This paper introduces an approach to regularize 2.5D surface normal and depth predictions at each pixel given a single input image. The approach infers and reasons about the underlying 3D planar surfaces depicted in the image to snap predicted normals and depths to inferred planar surfaces, all while maintaining fine detail within objects. Our approach comprises two components: (i) a fourstream convolutional neural network (CNN) where depths, surface normals, and likelihoods of planar region and planar boundary are predicted at each pixel, followed by (ii) a dense conditional random field (DCRF) that integrates the four predictions such that the normals and depths are compatible with each other and regularized by the planar region and planar boundary information. The DCRF is formulated such that gradients can be passed to the surface normal and depth CNNs via backpropagation. In addition, we propose new planar wise metrics to evaluate geometry consistency within planar surfaces, which are more tightly related to dependent 3D editing applications. We show that our regularization yields a 30% relative improvement in planar consistency on the NYU v2 dataset.

Ukrainian President Volodymyr Zelensky is set to visit Prime Minister Sir Keir Starmer in the UK on Tuesday to agree a new defence partnership aimed at tackling cheap attack drones. Downing Street said the deal would bring together Ukrainian expertise and the UK's industrial base to manufacture and supply drones and other capabilities. The two leaders are also expected to discuss further support Ukraine against Russia's full-scale invasion, now in its fourth year. Their meeting comes as the US-Israeli war with Iran enters a third week, during which US President Donald Trump has criticised the UK and other countries over the extent of their response to the conflict. Under the partnership between the UK and Ukraine, closer co-operation in the defence industries will also be sought with third countries as part of efforts to bolster international security.

How does our motor system solve the problem of anticipatory control in spite of a wide spectrum of response dynamics from different musculo-skeletal systems, transport delays as well as response latencies throughout the central nervous system? To a great extent, our highly-skilled motor responses are a result of a reactive feedback system, originating in the brain-stem and spinal cord, combined with a feed-forward anticipatory system, that is adaptively fine-tuned by sensory experience and originates in the cerebellum. Based on that interaction we design the counterfactual predictive control (CFPC) architecture, an anticipatory adaptive motor control scheme in which a feed-forward module, based on the cerebellum, steers an error feedback controller with counterfactual error signals. Those are signals that trigger reactions as actual errors would, but that do not code for any current of forthcoming errors. In order to determine the optimal learning strategy, we derive a novel learning rule for the feed-forward module that involves an eligibility trace and operates at the synaptic level. In particular, our eligibility trace provides a mechanism beyond co-incidence detection in that it convolves a history of prior synaptic inputs with error signals. In the context of cerebellar physiology, this solution implies that Purkinje cell synapses should generate eligibility traces using a forward model of the system being controlled. From an engineering perspective, CFPC provides a general-purpose anticipatory control architecture equipped with a learning rule that exploits the full dynamics of the closed-loop system.

We provide tight upper and lower bounds on the complexity of minimizing the average of m convex functions using gradient and prox oracles of the component functions. We show a significant gap between the complexity of deterministic vs randomized optimization. For smooth functions, we show that accelerated gradient descent (AGD) and an accelerated variant of SVRG are optimal in the deterministic and randomized settings respectively, and that a gradient oracle is sufficient for the optimal rate. For non-smooth functions, having access to prox oracles reduces the complexity and we present optimal methods based on smoothing that improve over methods using just gradient accesses.

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by incorporating temporal information and allowing for the possibility of time-varying models, significant improvements are possible in practice. However, despite the reported superior empirical performance of these dynamic models over their static counterparts, there is limited theoretical justification for introducing these more complex models. In this paper we aim to address this gap by studying the problem of recovering a dynamically evolving low-rank matrix from incomplete observations. First, we propose the locally weighted matrix smoothing (LOWEMS) framework as one possible approach to dynamic matrix recovery. We then establish error bounds for LOWEMS in both the {\em matrix sensing} and {\em matrix completion} observation models. Our results quantify the potential benefits of exploiting dynamic constraints both in terms of recovery accuracy and sample complexity. To illustrate these benefits we provide both synthetic and real-world experimental results.

We study fast learning rates when the losses are not necessarily bounded and may have a distribution with heavy tails. To enable such analyses, we introduce two new conditions: (i) the envelope function $\sup_{f \in \mathcal{F}}|\ell \circ f|$, where $\ell$ is the loss function and $\mathcal{F}$ is the hypothesis class, exists and is $L^r$-integrable, and (ii) $\ell$ satisfies the multi-scale Bernstein's condition on $\mathcal{F}$. Under these assumptions, we prove that learning rate faster than $O(n^{-1/2})$ can be obtained and, depending on $r$ and the multi-scale Bernstein's powers, can be arbitrarily close to $O(n^{-1})$. We then verify these assumptions and derive fast learning rates for the problem of vector quantization by $k$-means clustering with heavy-tailed distributions. The analyses enable us to obtain novel learning rates that extend and complement existing results in the literature from both theoretical and practical viewpoints.

In this paper we establish a duality between boosting and SVM, and use this to derive a novel discriminant dimensionality reduction algorithm. In particular, using the multiclass formulation of boosting and SVM we note that both use a combination of mapping and linear classification to maximize the multiclass margin. In SVM this is implemented using a pre-defined mapping (induced by the kernel) and optimizing the linear classifiers. In boosting the linear classifiers are pre-defined and the mapping (predictor) is learned through combination of weak learners. We argue that the intermediate mapping, e.g.

Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical physics computations, and proven in few specific cases. Here, we show how to rigorously prove the conjectured formula for the symmetric rank-one case. This allows to express the minimal mean-square-error and to characterize the detectability phase transitions in a large set of estimation problems ranging from community detection to sparse PCA. We also show that for a large set of parameters, an iterative algorithm called approximate message-passing is Bayes optimal. There exists, however, a gap between what currently known polynomial algorithms can do and what is expected information theoretically. Additionally, the proof technique has an interest of its own and exploits three essential ingredients: the interpolation method introduced in statistical physics by Guerra, the analysis of the approximate message-passing algorithm and the theory of spatial coupling and threshold saturation in coding. Our approach is generic and applicable to other open problems in statistical estimation where heuristic statistical physics predictions are available.

Learning accurate prior knowledge of natural images is of great importance for single image super-resolution (SR). Existing SR methods either learn the prior from the low/high-resolution patch pairs or estimate the prior models from the input low-resolution (LR) image. Specifically, high-frequency details are learned in the former methods. Though effective, they are heuristic and have limitations in dealing with blurred LR images; while the latter suffers from the limitations of frequency aliasing. In this paper, we propose to combine those two lines of ideas for image super-resolution. More specifically, the parametric sparse prior of the desirable high-resolution (HR) image patches are learned from both the input low-resolution (LR) image and a training image dataset. With the learned sparse priors, the sparse codes and thus the HR image patches can be accurately recovered by solving a sparse coding problem. Experimental results show that the proposed SR method outperforms existing state-of-the-art methods in terms of both subjective and objective image qualities.

In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function $\func$. Traditional methods for this problem assume just the availability of this single function. However, in many cases, cheap approximations to $\func$ may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of $\func$ in a small but promising region and speedily identify the optimum. We formalise this task as a \emph{multi-fidelity} bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop \mfgpucb, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour, and achieves better regret than strategies which ignore multi-fidelity information.