Policy evaluation with smooth and nonlinear function approximation has shown great potential for reinforcement learning. Compared to linear function approximation, it allows for using a richer class of approximation functions such as the neural networks. Traditional algorithms are based on two timescales stochastic approximation whose convergence rate is often slow. This paper focuses on an offline setting where a trajectory of m state-action pairs are observed. We formulate the policy evaluation problem as a non-convex primal-dual, finite-sum optimization problem, whose primal sub-problem is non-convex and dual sub-problem is strongly concave. We suggest a single-timescale primal-dual gradient algorithm with variance reduction, and show that it converges to an ɛ-stationary point using O(m/ɛ) calls (in expectation) to a gradient oracle.

Previous visual object tracking methods employ image-feature regression models or coordinate autoregression models for bounding box prediction. Image-feature regression methods heavily depend on matching results and do not utilize positional prior, while the autoregressive approach can only be trained using bounding boxes available in the training set, potentially resulting in suboptimal performance during testing with unseen data. Inspired by the diffusion model, denoising learning enhances the model's robustness to unseen data. Therefore, We introduce noise to bounding boxes, generating noisy boxes for training, thus enhancing model robustness on testing data. We propose a new paradigm to formulate the visual object tracking problem as a denoising learning process. However, tracking algorithms are usually asked to run in real-time, directly applying the diffusion model to object tracking would severely impair tracking speed.

Graph Neural Networks (GNNs) have emerged as the predominant approach for learning over graph-structured data. However, most GNNs operate as black-box models and require post-hoc explanations, which may not suffice in high-stakes scenarios where transparency is crucial. In this paper, we present a GNN that is interpretable by design. Our model, Graph Neural Additive Network (GNAN), is a novel extension of the interpretable class of Generalized Additive Models, and can be visualized and fully understood by humans. GNAN is designed to be fully interpretable, offering both global and local explanations at the feature and graph levels through direct visualization of the model. These visualizations describe exactly how the model uses the relationships between the target variable, the features, and the graph. We demonstrate the intelligibility of GNANs in a series of examples on different tasks and datasets. In addition, we show that the accuracy of GNAN is on par with black-box GNNs, making it suitable for critical applications where transparency is essential, alongside high accuracy.

Understanding the power of depth in feed-forward neural networks is an ongoing challenge in the field of deep learning theory. While current works account for the importance of depth for the expressive power of neural-networks, it remains an open question whether these benefits are exploited during a gradient-based optimization process. In this work we explore the relation between expressivity properties of deep networks and the ability to train them efficiently using gradientbased algorithms. We give a depth separation argument for distributions with fractal structure, showing that they can be expressed efficiently by deep networks, but not with shallow ones. These distributions have a natural coarse-to-fine structure, and we show that the balance between the coarse and fine details has a crucial effect on whether the optimization process is likely to succeed. We prove that when the distribution is concentrated on the fine details, gradient-based algorithms are likely to fail. Using this result we prove that, at least in some distributions, the success of learning deep networks depends on whether the distribution can be approximated by shallower networks, and we conjecture that this property holds in general.

See L39-44 for more details.

Despite the widespread adoption of Graph Neural Networks (GNNs), these models often incorporate off-the-shelf normalization layers like BatchNorm or InstanceNorm, which were not originally designed for GNNs. Consequently, these normalization layers may not effectively capture the unique characteristics of graph-structured data, potentially even weakening the expressive power of the overall architecture. While existing graph-specific normalization layers have been proposed, they often struggle to offer substantial and consistent benefits.

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is nonprobabilistic, even if it is generated by some stochastic process (such as a machine learning system). This is a poor fit for modern ML, particularly modern neural networks, which naturally generate a distribution. We initiate the study of algorithms with distributional predictions, where the prediction itself is a distribution. We focus on one of the simplest yet fundamental settings: binary search (or searching a sorted array).

When releasing outputs from confidential data, agencies need to balance the analytical usefulness of the released data with the obligation to protect data subjects' confidentiality. For releases satisfying differential privacy, this balance is reflected by the privacy budget, ε. We provide a framework for setting ε based on its relationship with Bayesian posterior probabilities of disclosure. The agency responsible for the data release decides how much posterior risk it is willing to accept at various levels of prior risk, which implies a unique ε. Agencies can evaluate different risk profiles to determine one that leads to an acceptable trade-off in risk and utility.

Video scene graph generation (VidSGG) has emerged as a transformative approach to capturing and interpreting the intricate relationships among objects and their temporal dynamics in video sequences. In this paper, we introduce the new Aero-Eye dataset that focuses on multi-object relationship modeling in aerial videos. Our AeroEye dataset features various drone scenes and includes a visually comprehensive and precise collection of predicates that capture the intricate relationships and spatial arrangements among objects. To this end, we propose the novel Cyclic Graph Transformer (CYCLO) approach that allows the model to capture both direct and long-range temporal dependencies by continuously updating the history of interactions in a circular manner. The proposed approach also allows one to handle sequences with inherent cyclical patterns and process object relationships in the correct sequential order. Therefore, it can effectively capture periodic and overlapping relationships while minimizing information loss. The extensive experiments on the AeroEye dataset demonstrate the effectiveness of the proposed CYCLO model, demonstrating its potential to perform scene understanding on drone videos. Finally, the CYCLO method consistently achieves State-of-the-Art (SOTA) results on two in-the-wild scene graph generation benchmarks, i.e., PVSG and ASPIRe.

Continual Pre-Training (CPT) on Large Language Models (LLMs) has been widely used to expand the model's fundamental understanding of specific downstream domains (e.g., math and code). For the CPT on domain-specific LLMs, one important question is how to choose the optimal mixture ratio between the generalcorpus (e.g., Dolma, Slim-pajama) and the downstream domain-corpus. Existing methods usually adopt laborious human efforts by grid-searching on a set of mixture ratios, which require high GPU training consumption costs. Besides, we cannot guarantee the selected ratio is optimal for the specific domain. To address the limitations of existing methods, inspired by the Scaling Law for performance prediction, we propose to investigate the Scaling Law of the Domain-specific Continual Pre-Training (D-CPT Law) to decide the optimal mixture ratio with acceptable training costs for LLMs of different sizes. Specifically, by fitting the D-CPT Law, we can easily predict the general and downstream performance of arbitrary mixture ratios, model sizes, and dataset sizes using small-scale training costs on limited experiments. Moreover, we also extend our standard D-CPT Law on cross-domain settings and propose the Cross-Domain D-CPT Law to predict the D-CPT law of target domains, where very small training costs (about 1% of the normal training costs) are needed for the target domains. Comprehensive experimental results on six downstream domains demonstrate the effectiveness and generalizability of our proposed D-CPT Law and Cross-Domain D-CPT Law.