The term (1 γ) is like a normalizer.

We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given dataset. In doing so, they define a Bayesian model without explicitly positing a prior distribution over latent global parameters; they instead adopt priors over the relational structure of the given dataset, a task that is much simpler. We show how we can learn such models from data, demonstrate that they are scalable to large datasets through mini-batch optimization and describe how we can make predictions for new points via their posterior predictive distribution. We experimentally evaluate FNPs on the tasks of toy regression and image classification and show that, when compared to baselines that employ global latent parameters, they offer both competitive predictions as well as more robust uncertainty estimates.

Combinatorial optimization problems are widespread but inherently challenging due to their discrete nature. The primary limitation of existing methods is that they can only access a small fraction of the solution space at each iteration, resulting in limited efficiency for searching the global optimal. To overcome this challenge, diverging from conventional efforts of expanding the solver's search scope, we focus on enabling information to actively propagate to the solver through heat diffusion.

Diffusion models have demonstrated competitive performance in missing data imputation (MDI) task. However, directly applying diffusion models to MDI produces suboptimal performance due to two primary defects. First, the sample diversity promoted by diffusion models hinders the accurate inference of missing values. Second, data masking reduces observable indices for model training, obstructing imputation performance. To address these challenges, we introduce Negative Entropy-regularized Wasserstein gradient flow for Imputation (NewImp), enhancing diffusion models for MDI from a gradient flow perspective. To handle the first defect, we incorporate a negative entropy regularization term into the cost functional to suppress diversity and improve accuracy. To handle the second defect, we demonstrate that the imputation procedure of NewImp, induced by the conditional distribution-related cost functional, can equivalently be replaced by that induced by the joint distribution, thereby naturally eliminating the need for data masking.

The Boolean Satisfiability (SAT) problem is the canonical NP-complete problem and is fundamental to computer science, with a wide array of applications in planning, verification, and theorem proving. Developing and evaluating practical SAT solvers relies on extensive empirical testing on a set of real-world benchmark formulas. However, the availability of such real-world SAT formulas is limited. While these benchmark formulas can be augmented with synthetically generated ones, existing approaches for doing so are heavily hand-crafted and fail to simultaneously capture a wide range of characteristics exhibited by real-world SAT instances. In this work, we present G2SAT, the first deep generative framework that learns to generate SAT formulas from a given set of input formulas. Our key insight is that SAT formulas can be transformed into latent bipartite graph representations which we model using a specialized deep generative neural network. We show that G2SAT can generate SAT formulas that closely resemble given real-world SAT instances, as measured by both graph metrics and SAT solver behavior. Further, we show that our synthetic SAT formulas could be used to improve SAT solver performance on real-world benchmarks, which opens up new opportunities for the continued development of SAT solvers and a deeper understanding of their performance.

Our paper differs from that work in at least 4 ways.

The study of object representations in computer vision has primarily focused on developing representations that are useful for image classification, object detection, or semantic segmentation as downstream tasks. In this work we aim to learn object representations that are useful for control and reinforcement learning (RL). To this end, we introduce Transporter, a neural network architecture for discovering concise geometric object representations in terms of keypoints or image-space coordinates. Our method learns from raw video frames in a fully unsupervised manner, by transporting learnt image features between video frames using a keypoint bottleneck. The discovered keypoints track objects and object parts across long time-horizons more accurately than recent similar methods. Furthermore, consistent long-term tracking enables two notable results in control domains - (1) using the keypoint co-ordinates and corresponding image features as inputs enables highly sample-efficient reinforcement learning; (2) learning to explore by controlling keypoint locations drastically reduces the search space, enabling deep exploration (leading to states unreachable through random action exploration) without any extrinsic rewards. Code for the model is available at: https://github.

We will make this discussion more explicit.

Modern discriminative predictors have been shown to match natural intelligences in specific perceptual tasks in image classification, object and part detection, boundary extraction, etc. However, a major advantage that natural intelligences still have is that they work well for all perceptual problems together, solving them efficiently and coherently in an integrated manner. In order to capture some of these advantages in machine perception, we ask two questions: whether deep neural networks can learn universal image representations, useful not only for a single task but for all of them, and how the solutions to the different tasks can be integrated in this framework. We answer by proposing a new architecture, which we call multinet, in which not only deep image features are shared between tasks, but where tasks can interact in a recurrent manner by encoding the results of their analysis in a common shared representation of the data. In this manner, we show that the performance of individual tasks in standard benchmarks can be improved first by sharing features between them and then, more significantly, by integrating their solutions in the common representation.

Multimodal physiological signals, such as EEG, EOG and EMG, provide rich and reliable physiological information for automated sleep staging (ASS). However, in the real world, the completeness of various modalities is difficult to guarantee, which seriously affects the performance of ASS based on multimodal learning. Furthermore, the exploration of temporal context information within PSs is also a serious challenge. To this end, we propose a robust multimodal sleep staging framework named contrastive imagination modality sleep network (CIMSleepNet). Specifically, CIMSleepNet handles the issue of arbitrary modal missing through the combination of modal awareness imagination module (MAIM) and semantic & modal calibration contrastive learning (SMCCL).