient convex surrogate loss minimization with consistency guarantees. For any task loss, we construct a convex surrogate that can be optimized via stochastic gradient descent and we prove tight bounds on the so-called "calibration function" relating the excess surrogate risk to the actual risk. In contrast to prior related work, we carefully monitor the effect of the exponential number of classes in the learning guarantees as well as on the optimization complexity. As an interesting consequence, we formalize the intuition that some task losses make learning harder than others, and that the classical 0-1 loss is ill-suited for structured prediction.

Case law is instrumental in shaping our understanding of human rights, including the right to adequate housing. The HUDOC database provides access to the textual content of case law from the European Court of Human Rights (ECtHR), along with some metadata. While this metadata includes valuable information, such as the application number and the articles addressed in a case, it often lacks detailed substantive insights, such as the specific issues a case covers. This underscores the need for detailed analysis to extract such information. However, given the size of the database - containing over 40,000 cases - an automated solution is essential. In this study, we focus on the right to adequate housing and aim to build models to detect cases related to housing and eviction issues. Our experiments show that the resulting models not only provide performance comparable to more sophisticated approaches but are also interpretable, offering explanations for their decisions by highlighting the most influential words. The application of these models led to the identification of new cases that were initially overlooked during data collection. This suggests that NLP approaches can be effectively applied to categorise case law based on the specific issues they address.

We address the problem of multi-class classification in the case where the number of classes is very large. We propose a double sampling strategy on top of a multi-class to binary reduction strategy, which transforms the original multi-class problem into a binary classification problem over pairs of examples. The aim of the sampling strategy is to overcome the curse of long-tailed class distributions exhibited in majority of large-scale multi-class classification problems and to reduce the number of pairs of examples in the expanded data. We show that this strategy does not alter the consistency of the empirical risk minimization principle defined over the double sample reduction. Experiments are carried out on DMOZ and Wikipedia collections with 10,000 to 100,000 classes where we show the efficiency of the proposed approach in terms of training and prediction time, memory consumption, and predictive performance with respect to state-of-the-art approaches.

The Universal Approximation Theorem posits that neural networks can theoretically possess unlimited approximation capacity with a suitable activation function and a freely chosen or trained set of parameters. However, a more practical scenario arises when these neural parameters, especially the nonlinear weights and biases, are bounded. This leads us to question: \textbf{Does the approximation capacity of a neural network remain universal, or does it have a limit when the parameters are practically bounded? And if it has a limit, how can it be measured?} Our theoretical study indicates that while universal approximation is theoretically feasible, in practical numerical scenarios, Deep Neural Networks (DNNs) with any analytic activation functions (such as Tanh and Sigmoid) can only be approximated by a finite-dimensional vector space under a bounded nonlinear parameter space (NP space), whether in a continuous or discrete sense. Based on this study, we introduce the concepts of \textit{$\epsilon$ outer measure} and \textit{Numerical Span Dimension (NSdim)} to quantify the approximation capacity limit of a family of networks both theoretically and practically. Furthermore, drawing on our new theoretical study and adopting a fresh perspective, we strive to understand the relationship between back-propagation neural networks and random parameter networks (such as the Extreme Learning Machine (ELM)) with both finite and infinite width. We also aim to provide fresh insights into regularization, the trade-off between width and depth, parameter space, width redundancy, condensation, and other related important issues.

This study extends the examination of the Efficient-Market Hypothesis in Bitcoin market during a five year fluctuation period, from September 1 2017 to September 1 2022, by analyzing 28,739,514 qualified tweets containing the targeted topic "Bitcoin". Unlike previous studies, we extracted fundamental keywords as an informative proxy for carrying out the study of the EMH in the Bitcoin market rather than focusing on sentiment analysis, information volume, or price data. We tested market efficiency in hourly, 4-hourly, and daily time periods to understand the speed and accuracy of market reactions towards the information within different thresholds. A sequence of machine learning methods and textual analyses were used, including measurements of distances of semantic vector spaces of information, keywords extraction and encoding model, and Light Gradient Boosting Machine (LGBM) classifiers. Our results suggest that 78.06% (83.08%), 84.63% (87.77%), and 94.03% (94.60%) of hourly, 4-hourly, and daily bullish (bearish) market movements can be attributed to public information within organic tweets.

We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more. We prove a universal approximation theorem for TVS-FNNs, which demonstrates their capacity to approximate any continuous function defined on this expanded input space.

Despite the potential of language model-based agents to solve real-world tasks such as web navigation, current methods still struggle with long-horizon tasks with complex action trajectories. In contrast, humans can flexibly solve complex tasks by learning reusable task workflows from past experiences and using them to guide future actions. To build agents that can similarly benefit from this process, we introduce Agent Workflow Memory (AWM), a method for inducing commonly reused routines, i.e., workflows, and selectively providing workflows to the agent to guide subsequent generations. AWM flexibly applies to both offline and online scenarios, where agents induce workflows from training examples beforehand or from test queries on the fly. We experiment on two major web navigation benchmarks -- Mind2Web and WebArena -- that collectively cover 1000+ tasks from 200+ domains across travel, shopping, and social media, among others. AWM substantially improves the baseline results by 24.6% and 51.1% relative success rate on Mind2Web and WebArena while reducing the number of steps taken to solve WebArena tasks successfully. Furthermore, online AWM robustly generalizes in cross-task, website, and domain evaluations, surpassing baselines from 8.9 to 14.0 absolute points as train-test task distribution gaps widen.

In the field of eXplainable AI (XAI) in language models, the progression from local explanations of individual decisions to global explanations with high-level concepts has laid the groundwork for mechanistic interpretability, which aims to decode the exact operations. However, this paradigm has not been adequately explored in image models, where existing methods have primarily focused on classspecific interpretations. This paper introduces a novel approach to systematically trace the entire pathway from input through all intermediate layers to the final output within the whole dataset. We utilize Pointwise Feature Vectors (PFVs) and Effective Receptive Fields (ERFs) to decompose model embeddings into interpretable Concept Vectors. Then, we calculate the relevance between concept vectors with our Generalized Integrated Gradients (GIG), enabling a comprehensive, dataset-wide analysis of model behavior. In the field of eXplainable AI (XAI), efforts have historically transitioned from Local explanation to Global explanation to Mechanistic Interpretability. While local explanation methods including Selvaraju et al. (2016); Montavon et al. (2017); Sundararajan et al. (2017); Han et al. (2024) have focused on explaining specific decisions for individual instances, global explanation methods seek to uncover overall patterns and behaviors applicable across the entire dataset (Wu et al., 2022; Xuanyuan et al., 2023; Singh et al., 2024).

Recent advancements in function calling and tool use have significantly enhanced the capabilities of large language models (LLMs) by enabling them to interact with external information sources and execute complex tasks. However, the limited context window of LLMs presents challenges when a large number of tools are available, necessitating efficient methods to manage prompt length and maintain accuracy. Existing approaches, such as fine-tuning LLMs or leveraging their reasoning capabilities, either require frequent retraining or incur significant latency overhead. A more efficient solution involves training smaller models to retrieve the most relevant tools for a given query, although this requires high quality, domain-specific data. To address those challenges, we present a novel framework for generating synthetic data for tool retrieval applications and an efficient data-driven tool retrieval strategy using small encoder models. Empowered by LLMs, we create ToolBank, a new tool retrieval dataset that reflects real human user usages. For tool retrieval methodologies, we propose novel approaches: (1) Tool2Vec: usage-driven tool embedding generation for tool retrieval, (2) ToolRefiner: a staged retrieval method that iteratively improves the quality of retrieved tools, and (3) MLC: framing tool retrieval as a multi-label classification problem. With these new methods, we achieve improvements of up to 27.28 in Recall@K on the ToolBench dataset and 30.5 in Recall@K on ToolBank. Additionally, we present further experimental results to rigorously validate our methods. Our code is available at \url{https://github.com/SqueezeAILab/Tool2Vec}