In this work, we investigate the use of sparsity-inducing regularizers during training of Convolution Neural Networks (CNNs). These regularizers encourage that fewer connections in the convolution and fully connected layers take non-zero values and in effect result in sparse connectivity between hidden units in the deep network. This in turn reduces the memory and runtime cost involved in deploying the learned CNNs. We show that training with such regularization can still be performed using stochastic gradient descent implying that it can be used easily in existing codebases. Experimental evaluation of our approach on MNIST, CIFAR, and ImageNet datasets shows that our regularizers can result in dramatic reductions in memory requirements. For instance, when applied on AlexNet, our method can reduce the memory consumption by a factor of four with minimal loss in accuracy.

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Batched Gaussian Process Bandit Optimization via Determinantal Point Processes

Nov 13, 2016

Tarun Kathuria, Amit Deshpande, Pushmeet Kohli

Gaussian Process bandit optimization has emerged as a powerful tool for optimizing noisy black box functions. One example in machine learning is hyper-parameter optimization where each evaluation of the target function requires training a model which may involve days or even weeks of computation. Most methods for this so-called "Bayesian optimization" only allow sequential exploration of the parameter space. However, it is often desirable to propose batches or sets of parameter values to explore simultaneously, especially when there are large parallel processing facilities at our disposal. Batch methods require modeling the interaction between the different evaluations in the batch, which can be expensive in complex scenarios. In this paper, we propose a new approach for parallelizing Bayesian optimization by modeling the diversity of a batch via Determinantal point processes (DPPs) whose kernels are learned automatically. This allows us to generalize a previous result as well as prove better regret bounds based on DPP sampling. Our experiments on a variety of synthetic and real-world robotics and hyper-parameter optimization tasks indicate that our DPP-based methods, especially those based on DPP sampling, outperform state-of-the-art methods.
Nov 13, 2016

Tarun Kathuria, Amit Deshpande, Pushmeet Kohli

* To appear at NIPS 2016

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Efficient Energy Minimization for Enforcing Statistics

Jul 30, 2013

Yongsub Lim, Kyomin Jung, Pushmeet Kohli

Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is not the ground truth solution. In many problem scenarios, the system has access to certain statistics of the ground truth. For instance, in image segmentation, the area and boundary length of the object may be known. In these cases, we want to estimate the most probable solution that is consistent with such statistics, i.e., satisfies certain equality or inequality constraints. The above constrained energy minimization problem is NP-hard in general, and is usually solved using Linear Programming formulations, which relax the integrality constraints. This paper proposes a novel method that finds the discrete optimal solution of such problems by maximizing the corresponding Lagrangian dual. This method can be applied to any constrained energy minimization problem whose unconstrained version is polynomial time solvable, and can handle multiple, equality or inequality, and linear or non-linear constraints. We demonstrate the efficacy of our method on the foreground/background image segmentation problem, and show that it produces impressive segmentation results with less error, and runs more than 20 times faster than the state-of-the-art LP relaxation based approaches.
Jul 30, 2013

Yongsub Lim, Kyomin Jung, Pushmeet Kohli

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Multi-dimensional Parametric Mincuts for Constrained MAP Inference

Jul 30, 2013

Yongsub Lim, Kyomin Jung, Pushmeet Kohli

In this paper, we propose novel algorithms for inferring the Maximum a Posteriori (MAP) solution of discrete pairwise random field models under multiple constraints. We show how this constrained discrete optimization problem can be formulated as a multi-dimensional parametric mincut problem via its Lagrangian dual, and prove that our algorithm isolates all constraint instances for which the problem can be solved exactly. These multiple solutions enable us to even deal with `soft constraints' (higher order penalty functions). Moreover, we propose two practical variants of our algorithm to solve problems with hard constraints. We also show how our method can be applied to solve various constrained discrete optimization problems such as submodular minimization and shortest path computation. Experimental evaluation using the foreground-background image segmentation problem with statistic constraints reveals that our method is faster and its results are closer to the ground truth labellings compared with the popular continuous relaxation based methods.
Jul 30, 2013

Yongsub Lim, Kyomin Jung, Pushmeet Kohli

* 19 pages

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Curvature Prior for MRF-based Segmentation and Shape Inpainting

Sep 07, 2011

Alexander Shekhovtsov, Pushmeet Kohli, Carsten Rother

Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher order image priors encode high level structural dependencies between pixels and are key to overcoming these problems. However, these priors in general lead to computationally intractable models. This paper addresses the problem of discovering compact representations of higher order priors which allow efficient inference. We propose a framework for solving this problem which uses a recently proposed representation of higher order functions where they are encoded as lower envelopes of linear functions. Maximum a Posterior inference on our learned models reduces to minimizing a pairwise function of discrete variables, which can be done approximately using standard methods. Although this is a primarily theoretical paper, we also demonstrate the practical effectiveness of our framework on the problem of learning a shape prior for image segmentation and reconstruction. We show that our framework can learn a compact representation that approximates a prior that encourages low curvature shapes. We evaluate the approximation accuracy, discuss properties of the trained model, and show various results for shape inpainting and image segmentation.
Sep 07, 2011

Alexander Shekhovtsov, Pushmeet Kohli, Carsten Rother

* 17 pages, 16 figures

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Learning an Interactive Segmentation System

Dec 13, 2009

Hannes Nickisch, Pushmeet Kohli, Carsten Rother

Many successful applications of computer vision to image or video manipulation are interactive by nature. However, parameters of such systems are often trained neglecting the user. Traditionally, interactive systems have been treated in the same manner as their fully automatic counterparts. Their performance is evaluated by computing the accuracy of their solutions under some fixed set of user interactions. This paper proposes a new evaluation and learning method which brings the user in the loop. It is based on the use of an active robot user - a simulated model of a human user. We show how this approach can be used to evaluate and learn parameters of state-of-the-art interactive segmentation systems. We also show how simulated user models can be integrated into the popular max-margin method for parameter learning and propose an algorithm to solve the resulting optimisation problem.
Dec 13, 2009

Hannes Nickisch, Pushmeet Kohli, Carsten Rother

* 11 pages, 7 figures, 4 tables

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Deep disentangled representations for volumetric reconstruction

Oct 12, 2016

Edward Grant, Pushmeet Kohli, Marcel van Gerven

We introduce a convolutional neural network for inferring a compact disentangled graphical description of objects from 2D images that can be used for volumetric reconstruction. The network comprises an encoder and a twin-tailed decoder. The encoder generates a disentangled graphics code. The first decoder generates a volume, and the second decoder reconstructs the input image using a novel training regime that allows the graphics code to learn a separate representation of the 3D object and a description of its lighting and pose conditions. We demonstrate this method by generating volumes and disentangled graphical descriptions from images and videos of faces and chairs.
Oct 12, 2016

Edward Grant, Pushmeet Kohli, Marcel van Gerven

**Click to Read Paper and Get Code**

Analysing Mathematical Reasoning Abilities of Neural Models

Apr 02, 2019

David Saxton, Edward Grefenstette, Felix Hill, Pushmeet Kohli

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.
Apr 02, 2019

David Saxton, Edward Grefenstette, Felix Hill, Pushmeet Kohli

**Click to Read Paper and Get Code**

Verification of deep probabilistic models

Dec 06, 2018

Krishnamurthy Dvijotham, Marta Garnelo, Alhussein Fawzi, Pushmeet Kohli

Probabilistic models are a critical part of the modern deep learning toolbox - ranging from generative models (VAEs, GANs), sequence to sequence models used in machine translation and speech processing to models over functional spaces (conditional neural processes, neural processes). Given the size and complexity of these models, safely deploying them in applications requires the development of tools to analyze their behavior rigorously and provide some guarantees that these models are consistent with a list of desirable properties or specifications. For example, a machine translation model should produce semantically equivalent outputs for innocuous changes in the input to the model. A functional regression model that is learning a distribution over monotonic functions should predict a larger value at a larger input. Verification of these properties requires a new framework that goes beyond notions of verification studied in deterministic feedforward networks, since requiring worst-case guarantees in probabilistic models is likely to produce conservative or vacuous results. We propose a novel formulation of verification for deep probabilistic models that take in conditioning inputs and sample latent variables in the course of producing an output: We require that the output of the model satisfies a linear constraint with high probability over the sampling of latent variables and for every choice of conditioning input to the model. We show that rigorous lower bounds on the probability that the constraint is satisfied can be obtained efficiently. Experiments with neural processes show that several properties of interest while modeling functional spaces can be modeled within this framework (monotonicity, convexity) and verified efficiently using our algorithms
Dec 06, 2018

Krishnamurthy Dvijotham, Marta Garnelo, Alhussein Fawzi, Pushmeet Kohli

* Accepted to NeurIPS 2018 Workshop on Security in Machine Learning

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Batched Large-scale Bayesian Optimization in High-dimensional Spaces

May 16, 2018

Zi Wang, Clement Gehring, Pushmeet Kohli, Stefanie Jegelka

Bayesian optimization (BO) has become an effective approach for black-box function optimization problems when function evaluations are expensive and the optimum can be achieved within a relatively small number of queries. However, many cases, such as the ones with high-dimensional inputs, may require a much larger number of observations for optimization. Despite an abundance of observations thanks to parallel experiments, current BO techniques have been limited to merely a few thousand observations. In this paper, we propose ensemble Bayesian optimization (EBO) to address three current challenges in BO simultaneously: (1) large-scale observations; (2) high dimensional input spaces; and (3) selections of batch queries that balance quality and diversity. The key idea of EBO is to operate on an ensemble of additive Gaussian process models, each of which possesses a randomized strategy to divide and conquer. We show unprecedented, previously impossible results of scaling up BO to tens of thousands of observations within minutes of computation.
May 16, 2018

Zi Wang, Clement Gehring, Pushmeet Kohli, Stefanie Jegelka

* Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS) 2018, Lanzarote, Spain

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Batched High-dimensional Bayesian Optimization via Structural Kernel Learning

Jan 06, 2018

Zi Wang, Chengtao Li, Stefanie Jegelka, Pushmeet Kohli

Optimization of high-dimensional black-box functions is an extremely challenging problem. While Bayesian optimization has emerged as a popular approach for optimizing black-box functions, its applicability has been limited to low-dimensional problems due to its computational and statistical challenges arising from high-dimensional settings. In this paper, we propose to tackle these challenges by (1) assuming a latent additive structure in the function and inferring it properly for more efficient and effective BO, and (2) performing multiple evaluations in parallel to reduce the number of iterations required by the method. Our novel approach learns the latent structure with Gibbs sampling and constructs batched queries using determinantal point processes. Experimental validations on both synthetic and real-world functions demonstrate that the proposed method outperforms the existing state-of-the-art approaches.
Jan 06, 2018

Zi Wang, Chengtao Li, Stefanie Jegelka, Pushmeet Kohli

* Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia, PMLR 70, 2017

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Zero-Shot Task Generalization with Multi-Task Deep Reinforcement Learning

Nov 07, 2017

Junhyuk Oh, Satinder Singh, Honglak Lee, Pushmeet Kohli

As a step towards developing zero-shot task generalization capabilities in reinforcement learning (RL), we introduce a new RL problem where the agent should learn to execute sequences of instructions after learning useful skills that solve subtasks. In this problem, we consider two types of generalizations: to previously unseen instructions and to longer sequences of instructions. For generalization over unseen instructions, we propose a new objective which encourages learning correspondences between similar subtasks by making analogies. For generalization over sequential instructions, we present a hierarchical architecture where a meta controller learns to use the acquired skills for executing the instructions. To deal with delayed reward, we propose a new neural architecture in the meta controller that learns when to update the subtask, which makes learning more efficient. Experimental results on a stochastic 3D domain show that the proposed ideas are crucial for generalization to longer instructions as well as unseen instructions.
Nov 07, 2017

Junhyuk Oh, Satinder Singh, Honglak Lee, Pushmeet Kohli

* ICML 2017

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Semantic Code Repair using Neuro-Symbolic Transformation Networks

Oct 30, 2017

Jacob Devlin, Jonathan Uesato, Rishabh Singh, Pushmeet Kohli

We study the problem of semantic code repair, which can be broadly defined as automatically fixing non-syntactic bugs in source code. The majority of past work in semantic code repair assumed access to unit tests against which candidate repairs could be validated. In contrast, the goal here is to develop a strong statistical model to accurately predict both bug locations and exact fixes without access to information about the intended correct behavior of the program. Achieving such a goal requires a robust contextual repair model, which we train on a large corpus of real-world source code that has been augmented with synthetically injected bugs. Our framework adopts a two-stage approach where first a large set of repair candidates are generated by rule-based processors, and then these candidates are scored by a statistical model using a novel neural network architecture which we refer to as Share, Specialize, and Compete. Specifically, the architecture (1) generates a shared encoding of the source code using an RNN over the abstract syntax tree, (2) scores each candidate repair using specialized network modules, and (3) then normalizes these scores together so they can compete against one another in comparable probability space. We evaluate our model on a real-world test set gathered from GitHub containing four common categories of bugs. Our model is able to predict the exact correct repair 41\% of the time with a single guess, compared to 13\% accuracy for an attentional sequence-to-sequence model.
Oct 30, 2017

Jacob Devlin, Jonathan Uesato, Rishabh Singh, Pushmeet Kohli

**Click to Read Paper and Get Code**

Learning Continuous Semantic Representations of Symbolic Expressions

Jun 10, 2017

Miltiadis Allamanis, Pankajan Chanthirasegaran, Pushmeet Kohli, Charles Sutton

Combining abstract, symbolic reasoning with continuous neural reasoning is a grand challenge of representation learning. As a step in this direction, we propose a new architecture, called neural equivalence networks, for the problem of learning continuous semantic representations of algebraic and logical expressions. These networks are trained to represent semantic equivalence, even of expressions that are syntactically very different. The challenge is that semantic representations must be computed in a syntax-directed manner, because semantics is compositional, but at the same time, small changes in syntax can lead to very large changes in semantics, which can be difficult for continuous neural architectures. We perform an exhaustive evaluation on the task of checking equivalence on a highly diverse class of symbolic algebraic and boolean expression types, showing that our model significantly outperforms existing architectures.
Jun 10, 2017

Miltiadis Allamanis, Pankajan Chanthirasegaran, Pushmeet Kohli, Charles Sutton

* Accepted to ICML 2017

**Click to Read Paper and Get Code**

This paper proposes a novel MAP inference framework for Markov Random Field (MRF) in parallel computing environments. The inference framework, dubbed Swarm Fusion, is a natural generalization of the Fusion Move method. Every thread (in a case of multi-threading environments) maintains and updates a solution. At each iteration, a thread can generate arbitrary number of solution proposals and take arbitrary number of concurrent solutions from the other threads to perform multi-way fusion in updating its solution. The framework is general, making popular existing inference techniques such as alpha-expansion, fusion move, parallel alpha-expansion, and hierarchical fusion, its special cases. We have evaluated the effectiveness of our approach against competing methods on three problems of varying difficulties, in particular, the stereo, the optical flow, and the layered depthmap estimation problems.

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Deep Multi-Modal Image Correspondence Learning

Dec 05, 2016

Chen Liu, Jiajun Wu, Pushmeet Kohli, Yasutaka Furukawa

Inference of correspondences between images from different modalities is an extremely important perceptual ability that enables humans to understand and recognize cross-modal concepts. In this paper, we consider an instance of this problem that involves matching photographs of building interiors with their corresponding floorplan. This is a particularly challenging problem because a floorplan, as a stylized architectural drawing, is very different in appearance from a color photograph. Furthermore, individual photographs by themselves depict only a part of a floorplan (e.g., kitchen, bathroom, and living room). We propose the use of a number of different neural network architectures for this task, which are trained and evaluated on a novel large-scale dataset of 5 million floorplan images and 80 million associated photographs. Experimental evaluation reveals that our neural network architectures are able to identify visual cues that result in reliable matches across these two quite different modalities. In fact, the trained networks are able to even outperform human subjects in several challenging image matching problems. Our result implies that neural networks are effective at perceptual tasks that require long periods of reasoning even for humans to solve.
Dec 05, 2016

Chen Liu, Jiajun Wu, Pushmeet Kohli, Yasutaka Furukawa

**Click to Read Paper and Get Code**

PerforatedCNNs: Acceleration through Elimination of Redundant Convolutions

Oct 16, 2016

Michael Figurnov, Aijan Ibraimova, Dmitry Vetrov, Pushmeet Kohli

We propose a novel approach to reduce the computational cost of evaluation of convolutional neural networks, a factor that has hindered their deployment in low-power devices such as mobile phones. Inspired by the loop perforation technique from source code optimization, we speed up the bottleneck convolutional layers by skipping their evaluation in some of the spatial positions. We propose and analyze several strategies of choosing these positions. We demonstrate that perforation can accelerate modern convolutional networks such as AlexNet and VGG-16 by a factor of 2x - 4x. Additionally, we show that perforation is complementary to the recently proposed acceleration method of Zhang et al.
Oct 16, 2016

Michael Figurnov, Aijan Ibraimova, Dmitry Vetrov, Pushmeet Kohli

* NIPS 2016

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Time-Sensitive Bayesian Information Aggregation for Crowdsourcing Systems

Apr 18, 2016

Matteo Venanzi, John Guiver, Pushmeet Kohli, Nick Jennings

Crowdsourcing systems commonly face the problem of aggregating multiple judgments provided by potentially unreliable workers. In addition, several aspects of the design of efficient crowdsourcing processes, such as defining worker's bonuses, fair prices and time limits of the tasks, involve knowledge of the likely duration of the task at hand. Bringing this together, in this work we introduce a new time--sensitive Bayesian aggregation method that simultaneously estimates a task's duration and obtains reliable aggregations of crowdsourced judgments. Our method, called BCCTime, builds on the key insight that the time taken by a worker to perform a task is an important indicator of the likely quality of the produced judgment. To capture this, BCCTime uses latent variables to represent the uncertainty about the workers' completion time, the tasks' duration and the workers' accuracy. To relate the quality of a judgment to the time a worker spends on a task, our model assumes that each task is completed within a latent time window within which all workers with a propensity to genuinely attempt the labelling task (i.e., no spammers) are expected to submit their judgments. In contrast, workers with a lower propensity to valid labeling, such as spammers, bots or lazy labelers, are assumed to perform tasks considerably faster or slower than the time required by normal workers. Specifically, we use efficient message-passing Bayesian inference to learn approximate posterior probabilities of (i) the confusion matrix of each worker, (ii) the propensity to valid labeling of each worker, (iii) the unbiased duration of each task and (iv) the true label of each task. Using two real-world public datasets for entity linking tasks, we show that BCCTime produces up to 11% more accurate classifications and up to 100% more informative estimates of a task's duration compared to state-of-the-art methods.
Apr 18, 2016

Matteo Venanzi, John Guiver, Pushmeet Kohli, Nick Jennings

**Click to Read Paper and Get Code**

Crowdsourcing and human computation has been employed in increasingly sophisticated projects that require the solution of a heterogeneous set of tasks. We explore the challenge of building or hiring an effective team, for performing tasks required for such projects on an ongoing basis, from an available pool of applicants or workers who have bid for the tasks. The recruiter needs to learn workers' skills and expertise by performing online tests and interviews, and would like to minimize the amount of budget or time spent in this process before committing to hiring the team. How can one optimally spend budget to learn the expertise of workers as part of recruiting a team? How can one exploit the similarities among tasks as well as underlying social ties or commonalities among the workers for faster learning? We tackle these decision-theoretic challenges by casting them as an instance of online learning for best action selection. We present algorithms with PAC bounds on the required budget to hire a near-optimal team with high confidence. Furthermore, we consider an embedding of the tasks and workers in an underlying graph that may arise from task similarities or social ties, and that can provide additional side-observations for faster learning. We then quantify the improvement in the bounds that we can achieve depending on the characteristic properties of this graph structure. We evaluate our methodology on simulated problem instances as well as on real-world crowdsourcing data collected from the oDesk platform. Our methodology and results present an interesting direction of research to tackle the challenges faced by a recruiter for contract-based crowdsourcing.

* Short version of this paper will appear in HCOMP'15

* Short version of this paper will appear in HCOMP'15

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Multi-utility Learning: Structured-output Learning with Multiple Annotation-specific Loss Functions

Jun 23, 2014

Roman Shapovalov, Dmitry Vetrov, Anton Osokin, Pushmeet Kohli

Structured-output learning is a challenging problem; particularly so because of the difficulty in obtaining large datasets of fully labelled instances for training. In this paper we try to overcome this difficulty by presenting a multi-utility learning framework for structured prediction that can learn from training instances with different forms of supervision. We propose a unified technique for inferring the loss functions most suitable for quantifying the consistency of solutions with the given weak annotation. We demonstrate the effectiveness of our framework on the challenging semantic image segmentation problem for which a wide variety of annotations can be used. For instance, the popular training datasets for semantic segmentation are composed of images with hard-to-generate full pixel labellings, as well as images with easy-to-obtain weak annotations, such as bounding boxes around objects, or image-level labels that specify which object categories are present in an image. Experimental evaluation shows that the use of annotation-specific loss functions dramatically improves segmentation accuracy compared to the baseline system where only one type of weak annotation is used.
Jun 23, 2014

Roman Shapovalov, Dmitry Vetrov, Anton Osokin, Pushmeet Kohli

**Click to Read Paper and Get Code**