Shepard's universal law of generalization is a remarkable hypothesis about how intelligent organisms should perceive similarity. In its broadest form, the universal law states that the level of perceived similarity between a pair of stimuli should decay as a concave function of their distance when embedded in an appropriate psychological space. While extensively studied, evidence in support of the universal law has relied on low-dimensional stimuli and small stimulus sets that are very different from their real-world counterparts. This is largely because pairwise comparisons - as required for similarity judgments - scale quadratically in the number of stimuli. We provide direct evidence for the universal law in a naturalistic high-dimensional regime by analyzing an existing dataset of 214, 200 human similarity judgments and a newly collected dataset of 390, 819 human generalization judgments (N = 2406 US participants) across three sets of natural images. The Universal Law of Generalization Holds for Naturalistic Stimuli Statement of Relevance Humans constantly form generalizations, whether when trying to identify the color of an object or reasoning about which action to take based on past experiences.

Random graph models are playing an increasingly important role in science and industry, and finds their applications in a variety of fields ranging from social and traffic networks, to recommendation systems and molecular genetics. In this paper, we perform an in-depth analysis of the random Kronecker graph model proposed in \cite{leskovec2010kronecker}, when the number of graph vertices $N$ is large. Built upon recent advances in random matrix theory, we show, in the dense regime, that the random Kronecker graph adjacency matrix follows approximately a signal-plus-noise model, with a small-rank (of order at most $\log N$) signal matrix that is linear in the graph parameters and a random noise matrix having a quarter-circle-form singular value distribution. This observation allows us to propose a ``denoise-and-solve'' meta algorithm to approximately infer the graph parameters, with reduced computational complexity and (asymptotic) performance guarantee. Numerical experiments of graph inference and graph classification on both synthetic and realistic graphs are provided to support the advantageous performance of the proposed approach.

Out-of-distribution (OoD) detection techniques are instrumental for safety-related neural networks. We are arguing, however, that current performance-oriented OoD detection techniques geared towards matching metrics such as expected calibration error, are not sufficient for establishing safety claims. What is missing is a rigorous design approach for developing, verifying, and validating OoD detectors. These design principles need to be aligned with the intended functionality and the operational domain. Here, we formulate some of the key technical challenges, together with a possible way forward, for developing a rigorous and safety-related design methodology for OoD detectors.

The goal of combining the robustness of neural networks and the expressiveness of symbolic methods has rekindled the interest in Neuro-Symbolic AI. Deep Probabilistic Programming Languages (DPPLs) have been developed for probabilistic logic programming to be carried out via the probability estimations of deep neural networks. However, recent SOTA DPPL approaches allow only for limited conditional probabilistic queries and do not offer the power of true joint probability estimation. In our work, we propose an easy integration of tractable probabilistic inference within a DPPL. To this end, we introduce SLASH, a novel DPPL that consists of Neural-Probabilistic Predicates (NPPs) and a logic program, united via answer set programming (ASP). NPPs are a novel design principle allowing for combining all deep model types and combinations thereof to be represented as a single probabilistic predicate. In this context, we introduce a novel $+/-$ notation for answering various types of probabilistic queries by adjusting the atom notations of a predicate. To scale well, we show how to prune the stochastically insignificant parts of the (ground) program, speeding up reasoning without sacrificing the predictive performance. We evaluate SLASH on a variety of different tasks, including the benchmark task of MNIST addition and Visual Question Answering (VQA).

Graph neural networks have been extensively studied for learning with inter-connected data. Despite this, recent evidence has revealed GNNs' deficiencies related to over-squashing, heterophily, handling long-range dependencies, edge incompleteness and particularly, the absence of graphs altogether. While a plausible solution is to learn new adaptive topology for message passing, issues concerning quadratic complexity hinder simultaneous guarantees for scalability and precision in large networks. In this paper, we introduce a novel all-pair message passing scheme for efficiently propagating node signals between arbitrary nodes, as an important building block for a pioneering Transformer-style network for node classification on large graphs, dubbed as \textsc{NodeFormer}. Specifically, the efficient computation is enabled by a kernerlized Gumbel-Softmax operator that reduces the algorithmic complexity to linearity w.r.t. node numbers for learning latent graph structures from large, potentially fully-connected graphs in a differentiable manner. We also provide accompanying theory as justification for our design. Extensive experiments demonstrate the promising efficacy of the method in various tasks including node classification on graphs (with up to 2M nodes) and graph-enhanced applications (e.g., image classification) where input graphs are missing.

The Gaussian process latent variable model (GPLVM) is a popular probabilistic method used for nonlinear dimension reduction, matrix factorization, and state-space modeling. Inference for GPLVMs is computationally tractable only when the data likelihood is Gaussian. Moreover, inference for GPLVMs has typically been restricted to obtaining maximum a posteriori point estimates, which can lead to overfitting, or variational approximations, which mischaracterize the posterior uncertainty. Here, we present a method to perform Markov chain Monte Carlo (MCMC) inference for generalized Bayesian nonlinear latent variable modeling. The crucial insight necessary to generalize GPLVMs to arbitrary observation models is that we approximate the kernel function in the Gaussian process mappings with random Fourier features; this allows us to compute the gradient of the posterior in closed form with respect to the latent variables. We show that we can generalize GPLVMs to non-Gaussian observations, such as Poisson, negative binomial, and multinomial distributions, using our random feature latent variable model (RFLVM). Our generalized RFLVMs perform on par with state-of-the-art latent variable models on a wide range of applications, including motion capture, images, and text data for the purpose of estimating the latent structure and imputing the missing data of these complex data sets. Keywords: Latent variable modeling, Gaussian processes, probabilistic modeling.

Objective: Seizure prediction is of great importance to improve the life of patients. The focal point is to distinguish preictal states from interictal ones. With the development of machine learning, seizure prediction methods have achieved significant progress. However, the severe imbalance problem between preictal and interictal data still poses a great challenge, restricting the performance of classifiers. Data augmentation is an intuitive way to solve this problem. Existing data augmentation methods generate samples by overlapping or recombining data. The distribution of generated samples is limited by original data, because such transformations cannot fully explore the feature space and offer new information. As the epileptic EEG representation varies among seizures, these generated samples cannot provide enough diversity to achieve high performance on a new seizure. As a consequence, we propose a novel data augmentation method with diffusion model called DiffEEG. Methods: Diffusion models are a class of generative models that consist of two processes. Specifically, in the diffusion process, the model adds noise to the input EEG sample step by step and converts the noisy sample into output random noise, exploring the distribution of data by minimizing the loss between the output and the noise added. In the denoised process, the model samples the synthetic data by removing the noise gradually, diffusing the data distribution to outward areas and narrowing the distance between different clusters. Results: We compared DiffEEG with existing methods, and integrated them into three representative classifiers. The experiments indicate that DiffEEG could further improve the performance and shows superiority to existing methods. Conclusion: This paper proposes a novel and effective method to solve the imbalanced problem and demonstrates the effectiveness and generality of our method.

We present a novel learning-based method that achieves state-of-the-art performance on several heart rate estimation benchmarks extracted from photoplethysmography signals (PPG). We consider the evolution of the heart rate in the context of a discrete-time stochastic process that we represent as a hidden Markov model. We derive a distribution over possible heart rate values for a given PPG signal window through a trained neural network. Using belief propagation, we incorporate the statistical distribution of heart rate changes to refine these estimates in a temporal context. From this, we obtain a quantized probability distribution over the range of possible heart rate values that captures a meaningful and well-calibrated estimate of the inherent predictive uncertainty. We show the robustness of our method on eight public datasets with three different cross-validation experiments.

An alternative to stratified is parallel integration. In contrast to stratified frameworks, parallel integration applies in settings Parallel neurosymbolic architectures have been in which the same task can be solved both symbolically applied effectively in NLP by distilling knowledge and sub-symbolically and the aim is to increase the accuracy from a logic theory into a deep model. However, of the end task by distilling knowledge from the logic prior art faces several limitations including component into the neural one and vice versa. Two parallel supporting restricted forms of logic theories and neurosymbolic frameworks have been proposed recently: relying on the assumption of independence between Teacher-Student (T-S) by Hu et al. (Hu et al., 2016a;b) and the logic and the deep network.

This survey paper provides a comprehensive review of the use of diffusion models in natural language processing (NLP). Diffusion models are a class of mathematical models that aim to capture the diffusion of information or signals across a network or manifold. In NLP, diffusion models have been used in a variety of applications, such as natural language generation, sentiment analysis, topic modeling, and machine translation. This paper discusses the different formulations of diffusion models used in NLP, their strengths and limitations, and their applications. We also perform a thorough comparison between diffusion models and alternative generative models, specifically highlighting the autoregressive (AR) models, while also examining how diverse architectures incorporate the Transformer in conjunction with diffusion models. Compared to AR models, diffusion models have significant advantages for parallel generation, text interpolation, token-level controls such as syntactic structures and semantic contents, and robustness. Exploring further permutations of integrating Transformers into diffusion models would be a valuable pursuit. Also, the development of multimodal diffusion models and large-scale diffusion language models with notable capabilities for few-shot learning would be important directions for the future advance of diffusion models in NLP.