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Neuro-symbolic hybrid systems are promising for integrating machine learning and symbolic reasoning, where perception models are facilitated with information inferred from a symbolic knowledge base through logical reasoning. Despite empirical evidence showing the ability of hybrid systems to learn accurate perception models, the theoretical understanding of learnability is still lacking. Hence, it remains unclear why a hybrid system succeeds for a specific task and when it may fail given a different knowledge base. In this paper, we introduce a novel way of characterising supervision signals from a knowledge base, and establish a criterion for determining the knowledge's efficacy in facilitating successful learning. This, for the first time, allows us to address the two questions above by inspecting the knowledge base under investigation. Our analysis suggests that many knowledge bases satisfy the criterion, thus enabling effective learning, while some fail to satisfy it, indicating potential failures. Comprehensive experiments confirm the utility of our criterion on benchmark tasks.

In the field of natural language processing, the rapid development of large language model (LLM) has attracted more and more attention. LLMs have shown a high level of creativity in various tasks, but the methods for assessing such creativity are inadequate. The assessment of LLM creativity needs to consider differences from humans, requiring multi-dimensional measurement while balancing accuracy and efficiency. This paper aims to establish an efficient framework for assessing the level of creativity in LLMs. By adapting the modified Torrance Tests of Creative Thinking, the research evaluates the creative performance of various LLMs across 7 tasks, emphasizing 4 criteria including Fluency, Flexibility, Originality, and Elaboration. In this context, we develop a comprehensive dataset of 700 questions for testing and an LLM-based evaluation method. In addition, this study presents a novel analysis of LLMs' responses to diverse prompts and role-play situations. We found that the creativity of LLMs primarily falls short in originality, while excelling in elaboration. Besides, the use of prompts and the role-play settings of the model significantly influence creativity. Additionally, the experimental results also indicate that collaboration among multiple LLMs can enhance originality. Notably, our findings reveal a consensus between human evaluations and LLMs regarding the personality traits that influence creativity. The findings underscore the significant impact of LLM design on creativity and bridges artificial intelligence and human creativity, offering insights into LLMs' creativity and potential applications.

A pervasive phenomenon in machine learning applications is distribution shift, where training and deployment conditions for a machine learning model differ. As distribution shift typically results in a degradation in performance, much attention has been devoted to algorithmic interventions that mitigate these detrimental effects. In this paper, we study the effect of distribution shift in the presence of model misspecification, specifically focusing on $L_{\infty}$-misspecified regression and adversarial covariate shift, where the regression target remains fixed while the covariate distribution changes arbitrarily. We show that empirical risk minimization, or standard least squares regression, can result in undesirable misspecification amplification where the error due to misspecification is amplified by the density ratio between the training and testing distributions. As our main result, we develop a new algorithm -- inspired by robust optimization techniques -- that avoids this undesirable behavior, resulting in no misspecification amplification while still obtaining optimal statistical rates. As applications, we use this regression procedure to obtain new guarantees in offline and online reinforcement learning with misspecification and establish new separations between previously studied structural conditions and notions of coverage.

A basic question within the emerging field of mechanistic interpretability is the degree to which neural networks learn the same underlying mechanisms. In other words, are neural mechanisms universal across different models? In this work, we study the universality of individual neurons across GPT2 models trained from different initial random seeds, motivated by the hypothesis that universal neurons are likely to be interpretable. In particular, we compute pairwise correlations of neuron activations over 100 million tokens for every neuron pair across five different seeds and find that 1-5\% of neurons are universal, that is, pairs of neurons which consistently activate on the same inputs. We then study these universal neurons in detail, finding that they usually have clear interpretations and taxonomize them into a small number of neuron families. We conclude by studying patterns in neuron weights to establish several universal functional roles of neurons in simple circuits: deactivating attention heads, changing the entropy of the next token distribution, and predicting the next token to (not) be within a particular set.

When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appeared permanently. So far, model classes were used which do not allow for ties; randomization has been another attempt to overcome this problem. Often, time periods with constant values even have been counted as times of monotone increase. To overcome this, a new approach is proposed: it explicitly allows for ties and, hence, considers more patterns than before. Ties are no longer seen as nuisance, but to carry valuable information. Limit theorems in the new framework are provided, both, for a single time series and for the dependence between two time series. The methods are used on hydrological data sets. It is common to distinguish five flood classes (plus 'absence of flood'). Considering data vectors of these classes at a certain gauge in a river basin, one will usually encounter several ties. Co-monotonic behavior between the data sets of two gauges (increasing, constant, decreasing) can be detected by the method as well as spatial patterns. Thus, it helps to analyze the strength of dependence between different gauges in an intuitive way. This knowledge can be used to asses risk and to plan future construction projects.

Integrating different functionalities, conventionally implemented as dedicated systems, into a single platform allows utilising the available resources more efficiently. We consider an integrated sensing and power transfer (ISAPT) system and propose the joint optimisation of the rectangular pulse-shaped transmit signal and the beamforming vector to combine sensing and wireless power transfer (WPT) functionalities efficiently. In contrast to prior works, we adopt an accurate non-linear circuit-based energy harvesting (EH) model. We formulate and solve a non-convex optimisation problem for a general number of EH receivers to maximise a weighted sum of the average harvested powers at the EH receivers while ensuring the received echo signal reflected by a sensing target (ST) has sufficient power for estimating the range to the ST with a prescribed accuracy within the considered coverage region. The average harvested power is shown to monotonically increase with the pulse duration when the average transmit power budget is sufficiently large. We discuss the trade-off between sensing performance and power transfer for the considered ISAPT system. The proposed approach significantly outperforms a heuristic baseline scheme based on a linear EH model, which linearly combines energy beamforming with the beamsteering vector in the direction to the ST as its transmit strategy.

This paper discusses the control of coherent structures in turbulent flows, which has broad applications among complex systems in science and technology. Mean field games have been proved a powerful tool and are proposed here to control the stochastic Lagrangian tracers as players tracking the flow field. We derive optimal control solutions for general nonlinear fluid systems using mean field game models, and develop computational algorithms to efficiently solve the resulting coupled forward and backward mean field system. A precise link is established for the control of Lagrangian tracers and the scalar vorticity field based on the functional Hamilton-Jacobi equations derived from the mean field models. New iterative numerical strategy is then constructed to compute the optimal solution with fast convergence. We verify the skill of the mean field control models and illustrate their practical efficiency on a prototype model modified from the viscous Burger's equation under various cost functions in both deterministic and stochastic formulations. The good model performance implies potential effectiveness of the strategy for more general high-dimensional turbulent systems.

Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.