The lifted multicut problem is a combinatorial optimization problem whose feasible solutions relate one-to-one to the decompositions of a graph $G = (V, E)$. Given an augmentation $\widehat{G} = (V, E \cup F)$ of $G$ and given costs $c \in \mathbb{R}^{E \cup F}$, the objective is to minimize the sum of those $c_{uw}$ with $uw \in E \cup F$ for which $u$ and $w$ are in distinct components. For $F = \emptyset$, the problem specializes to the multicut problem, and for $E = \tbinom{V}{2}$ to the clique partitioning problem. We study a binary linear program formulation of the lifted multicut problem. More specifically, we contribute to the analysis of the associated lifted multicut polytopes: Firstly, we establish a necessary, sufficient and efficiently decidable condition for a lower box inequality to define a facet. Secondly, we show that deciding whether a cut inequality of the binary linear program defines a facet is NP-hard.
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Fairness is a critical objective in policy design and algorithmic decision-making. Identifying the causal pathways of unfairness requires knowledge of the underlying structural causal model, which may be incomplete or unavailable. This limits the practicality of causal fairness analysis in complex or low-knowledge domains. To mitigate this practicality gap, we advocate for developing efficient causal discovery methods for fairness applications. To this end, we introduce local discovery for direct discrimination (LD3): a polynomial-time algorithm that recovers structural evidence of direct discrimination. LD3 performs a linear number of conditional independence tests with respect to variable set size. Moreover, we propose a graphical criterion for identifying the weighted controlled direct effect (CDE), a qualitative measure of direct discrimination. We prove that this criterion is satisfied by the knowledge returned by LD3, increasing the accessibility of the weighted CDE as a causal fairness measure. Taking liver transplant allocation as a case study, we highlight the potential impact of LD3 for modeling fairness in complex decision systems. Results on real-world data demonstrate more plausible causal relations than baselines, which took 197x to 5870x longer to execute.
We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set of limit probabilities is a finite union of closed intervals. Moreover, we characterize the degree sequences for which this closure set is the interval $[0,1]$, a property that is intimately related with the probability that the random graph is acyclic. As a side result, we compile a full description of the cycle distribution of random graphs and study their fragment (disjoint union of unicyclic components) in the subcritical regime. Finally, we amend the proof of the existence of limit probabilities for first order properties in random graphs with a given degree sequence; this result was already claimed by Lynch~[IEEE LICS 2003] but his proof contained some inaccuracies.
Data uncertainties, such as sensor noise, occlusions or limitations in the acquisition method can introduce irreducible ambiguities in images, which result in varying, yet plausible, semantic hypotheses. In Machine Learning, this ambiguity is commonly referred to as aleatoric uncertainty. In image segmentation, latent density models can be utilized to address this problem. The most popular approach is the Probabilistic U-Net (PU-Net), which uses latent Normal densities to optimize the conditional data log-likelihood Evidence Lower Bound. In this work, we demonstrate that the PU-Net latent space is severely sparse and heavily under-utilized. To address this, we introduce mutual information maximization and entropy-regularized Sinkhorn Divergence in the latent space to promote homogeneity across all latent dimensions, effectively improving gradient-descent updates and latent space informativeness. Our results show that by applying this on public datasets of various clinical segmentation problems, our proposed methodology receives up to 11% performance gains compared against preceding latent variable models for probabilistic segmentation on the Hungarian-Matched Intersection over Union. The results indicate that encouraging a homogeneous latent space significantly improves latent density modeling for medical image segmentation.
Counterfactual explanations provide a popular method for analyzing the predictions of black-box systems, and they can offer the opportunity for computational recourse by suggesting actionable changes on how to change the input to obtain a different (i.e.\ more favorable) system output. However, recent work highlighted their vulnerability to different types of manipulations. This work studies the vulnerability of counterfactual explanations to data poisoning. We formally introduce and investigate data poisoning in the context of counterfactual explanations for increasing the cost of recourse on three different levels: locally for a single instance, or a sub-group of instances, or globally for all instances. In this context, we characterize and prove the correctness of several different data poisonings. We also empirically demonstrate that state-of-the-art counterfactual generation methods and toolboxes are vulnerable to such data poisoning.
The classical theory of Kosambi-Cartan-Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in terms of five geometrical invariants, of which the second corresponds to the so-called Jacobi stability of the system. Different from that of the Lyapunov stability that has been studied extensively in the literature, the analysis of the Jacobi stability has been investigated more recently using geometrical concepts and tools. It turns out that the existing work on the Jacobi stability analysis remains theoretical and the problem of algorithmic and symbolic treatment of Jacobi stability analysis has yet to be addressed. In this paper, we initiate our study on the problem for a class of ODE systems of arbitrary dimension and propose two algorithmic schemes using symbolic computation to check whether a nonlinear dynamical system may exhibit Jacobi stability. The first scheme, based on the construction of the complex root structure of a characteristic polynomial and on the method of quantifier elimination, is capable of detecting the existence of the Jacobi stability of the given dynamical system. The second algorithmic scheme exploits the method of semi-algebraic system solving and allows one to determine conditions on the parameters for a given dynamical system to have a prescribed number of Jacobi stable fixed points. Several examples are presented to demonstrate the effectiveness of the proposed algorithmic schemes.
Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.
Believable proxies of human behavior can empower interactive applications ranging from immersive environments to rehearsal spaces for interpersonal communication to prototyping tools. In this paper, we introduce generative agents--computational software agents that simulate believable human behavior. Generative agents wake up, cook breakfast, and head to work; artists paint, while authors write; they form opinions, notice each other, and initiate conversations; they remember and reflect on days past as they plan the next day. To enable generative agents, we describe an architecture that extends a large language model to store a complete record of the agent's experiences using natural language, synthesize those memories over time into higher-level reflections, and retrieve them dynamically to plan behavior. We instantiate generative agents to populate an interactive sandbox environment inspired by The Sims, where end users can interact with a small town of twenty five agents using natural language. In an evaluation, these generative agents produce believable individual and emergent social behaviors: for example, starting with only a single user-specified notion that one agent wants to throw a Valentine's Day party, the agents autonomously spread invitations to the party over the next two days, make new acquaintances, ask each other out on dates to the party, and coordinate to show up for the party together at the right time. We demonstrate through ablation that the components of our agent architecture--observation, planning, and reflection--each contribute critically to the believability of agent behavior. By fusing large language models with computational, interactive agents, this work introduces architectural and interaction patterns for enabling believable simulations of human behavior.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.
We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.
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