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In this work we present point-level region contrast, a self-supervised pre-training approach for the task of object detection. This approach is motivated by the two key factors in detection: localization and recognition. While accurate localization favors models that operate at the pixel- or point-level, correct recognition typically relies on a more holistic, region-level view of objects. Incorporating this perspective in pre-training, our approach performs contrastive learning by directly sampling individual point pairs from different regions. Compared to an aggregated representation per region, our approach is more robust to the change in input region quality, and further enables us to implicitly improve initial region assignments via online knowledge distillation during training. Both advantages are important when dealing with imperfect regions encountered in the unsupervised setting. Experiments show point-level region contrast improves on state-of-the-art pre-training methods for object detection and segmentation across multiple tasks and datasets, and we provide extensive ablation studies and visualizations to aid understanding. Code will be made available.

We study online convex optimization with switching costs, a practically important but also extremely challenging problem due to the lack of complete offline information. By tapping into the power of machine learning (ML) based optimizers, ML-augmented online algorithms (also referred to as expert calibration in this paper) have been emerging as state of the art, with provable worst-case performance guarantees. Nonetheless, by using the standard practice of training an ML model as a standalone optimizer and plugging it into an ML-augmented algorithm, the average cost performance can be even worse than purely using ML predictions. In order to address the "how to learn" challenge, we propose EC-L2O (expert-calibrated learning to optimize), which trains an ML-based optimizer by explicitly taking into account the downstream expert calibrator. To accomplish this, we propose a new differentiable expert calibrator that generalizes regularized online balanced descent and offers a provably better competitive ratio than pure ML predictions when the prediction error is large. For training, our loss function is a weighted sum of two different losses -- one minimizing the average ML prediction error for better robustness, and the other one minimizing the post-calibration average cost. We also provide theoretical analysis for EC-L2O, highlighting that expert calibration can be even beneficial for the average cost performance and that the high-percentile tail ratio of the cost achieved by EC-L2O to that of the offline optimal oracle (i.e., tail cost ratio) can be bounded. Finally, we test EC-L2O by running simulations for sustainable datacenter demand response. Our results demonstrate that EC-L2O can empirically achieve a lower average cost as well as a lower competitive ratio than the existing baseline algorithms.

Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this paper a reformulation of the usual set-theoretical semantics of the description logic $\mathcal{ALC}$ by using categorical language. In this setting, ALC concepts are represented as objects, concept subsumptions as arrows, and memberships as logical quantifiers over objects and arrows of categories. Such a category-theoretical semantics provides a more modular representation of the semantics of $\mathcal{ALC}$ and a new way to design algorithms for reasoning.

We provide a decision theoretic analysis of bandit experiments. The setting corresponds to a dynamic programming problem, but solving this directly is typically infeasible. Working within the framework of diffusion asymptotics, we define suitable notions of asymptotic Bayes and minimax risk for bandit experiments. For normally distributed rewards, the minimal Bayes risk can be characterized as the solution to a nonlinear second-order partial differential equation (PDE). Using a limit of experiments approach, we show that this PDE characterization also holds asymptotically under both parametric and non-parametric distribution of the rewards. The approach further describes the state variables it is asymptotically sufficient to restrict attention to, and therefore suggests a practical strategy for dimension reduction. The upshot is that we can approximate the dynamic programming problem defining the bandit experiment with a PDE which can be efficiently solved using sparse matrix routines. We derive the optimal Bayes and minimax policies from the numerical solutions to these equations. The proposed policies substantially dominate existing methods such as Thompson sampling. The framework also allows for substantial generalizations to the bandit problem such as time discounting and pure exploration motives.

Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by extending a minimal modal base logic of static functional dependencies. We define a logic for dynamical systems with single time steps, provide a complete axiomatic proof calculus, and show the decidability of the satisfiability problem for a substantial fragment. The system comes in two guises: modal and first-order, that naturally complement each other. Next, we consider a timed semantics for our logic, as an intermediate between state spaces and temporal universes for the unfoldings of a dynamical system. We prove completeness and decidability by combining techniques from dynamic-epistemic logic and modal logic of functional dependencies with complex terms for objects. Also, we extend these results to the timed logic with functional symbols and term identity. Finally, we conclude with a brief outlook on how the system proposed here connects with richer temporal logics of system behavior, and with dynamic topological logic.

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through H\"older classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structures or have H\"older densities, when the network architectures are chosen properly. In particular, for distributions concentrated around a low-dimensional set, we show that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into the generator and discriminator approximation error and the statistical error, which may be of independent interest.

One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.

Recent advances in computer vision has led to a growth of interest in deploying visual analytics model on mobile devices. However, most mobile devices have limited computing power, which prohibits them from running large scale visual analytics neural networks. An emerging approach to solve this problem is to offload the computation of these neural networks to computing resources at an edge server. Efficient computation offloading requires optimizing the trade-off between multiple objectives including compressed data rate, analytics performance, and computation speed. In this work, we consider a "split computation" system to offload a part of the computation of the YOLO object detection model. We propose a learnable feature compression approach to compress the intermediate YOLO features with light-weight computation. We train the feature compression and decompression module together with the YOLO model to optimize the object detection accuracy under a rate constraint. Compared to baseline methods that apply either standard image compression or learned image compression at the mobile and perform image decompression and YOLO at the edge, the proposed system achieves higher detection accuracy at the low to medium rate range. Furthermore, the proposed system requires substantially lower computation time on the mobile device with CPU only.

We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting directions. Then we give a new information-theoretic proof of a finite version of de Finetti's classical representation theorem for finite-valued random variables. We derive an upper bound on the relative entropy between the distribution of the first $k$ in a sequence of $n$ exchangeable random variables, and an appropriate mixture over product distributions. The mixing measure is characterised as the law of the empirical measure of the original sequence, and de Finetti's result is recovered as a corollary. The proof is nicely motivated by the Gibbs conditioning principle in connection with statistical mechanics, and it follows along an appealing sequence of steps. The technical estimates required for these steps are obtained via the use of a collection of combinatorial tools known within information theory as `the method of types.'