Integral Equations and Machine Learning

As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, reinforcement learning techniques may be used for photorealistic image synthesis: Efficiency may be dramatically improved by guiding light transport paths by an approximate solution of the integral equation that is learned during rendering. In the light of the recent advances in reinforcement learning for playing games, we investigate the representation of an approximate solution of an integral equation by artificial neural networks and derive a loss function for that purpose. The resulting Monte Carlo and quasi-Monte Carlo methods train neural networks with standard information instead of linear information and naturally are able to generate an arbitrary number of training samples. The methods are demonstrated for applications in light transport simulation

Formal Policy Synthesis for Continuous-Space Systems via Reinforcement Learning

This paper studies satisfaction of temporal properties on unknown stochastic processes that have continuous state spaces. We show how reinforcement learning (RL) can be applied for computing policies that are finite-memory and deterministic using only the paths of the stochastic process. We address properties expressed in linear temporal logic (LTL) and use their automaton representation to give a path-dependent reward function maximised via the RL algorithm. We develop the required assumptions and theories for the convergence of the learned policy to the optimal policy in the continuous state space. To improve the performance of the learning on the constructed sparse reward function, we propose a sequential learning procedure based on a sequence of labelling functions obtained from the positive normal form of the LTL specification. We use this procedure to guide the RL algorithm towards a policy that converges to an optimal policy under suitable assumptions on the process. We demonstrate the approach on a 4-dim cart-pole system and 6-dim boat driving problem.Comment: This is the extended version of the paper accepted in the 16th International Conference on integrated Formal Methods (iFM

Context-Aware Synthesis and Placement of Object Instances

Learning to insert an object instance into an image in a semantically coherent manner is a challenging and interesting problem. Solving it requires (a) determining a location to place an object in the scene and (b) determining its appearance at the location. Such an object insertion model can potentially facilitate numerous image editing and scene parsing applications. In this paper, we propose an end-to-end trainable neural network for the task of inserting an object instance mask of a specified class into the semantic label map of an image. Our network consists of two generative modules where one determines where the inserted object mask should be (i.e., location and scale) and the other determines what the object mask shape (and pose) should look like. The two modules are connected together via a spatial transformation network and jointly trained. We devise a learning procedure that leverage both supervised and unsupervised data and show our model can insert an object at diverse locations with various appearances. We conduct extensive experimental validations with comparisons to strong baselines to verify the effectiveness of the proposed network

Inverse Transport Networks

We introduce inverse transport networks as a learning architecture for inverse rendering problems where, given input image measurements, we seek to infer physical scene parameters such as shape, material, and illumination. During training, these networks are evaluated not only in terms of how close they can predict groundtruth parameters, but also in terms of whether the parameters they produce can be used, together with physically-accurate graphics renderers, to reproduce the input image measurements. To en- able training of inverse transport networks using stochastic gradient descent, we additionally create a general-purpose, physically-accurate differentiable renderer, which can be used to estimate derivatives of images with respect to arbitrary physical scene parameters. Our experiments demonstrate that inverse transport networks can be trained efficiently using differentiable rendering, and that they generalize to scenes with completely unseen geometry and illumination better than networks trained without appearance- matching regularization

Evolutionary Cell Aided Design for Neural Network Architectures

Mathematical theory shows us that multilayer feedforward Artificial Neural Networks(ANNs) are universal function approximators, capable of approximating any measurable function to any desired degree of accuracy. In practice designing practical and efficient neural network architectures require significant effort and expertise. We present a novel software framework called Evolutionary Cell Aided Design(ECAD) meant to aid in the exploration and design of efficient Neural Network Architectures(NNAs) for reconfigurable hardware. Given a general neural network structure and a set of constraints and fitness functions, the framework will explore both the space of possible NNA and the space of possible hardware designs, using evolutionary algorithms, and attempt to find the fittest co-design solutions according to a predefined set of goals. We test the framework on an image classification task and use the MNIST data set of hand written digits with an Intel Arria 10 GX 1150 device as our target platform. We design and implement a modular and scalable 2D systolic array with enhancements for machine learning that can be used by the framework for the hardware search space. Our results demonstrate the ability to pair neural network design and hardware development together using an evolutionary algorithm and removing traditional human-in-the-loop development tasks. By running various experiments of the fittest solutions for neural network and hardware searches, we demonstrate the full end-to-end capabilities of the ECAD framework.Comment: Text and image edit

Neural Logic Machines

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.Comment: ICLR 2019. Project page: https://sites.google.com/view/neural-logic-machine

Learning from Longitudinal Face Demonstration - Where Tractable Deep Modeling Meets Inverse Reinforcement Learning

This paper presents a novel Subject-dependent Deep Aging Path (SDAP), which inherits the merits of both Generative Probabilistic Modeling and Inverse Reinforcement Learning to model the facial structures and the longitudinal face aging process of a given subject. The proposed SDAP is optimized using tractable log-likelihood objective functions with Convolutional Neural Networks (CNNs) based deep feature extraction. Instead of applying a fixed aging development path for all input faces and subjects, SDAP is able to provide the most appropriate aging development path for individual subject that optimizes the reward aging formulation. Unlike previous methods that can take only one image as the input, SDAP further allows multiple images as inputs, i.e. all information of a subject at either the same or different ages, to produce the optimal aging path for the given subject. Finally, SDAP allows efficiently synthesizing in-the-wild aging faces. The proposed model is experimented in both tasks of face aging synthesis and cross-age face verification. The experimental results consistently show SDAP achieves the state-of-the-art performance on numerous face aging databases, i.e. FG-NET, MORPH, AginG Faces in the Wild (AGFW), and Cross-Age Celebrity Dataset (CACD). Furthermore, we also evaluate the performance of SDAP on large-scale Megaface challenge to demonstrate the advantages of the proposed solution

Neural-Network Guided Expression Transformation

Optimizing compilers, as well as other translator systems, often work by rewriting expressions according to equivalence preserving rules. Given an input expression and its optimized form, finding the sequence of rules that were applied is a non-trivial task. Most of the time, the tools provide no proof, of any kind, of the equivalence between the original expression and its optimized form. In this work, we propose to reconstruct proofs of equivalence of simple mathematical expressions, after the fact, by finding paths of equivalence preserving transformations between expressions. We propose to find those sequences of transformations using a search algorithm, guided by a neural network heuristic. Using a Tree-LSTM recursive neural network, we learn a distributed representation of expressions where the Manhattan distance between vectors approximately corresponds to the rewrite distance between expressions. We then show how the neural network can be efficiently used to search for transformation paths, leading to substantial gain in speed compared to an uninformed exhaustive search. In one of our experiments, our neural-network guided search algorithm is able to solve more instances with a 2 seconds timeout per instance than breadth-first search does with a 5 minutes timeout per instance

Neural Style Transfer: A Review

The seminal work of Gatys et al. demonstrated the power of Convolutional Neural Networks (CNNs) in creating artistic imagery by separating and recombining image content and style. This process of using CNNs to render a content image in different styles is referred to as Neural Style Transfer (NST). Since then, NST has become a trending topic both in academic literature and industrial applications. It is receiving increasing attention and a variety of approaches are proposed to either improve or extend the original NST algorithm. In this paper, we aim to provide a comprehensive overview of the current progress towards NST. We first propose a taxonomy of current algorithms in the field of NST. Then, we present several evaluation methods and compare different NST algorithms both qualitatively and quantitatively. The review concludes with a discussion of various applications of NST and open problems for future research. A list of papers discussed in this review, corresponding codes, pre-trained models and more comparison results are publicly available at https://github.com/ycjing/Neural-Style-Transfer-Papers.Comment: Project page: https://github.com/ycjing/Neural-Style-Transfer-Paper

Introspective Generative Modeling: Decide Discriminatively

We study unsupervised learning by developing introspective generative modeling (IGM) that attains a generator using progressively learned deep convolutional neural networks. The generator is itself a discriminator, capable of introspection: being able to self-evaluate the difference between its generated samples and the given training data. When followed by repeated discriminative learning, desirable properties of modern discriminative classifiers are directly inherited by the generator. IGM learns a cascade of CNN classifiers using a synthesis-by-classification algorithm. In the experiments, we observe encouraging results on a number of applications including texture modeling, artistic style transferring, face modeling, and semi-supervised learning.Comment: 10 pages, 9 figure