The vital role of analogical reasoning in human cognition allows us to grasp novel concepts by linking them with familiar ones through shared relational structures. Despite the attention previous research has given to word analogies, this work suggests that Large Language Models (LLMs) often overlook the structures that underpin these analogies, raising questions about the efficacy of word analogies as a measure of analogical reasoning skills akin to human cognition. In response to this, our paper introduces a task of analogical structure abduction, grounded in cognitive psychology, designed to abduce structures that form an analogy between two systems. In support of this task, we establish a benchmark called SCAR, containing 400 scientific analogies from 13 distinct fields, tailored for evaluating analogical reasoning with structure abduction. The empirical evidence underlines the continued challenges faced by LLMs, including ChatGPT and GPT-4, in mastering this task, signifying the need for future exploration to enhance their abilities.

While reinforcement learning (RL) algorithms have been successfully applied to numerous tasks, their reliance on neural networks makes their behavior difficult to understand and trust. Counterfactual explanations are human-friendly explanations that offer users actionable advice on how to alter the model inputs to achieve the desired output from a black-box system. However, current approaches to generating counterfactuals in RL ignore the stochastic and sequential nature of RL tasks and can produce counterfactuals that are difficult to obtain or do not deliver the desired outcome. In this work, we propose RACCER, the first RL-specific approach to generating counterfactual explanations for the behavior of RL agents. We first propose and implement a set of RL-specific counterfactual properties that ensure easily reachable counterfactuals with highly probable desired outcomes. We use a heuristic tree search of the agent's execution trajectories to find the most suitable counterfactuals based on the defined properties. We evaluate RACCER in two tasks as well as conduct a user study to show that RL-specific counterfactuals help users better understand agents' behavior compared to the current state-of-the-art approaches.

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.

A hierarchical Bayesian framework is introduced for developing rich mixture models for real-valued time series, partly motivated by important applications in financial time series analysis. At the top level, meaningful discrete states are identified as appropriately quantised values of some of the most recent samples. These observable states are described as a discrete context-tree model. At the bottom level, a different, arbitrary model for real-valued time series -- a base model -- is associated with each state. This defines a very general framework that can be used in conjunction with any existing model class to build flexible and interpretable mixture models. We call this the Bayesian Context Trees State Space Model, or the BCT-X framework. Efficient algorithms are introduced that allow for effective, exact Bayesian inference and learning in this setting; in particular, the maximum a posteriori probability (MAP) context-tree model can be identified. These algorithms can be updated sequentially, facilitating efficient online forecasting. The utility of the general framework is illustrated in two particular instances: When autoregressive (AR) models are used as base models, resulting in a nonlinear AR mixture model, and when conditional heteroscedastic (ARCH) models are used, resulting in a mixture model that offers a powerful and systematic way of modelling the well-known volatility asymmetries in financial data. In forecasting, the BCT-X methods are found to outperform state-of-the-art techniques on simulated and real-world data, both in terms of accuracy and computational requirements. In modelling, the BCT-X structure finds natural structure present in the data. In particular, the BCT-ARCH model reveals a novel, important feature of stock market index data, in the form of an enhanced leverage effect.

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case. Bayesian inference has been very successful because this technique provides a representation of the parameters as a posterior probability distribution, with uncertainties informed by the precision of the experimental measurements. During the last couple of decades, many specific advances have been proposed and employed in order to solve a large variety of different problems. In this work, we present a Markov Chain Monte Carlo (MCMC) algorithm that integrates many of those concepts into a single MCMC package. For this purpose, we have built {\tt Eryn}, a user-friendly and multipurpose toolbox for Bayesian inference, which can be utilized for solving parameter estimation and model selection problems, ranging from simple inference questions, to those with large-scale model variation requiring trans-dimensional MCMC methods, like the LISA global fit problem. In this paper, we describe this sampler package and illustrate its capabilities on a variety of use cases.

Backward propagation (BP) is widely used to compute the gradients in neural network training. However, it is hard to implement BP on edge devices due to the lack of hardware and software resources to support automatic differentiation. This has tremendously increased the design complexity and time-to-market of on-device training accelerators. This paper presents a completely BP-free framework that only requires forward propagation to train realistic neural networks. Our technical contributions are three-fold. Firstly, we present a tensor-compressed variance reduction approach to greatly improve the scalability of zeroth-order (ZO) optimization, making it feasible to handle a network size that is beyond the capability of previous ZO approaches. Secondly, we present a hybrid gradient evaluation approach to improve the efficiency of ZO training. Finally, we extend our BP-free training framework to physics-informed neural networks (PINNs) by proposing a sparse-grid approach to estimate the derivatives in the loss function without using BP. Our BP-free training only loses little accuracy on the MNIST dataset compared with standard first-order training. We also demonstrate successful results in training a PINN for solving a 20-dim Hamiltonian-Jacobi-Bellman PDE. This memory-efficient and BP-free approach may serve as a foundation for the near-future on-device training on many resource-constraint platforms (e.g., FPGA, ASIC, micro-controllers, and photonic chips).

Symbolic Regression is the study of algorithms that automate the search for analytic expressions that fit data. While recent advances in deep learning have generated renewed interest in such approaches, the development of symbolic regression methods has not been focused on physics, where we have important additional constraints due to the units associated with our data. Here we present $\Phi$-SO, a Physical Symbolic Optimization framework for recovering analytical symbolic expressions from physics data using deep reinforcement learning techniques by learning units constraints. Our system is built, from the ground up, to propose solutions where the physical units are consistent by construction. This is useful not only in eliminating physically impossible solutions, but because the "grammatical" rules of dimensional analysis restrict enormously the freedom of the equation generator, thus vastly improving performance. The algorithm can be used to fit noiseless data, which can be useful for instance when attempting to derive an analytical property of a physical model, and it can also be used to obtain analytical approximations to noisy data. We test our machinery on a standard benchmark of equations from the Feynman Lectures on Physics and other physics textbooks, achieving state-of-the-art performance in the presence of noise (exceeding 0.1%) and show that it is robust even in the presence of substantial (10%) noise. We showcase its abilities on a panel of examples from astrophysics.

In the wheat nutrient deficiencies classification challenge, we present the DividE and EnseMble (DEEM) method for progressive test data predictions. We find that (1) test images are provided in the challenge; (2) samples are equipped with their collection dates; (3) the samples of different dates show notable discrepancies. Based on the findings, we partition the dataset into discrete groups by the dates and train models on each divided group. We then adopt the pseudo-labeling approach to label the test data and incorporate those with high confidence into the training set. In pseudo-labeling, we leverage models ensemble with different architectures to enhance the reliability of predictions. The pseudo-labeling and ensembled model training are iteratively conducted until all test samples are labeled. Finally, the separated models for each group are unified to obtain the model for the whole dataset. Our method achieves an average of 93.6\% Top-1 test accuracy~(94.0\% on WW2020 and 93.2\% on WR2021) and wins the 1$st$ place in the Deep Nutrient Deficiency Challenge~\footnote{https://cvppa2023.github.io/challenges/}.

AI models have become extremely popular and accessible to the general public. However, they are continuously under the scanner due to their demonstrable biases toward various sections of the society like people of color and non-binary people. In this study, we audit three existing gender analyzers -- uClassify, Readable and HackerFactor, for biases against non-binary individuals. These tools are designed to predict only the cisgender binary labels, which leads to discrimination against non-binary members of the society. We curate two datasets -- Reddit comments (660k) and, Tumblr posts (2.05M) and our experimental evaluation shows that the tools are highly inaccurate with the overall accuracy being ~50% on all platforms. Predictions for non-binary comments on all platforms are mostly female, thus propagating the societal bias that non-binary individuals are effeminate. To address this, we fine-tune a BERT multi-label classifier on the two datasets in multiple combinations, observe an overall performance of ~77% on the most realistically deployable setting and a surprisingly higher performance of 90% for the non-binary class. We also audit ChatGPT using zero-shot prompts on a small dataset (due to high pricing) and observe an average accuracy of 58% for Reddit and Tumblr combined (with overall better results for Reddit). Thus, we show that existing systems, including highly advanced ones like ChatGPT are biased, and need better audits and moderation and, that such societal biases can be addressed and alleviated through simple off-the-shelf models like BERT trained on more gender inclusive datasets.

Many recent works in simulation-based inference (SBI) rely on deep generative models to approximate complex, high-dimensional posterior distributions. However, evaluating whether or not these approximations can be trusted remains a challenge. Most approaches evaluate the posterior estimator only in expectation over the observation space. This limits their interpretability and is not sufficient to identify for which observations the approximation can be trusted or should be improved. Building upon the well-known classifier two-sample test (C2ST), we introduce L-C2ST, a new method that allows for a local evaluation of the posterior estimator at any given observation. It offers theoretically grounded and easy to interpret -- e.g. graphical -- diagnostics, and unlike C2ST, does not require access to samples from the true posterior. In the case of normalizing flow-based posterior estimators, L-C2ST can be specialized to offer better statistical power, while being computationally more efficient. On standard SBI benchmarks, L-C2ST provides comparable results to C2ST and outperforms alternative local approaches such as coverage tests based on highest predictive density (HPD). We further highlight the importance of local evaluation and the benefit of interpretability of L-C2ST on a challenging application from computational neuroscience.