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I generalize state-of-the-art approaches that decompose differences in the distribution of a variable of interest between two groups into a portion explained by covariates and a residual portion. The method that I propose relaxes the overlapping supports assumption, allowing the groups being compared to not necessarily share exactly the same covariate support. I illustrate my method revisiting the black-white wealth gap in the U.S. as a function of labor income and other variables. Traditionally used decomposition methods would trim (or assign zero weight to) observations that lie outside the common covariate support region. On the other hand, by allowing all observations to contribute to the existing wealth gap, I find that otherwise trimmed observations contribute from 3% to 19% to the overall wealth gap, at different portions of the wealth distribution.

As artificial intelligence becomes increasingly prevalent in scientific research, data-driven methodologies appear to overshadow traditional methods in resolving scientific problems. In this Perspective, we revisit a classic classification of scientific problems and rethink the evolution of scientific paradigms from the standpoint of data, algorithms, and computational power. We observe that the strengths of new paradigms have expanded the range of resolvable scientific problems, but the continued advancement of data, algorithms, and computational power is unlikely to bring a new paradigm. To tackle unresolved problems of organised complexity in more intricate systems, we argue that the integration of paradigms is a promising approach. Consequently, we propose behavioural rehearsing, checking what will happen in such systems through multiple times of simulation. One of the methodologies to realise it, sophisticated behavioural simulation (SBS), represents a higher level of paradigms integration based on foundational models to simulate complex social systems involving sophisticated human strategies and behaviours. SBS extends beyond the capabilities of traditional agent-based modelling simulation (ABMS), and therefore, makes behavioural rehearsing a potential solution to problems of organised complexity in complex human systems.

A fundamental problem in mathematics and network analysis is to find conditions under which a graph can be partitioned into smaller pieces. The most important tool for this partitioning is the Fiedler vector or discrete Cheeger inequality. These results relate the graph spectrum (eigenvalues of the normalized adjacency matrix) to the ability to break a graph into two pieces, with few edge deletions. An entire subfield of mathematics, called spectral graph theory, has emerged from these results. Yet these results do not say anything about the rich community structure exhibited by real-world networks, which typically have a significant fraction of edges contained in numerous densely clustered blocks. Inspired by the properties of real-world networks, we discover a new spectral condition that relates eigenvalue powers to a network decomposition into densely clustered blocks. We call this the \emph{spectral triadic decomposition}. Our relationship exactly predicts the existence of community structure, as commonly seen in real networked data. Our proof provides an efficient algorithm to produce the spectral triadic decomposition. We observe on numerous social, coauthorship, and citation network datasets that these decompositions have significant correlation with semantically meaningful communities.

Partially observable Markov decision processes (POMDPs) rely on the key assumption that probability distributions are precisely known. Robust POMDPs (RPOMDPs) alleviate this concern by defining imprecise probabilities, referred to as uncertainty sets. While robust MDPs have been studied extensively, work on RPOMDPs is limited and primarily focuses on algorithmic solution methods. We expand the theoretical understanding of RPOMDPs by showing that 1) different assumptions on the uncertainty sets affect optimal policies and values; 2) RPOMDPs have a partially observable stochastic game (POSG) semantic; and 3) the same RPOMDP with different assumptions leads to semantically different POSGs and, thus, different policies and values. These novel semantics for RPOMDPS give access to results for the widely studied POSG model; concretely, we show the existence of a Nash equilibrium. Finally, we classify the existing RPOMDP literature using our semantics, clarifying under which uncertainty assumptions these existing works operate.

To understand and summarize approval preferences and other binary evaluation data, it is useful to order the items on an axis which explains the data. In a political election using approval voting, this could be an ideological left-right axis such that each voter approves adjacent candidates, an analogue of single-peakedness. In a perfect axis, every approval set would be an interval, which is usually not possible, and so we need to choose an axis that gets closest to this ideal. The literature has developed algorithms for optimizing several objective functions (e.g., minimize the number of added approvals needed to get a perfect axis), but provides little help with choosing among different objectives. In this paper, we take a social choice approach and compare 5 different axis selection rules axiomatically, by studying the properties they satisfy. We establish some impossibility theorems, and characterize (within the class of scoring rules) the rule that chooses the axes that maximize the number of votes that form intervals, using the axioms of ballot monotonicity and resistance to cloning. Finally, we study the behavior of the rules on data from French election surveys, on the votes of justices of the US Supreme Court, and on synthetic data.

Recent research in causal inference has made important progress in addressing challenges to the external validity of trial findings. Such methods weight trial participant data to more closely resemble the distribution of effect-modifying covariates in a well-defined target population. In the presence of participant non-adherence to study medication, these methods effectively transport an intention-to-treat effect that averages over heterogeneous compliance behaviors. In this paper, we develop a principal stratification framework to identify causal effects conditioning on both on compliance behavior and membership in the target population. We also develop non-parametric efficiency theory for and construct efficient estimators of such "transported" principal causal effects and characterize their finite-sample performance in simulation experiments. While this work focuses on treatment non-adherence, the framework is applicable to a broad class of estimands that target effects in clinically-relevant, possibly latent subsets of a target population.

Autonomous driving perception models are typically composed of multiple functional modules that interact through complex relationships to accomplish environment understanding. However, perception models are predominantly optimized as a black box through end-to-end training, lacking independent evaluation of functional modules, which poses difficulties for interpretability and optimization. Pioneering in the issue, we propose an evaluation method based on feature map analysis to gauge the convergence of model, thereby assessing functional modules' training maturity. We construct a quantitative metric named as the Feature Map Convergence Score (FMCS) and develop Feature Map Convergence Evaluation Network (FMCE-Net) to measure and predict the convergence degree of models respectively. FMCE-Net achieves remarkable predictive accuracy for FMCS across multiple image classification experiments, validating the efficacy and robustness of the introduced approach. To the best of our knowledge, this is the first independent evaluation method for functional modules, offering a new paradigm for the training assessment towards perception models.

AlphaFold can be used for both single-chain and multi-chain protein structure prediction, while the latter becomes extremely challenging as the number of chains increases. In this work, by taking each chain as a node and assembly actions as edges, we show that an acyclic undirected connected graph can be used to predict the structure of multi-chain protein complexes (a.k.a., protein complex modelling, PCM). However, there are still two challenges: 1) The huge combinatorial optimization space of $N^{N-2}$ ($N$ is the number of chains) for the PCM problem can easily lead to high computational cost. 2) The scales of protein complexes exhibit distribution shift due to variance in chain numbers, which calls for the generalization in modelling complexes of various scales. To address these challenges, we propose GAPN, a Generative Adversarial Policy Network powered by domain-specific rewards and adversarial loss through policy gradient for automatic PCM prediction. Specifically, GAPN learns to efficiently search through the immense assembly space and optimize the direct docking reward through policy gradient. Importantly, we design an adversarial reward function to enhance the receptive field of our model. In this way, GAPN will simultaneously focus on a specific batch of complexes and the global assembly rules learned from complexes with varied chain numbers. Empirically, we have achieved both significant accuracy (measured by RMSD and TM-Score) and efficiency improvements compared to leading PCM softwares.

Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.