Daily Papers

Conventional multi-label recognition methods often focus on label confidence, frequently overlooking the pivotal role of partial order relations consistent with human preference. To resolve these issues, we introduce a novel method for multimodal label relevance ranking, named Label Relevance Ranking with Proximal Policy Optimization (LR2PPO), which effectively discerns partial order relations among labels. LR2PPO first utilizes partial order pairs in the target domain to train a reward model, which aims to capture human preference intrinsic to the specific scenario. Furthermore, we meticulously design state representation and a policy loss tailored for ranking tasks, enabling LR2PPO to boost the performance of label relevance ranking model and largely reduce the requirement of partial order annotation for transferring to new scenes. To assist in the evaluation of our approach and similar methods, we further propose a novel benchmark dataset, LRMovieNet, featuring multimodal labels and their corresponding partial order data. Extensive experiments demonstrate that our LR2PPO algorithm achieves state-of-the-art performance, proving its effectiveness in addressing the multimodal label relevance ranking problem. Codes and the proposed LRMovieNet dataset are publicly available at https://github.com/ChazzyGordon/LR2PPO.

Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar\'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic space. The shadow cones framework generalizes entailment cones to a broad class of formulations and hyperbolic space models beyond the Poincar\'e ball. This results in clear advantages over existing constructions: for example, shadow cones possess better optimization properties over constructions limited to the Poincar\'e ball. Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. These results indicate that shadow cones are an effective way to model partial orders in hyperbolic space, offering physically intuitive and novel insights about the nature of such structures.

We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both temporal and contemporaneous causal relations. One may ask if temporal and contemporaneous relations should be treated differently. The presented algorithm gradually refines a causal graph by learning long-term temporal relations before short-term ones, where contemporaneous relations are learned last. This ordering of causal relations to be learnt leads to a reduction in the required number of statistical tests. We validate this reduction empirically and demonstrate that it leads to higher accuracy for synthetic data and more plausible causal graphs for real-world data compared to state-of-the-art algorithms.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

Graph generation has been dominated by autoregressive models due to their simplicity and effectiveness, despite their sensitivity to ordering. Yet diffusion models have garnered increasing attention, as they offer comparable performance while being permutation-invariant. Current graph diffusion models generate graphs in a one-shot fashion, but they require extra features and thousands of denoising steps to achieve optimal performance. We introduce PARD, a Permutation-invariant Auto Regressive Diffusion model that integrates diffusion models with autoregressive methods. PARD harnesses the effectiveness and efficiency of the autoregressive model while maintaining permutation invariance without ordering sensitivity. Specifically, we show that contrary to sets, elements in a graph are not entirely unordered and there is a unique partial order for nodes and edges. With this partial order, PARD generates a graph in a block-by-block, autoregressive fashion, where each block's probability is conditionally modeled by a shared diffusion model with an equivariant network. To ensure efficiency while being expressive, we further propose a higher-order graph transformer, which integrates transformer with PPGN. Like GPT, we extend the higher-order graph transformer to support parallel training of all blocks. Without any extra features, PARD achieves state-of-the-art performance on molecular and non-molecular datasets, and scales to large datasets like MOSES containing 1.9M molecules.

A sequence of operators T_n from a Hilbert space {mathfrak H} to Hilbert spaces {mathfrak K}_n which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator T from {mathfrak H} to a Hilbert space {mathfrak K}. Moreover, the closability or closedness of T_n is preserved in the limit. The closures converge likewise and the connection between the limits is investigated. There is no similar way of dealing directly with linear relations. However, the sequence of closures is still nondecreasing and then the convergence is governed by the monotonicity principle. There are some related results for nonincreasing sequences.

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2\%uparrow in prediction accuracy over four datasets therein.

Understanding the abilities of LLMs to reason about natural language plans, such as instructional text and recipes, is critical to reliably using them in decision-making systems. A fundamental aspect of plans is the temporal order in which their steps needs to be executed, which reflects the underlying causal dependencies between them. We introduce CaT-Bench, a benchmark of Step Order Prediction questions, which test whether a step must necessarily occur before or after another in cooking recipe plans. We use this to evaluate how well frontier LLMs understand causal and temporal dependencies. We find that SOTA LLMs are underwhelming (best zero-shot is only 0.59 in F1), and are biased towards predicting dependence more often, perhaps relying on temporal order of steps as a heuristic. While prompting for explanations and using few-shot examples improve performance, the best F1 result is only 0.73. Further, human evaluation of explanations along with answer correctness show that, on average, humans do not agree with model reasoning. Surprisingly, we also find that explaining after answering leads to better performance than normal chain-of-thought prompting, and LLM answers are not consistent across questions about the same step pairs. Overall, results show that LLMs' ability to detect dependence between steps has significant room for improvement.

Many production processes are characterized by numerous and complex cause-and-effect relationships. Since they are only partially known they pose a challenge to effective process control. In this work we present how Structural Equation Models can be used for deriving cause-and-effect relationships from the combination of prior knowledge and process data in the manufacturing domain. Compared to existing applications, we do not assume linear relationships leading to more informative results.

We consider higher-order linear-chain conditional random fields (HO-LC-CRFs) for sequence modelling, and use sum-product networks (SPNs) for representing higher-order input- and output-dependent factors. SPNs are a recently introduced class of deep models for which exact and efficient inference can be performed. By combining HO-LC-CRFs with SPNs, expressive models over both the output labels and the hidden variables are instantiated while still enabling efficient exact inference. Furthermore, the use of higher-order factors allows us to capture relations of multiple input segments and multiple output labels as often present in real-world data. These relations can not be modelled by the commonly used first-order models and higher-order models with local factors including only a single output label. We demonstrate the effectiveness of our proposed models for sequence labeling. In extensive experiments, we outperform other state-of-the-art methods in optical character recognition and achieve competitive results in phone classification.

Relations such as "is influenced by", "is known for" or "is a competitor of" are inherently graded: we can rank entity pairs based on how well they satisfy these relations, but it is hard to draw a line between those pairs that satisfy them and those that do not. Such graded relations play a central role in many applications, yet they are typically not covered by existing Knowledge Graphs. In this paper, we consider the possibility of using Large Language Models (LLMs) to fill this gap. To this end, we introduce a new benchmark, in which entity pairs have to be ranked according to how much they satisfy a given graded relation. The task is formulated as a few-shot ranking problem, where models only have access to a description of the relation and five prototypical instances. We use the proposed benchmark to evaluate state-of-the-art relation embedding strategies as well as several recent LLMs, covering both publicly available LLMs and closed models such as GPT-4. Overall, we find a strong correlation between model size and performance, with smaller Language Models struggling to outperform a naive baseline. The results of the largest Flan-T5 and OPT models are remarkably strong, although a clear gap with human performance remains.

This article presents Individual Conditional Expectation (ICE) plots, a tool for visualizing the model estimated by any supervised learning algorithm. Classical partial dependence plots (PDPs) help visualize the average partial relationship between the predicted response and one or more features. In the presence of substantial interaction effects, the partial response relationship can be heterogeneous. Thus, an average curve, such as the PDP, can obfuscate the complexity of the modeled relationship. Accordingly, ICE plots refine the partial dependence plot by graphing the functional relationship between the predicted response and the feature for individual observations. Specifically, ICE plots highlight the variation in the fitted values across the range of a covariate, suggesting where and to what extent heterogeneities might exist. In addition to providing a plotting suite for exploratory analysis, we include a visual test for additive structure in the data generating model. Through simulated examples and real data sets, we demonstrate how ICE plots can shed light on estimated models in ways PDPs cannot. Procedures outlined are available in the R package ICEbox.

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. To understand the importance of this structure in optimization problems we consider the problem of maximizing function value under various types of constraints. To demonstrate the modeling power of submodular order functions we show applications in two different settings. First, we apply our results to the extensively studied problem of assortment optimization. While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order. Consequently, we obtain new and in some cases the first constant factor guarantee for constrained assortment optimization in fundamental choice models. As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model. We recover some best known guarantees for this problem as a corollary of our results.

Causal precedence between biochemical interactions is crucial in the biomedical domain, because it transforms collections of individual interactions, e.g., bindings and phosphorylations, into the causal mechanisms needed to inform meaningful search and inference. Here, we analyze causal precedence in the biomedical domain as distinct from open-domain, temporal precedence. First, we describe a novel, hand-annotated text corpus of causal precedence in the biomedical domain. Second, we use this corpus to investigate a battery of models of precedence, covering rule-based, feature-based, and latent representation models. The highest-performing individual model achieved a micro F1 of 43 points, approaching the best performers on the simpler temporal-only precedence tasks. Feature-based and latent representation models each outperform the rule-based models, but their performance is complementary to one another. We apply a sieve-based architecture to capitalize on this lack of overlap, achieving a micro F1 score of 46 points.

Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the sequence-to-sequence (seq2seq) framework which employs the chain rule to efficiently represent the joint probability of sequences. In many cases, however, variable sized inputs and/or outputs might not be naturally expressed as sequences. For instance, it is not clear how to input a set of numbers into a model where the task is to sort them; similarly, we do not know how to organize outputs when they correspond to random variables and the task is to model their unknown joint probability. In this paper, we first show using various examples that the order in which we organize input and/or output data matters significantly when learning an underlying model. We then discuss an extension of the seq2seq framework that goes beyond sequences and handles input sets in a principled way. In addition, we propose a loss which, by searching over possible orders during training, deals with the lack of structure of output sets. We show empirical evidence of our claims regarding ordering, and on the modifications to the seq2seq framework on benchmark language modeling and parsing tasks, as well as two artificial tasks -- sorting numbers and estimating the joint probability of unknown graphical models.

In order to avoid well-know paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type_0 : Type_1 : cdots . Such type systems are called cumulative if for any type A we have that A : Type_{i} implies A : Type_{i+1}. The predicative calculus of inductive constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present and establish the soundness of the predicative calculus of cumulative inductive constructions (pCuIC) which extends the cumulativity relation to inductive types.

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

A key to knowledge graph embedding (KGE) is to choose a proper representation space, e.g., point-wise Euclidean space and complex vector space. In this paper, we propose a unified perspective of embedding and introduce uncertainty into KGE from the view of group theory. Our model can incorporate existing models (i.e., generality), ensure the computation is tractable (i.e., efficiency) and enjoy the expressive power of complex random variables (i.e., expressiveness). The core idea is that we embed entities/relations as elements of a symmetric group, i.e., permutations of a set. Permutations of different sets can reflect different properties of embedding. And the group operation of symmetric groups is easy to compute. In specific, we show that the embedding of many existing models, point vectors, can be seen as elements of a symmetric group. To reflect uncertainty, we first embed entities/relations as permutations of a set of random variables. A permutation can transform a simple random variable into a complex random variable for greater expressiveness, called a normalizing flow. We then define scoring functions by measuring the similarity of two normalizing flows, namely NFE. We construct several instantiating models and prove that they are able to learn logical rules. Experimental results demonstrate the effectiveness of introducing uncertainty and our model. The code is available at https://github.com/changyi7231/NFE.

For a sequence of random variables (X_1, X_2, ldots, X_n), n geq 1, that are independent and identically distributed with a regularly varying tail with index -alpha, alpha geq 0, we show that the contribution of the maximum term M_n triangleq max(X_1,ldots,X_n) in the sum S_n triangleq X_1 + cdots +X_n, as n to infty, decreases monotonically with alpha in stochastic ordering sense.

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for example, communication within a group rather than person-to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental differences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.

Happiness computing based on large-scale online web data and machine learning methods is an emerging research topic that underpins a range of issues, from personal growth to social stability. Many advanced Machine Learning (ML) models with explanations are used to compute the happiness online assessment while maintaining high accuracy of results. However, domain knowledge constraints, such as the primary and secondary relations of happiness factors, are absent from these models, which limits the association between computing results and the right reasons for why they occurred. This article attempts to provide new insights into the explanation consistency from an empirical study perspective. Then we study how to represent and introduce domain knowledge constraints to make ML models more trustworthy. We achieve this through: (1) proving that multiple prediction models with additive factor attributions will have the desirable property of primary and secondary relations consistency, and (2) showing that factor relations with quantity can be represented as an importance distribution for encoding domain knowledge. Factor explanation difference is penalized by the Kullback-Leibler divergence-based loss among computing models. Experimental results using two online web datasets show that domain knowledge of stable factor relations exists. Using this knowledge not only improves happiness computing accuracy but also reveals more significative happiness factors for assisting decisions well.

Procedures are inherently hierarchical. To "make videos", one may need to "purchase a camera", which in turn may require one to "set a budget". While such hierarchical knowledge is critical for reasoning about complex procedures, most existing work has treated procedures as shallow structures without modeling the parent-child relation. In this work, we attempt to construct an open-domain hierarchical knowledge-base (KB) of procedures based on wikiHow, a website containing more than 110k instructional articles, each documenting the steps to carry out a complex procedure. To this end, we develop a simple and efficient method that links steps (e.g., "purchase a camera") in an article to other articles with similar goals (e.g., "how to choose a camera"), recursively constructing the KB. Our method significantly outperforms several strong baselines according to automatic evaluation, human judgment, and application to downstream tasks such as instructional video retrieval. A demo with partial data can be found at https://wikihow-hierarchy.github.io. The code and the data are at https://github.com/shuyanzhou/wikihow_hierarchy.

In large language models (LLMs), certain neurons can store distinct pieces of knowledge learned during pretraining. While knowledge typically appears as a combination of relations and entities, it remains unclear whether some neurons focus on a relation itself -- independent of any entity. We hypothesize such neurons detect a relation in the input text and guide generation involving such a relation. To investigate this, we study the Llama-2 family on a chosen set of relations with a statistics-based method. Our experiments demonstrate the existence of relation-specific neurons. We measure the effect of selectively deactivating candidate neurons specific to relation r on the LLM's ability to handle (1) facts whose relation is r and (2) facts whose relation is a different relation r' neq r. With respect to their capacity for encoding relation information, we give evidence for the following three properties of relation-specific neurons. (i) Neuron cumulativity. The neurons for r present a cumulative effect so that deactivating a larger portion of them results in the degradation of more facts in r. (ii) Neuron versatility. Neurons can be shared across multiple closely related as well as less related relations. Some relation neurons transfer across languages. (iii) Neuron interference. Deactivating neurons specific to one relation can improve LLM generation performance for facts of other relations. We will make our code publicly available at https://github.com/cisnlp/relation-specific-neurons.

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.