Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

This paper presents a new reflectance model for rendering computer synthesized images. The model accounts for the relative brightness of different materials and light sources in the same scene. It describes the directional distribution of the reflected light and a color shift that occurs as the reflectance changes with incidence angle. The paper presents a method for obtaining the spectral energy distribution of the light reflected from an object made of a specific real material and discusses a procedure for accurately reproducing the color associated with the spectral energy distribution. The model is applied to the simulation of a metal and a plastic.

A reflectance model for computer graphics

Neural graphics primitives, parameterized by fully connected neural networks, can be costly to train and evaluate. We reduce this cost with a versatile new input encoding that permits the use of a smaller network without sacrificing quality, thus significantly reducing the number of floating point and memory access operations: a small neural network is augmented by a multiresolution hash table of trainable feature vectors whose values are optimized through stochastic gradient descent. The multiresolution structure allows the network to disambiguate hash collisions, making for a simple architecture that is trivial to parallelize on modern GPUs. We leverage this parallelism by implementing the whole system using fully-fused CUDA kernels with a focus on minimizing wasted bandwidth and compute operations. We achieve a combined speedup of several orders of magnitude, enabling training of high-quality neural graphics primitives in a matter of seconds, and rendering in tens of milliseconds at a resolution of 1920×1080.

/pdf/instant-neural-graphics-primitives-with-a-multiresolution-g4qducu3.pdf

Instant neural graphics primitives with a multiresolution hash encoding

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent work on normalizing flows, ranging from improving their expressive power to expanding their application. We believe the field has now matured and is in need of a unified perspective. In this review, we attempt to provide such a perspective by describing flows through the lens of probabilistic modeling and inference. We place special emphasis on the fundamental principles of flow design, and discuss foundational topics such as expressive power and computational trade-offs. We also broaden the conceptual framing of flows by relating them to more general probability transformations. Lastly, we summarize the use of flows for tasks such as generative modeling, approximate inference, and supervised learning.

Normalizing Flows for Probabilistic Modeling and Inference

Normalizing Flows are generative models which produce tractable distributions where both sampling and density evaluation can be efficient and exact. The goal of this survey article is to give a coherent and comprehensive review of the literature around the construction and use of Normalizing Flows for distribution learning. We aim to provide context and explanation of the models, review current state-of-the-art literature, and identify open questions and promising future directions.

Normalizing Flows: An Introduction and Review of Current Methods

Regression-based algorithms have shown to be good at denoising Monte Carlo (MC) renderings by leveraging its inexpensive by-products (e.g., feature buffers). However, when using higher-order models to handle complex cases, these techniques often overfit to noise in the input. For this reason, supervised learning methods have been proposed that train on a large collection of reference examples, but they use explicit filters that limit their denoising ability. To address these problems, we propose a novel, supervised learning approach that allows the filtering kernel to be more complex and general by leveraging a deep convolutional neural network (CNN) architecture. In one embodiment of our framework, the CNN directly predicts the final denoised pixel value as a highly non-linear combination of the input features. In a second approach, we introduce a novel, kernel-prediction network which uses the CNN to estimate the local weighting kernels used to compute each denoised pixel from its neighbors. We train and evaluate our networks on production data and observe improvements over state-of-the-art MC denoisers, showing that our methods generalize well to a variety of scenes. We conclude by analyzing various components of our architecture and identify areas of further research in deep learning for MC denoising.

/pdf/kernel-predicting-convolutional-networks-for-denoising-monte-2negipnodh.pdf

Kernel-predicting convolutional networks for denoising Monte Carlo renderings

We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its application to integration problems. First, we introduce piecewise-polynomial coupling transforms that greatly increase the modeling power of individual coupling layers. Second, we propose to preprocess the inputs of neural networks using one-blob encoding, which stimulates localization of computation and improves inference. Third, we derive a gradient-descent-based optimization for the Kullback-Leibler and the χ2 divergence for the specific application of Monte Carlo integration with unnormalized stochastic estimates of the target distribution. Our approach enables fast and accurate inference and efficient sample generation independently of the dimensionality of the integration domain. We show its benefits on generating natural images and in two applications to light-transport simulation: first, we demonstrate learning of joint path-sampling densities in the primary sample space and importance sampling of multi-dimensional path prefixes thereof. Second, we use our technique to extract conditional directional densities driven by the product of incident illumination and the BSDF in the rendering equation, and we leverage the densities for path guiding. In all applications, our approach yields on-par or higher performance than competing techniques at equal sample count.

Neural Importance Sampling

We present a modular convolutional architecture for denoising rendered images. We expand on the capabilities of kernel-predicting networks by combining them with a number of task-specific modules, and optimizing the assembly using an asymmetric loss. The source-aware encoder---the first module in the assembly---extracts low-level features and embeds them into a common feature space, enabling quick adaptation of a trained network to novel data. The spatial and temporal modules extract abstract, high-level features for kernel-based reconstruction, which is performed at three different spatial scales to reduce low-frequency artifacts. The complete network is trained using a class of asymmetric loss functions that are designed to preserve details and provide the user with a direct control over the variance-bias trade-off during inference. We also propose an error-predicting module for inferring reconstruction error maps that can be used to drive adaptive sampling. Finally, we present a theoretical analysis of convergence rates of kernel-predicting architectures, shedding light on why kernel prediction performs better than synthesizing the colors directly, complementing the empirical evidence presented in this and previous works. We demonstrate that our networks attain results that compare favorably to state-of-the-art methods in terms of detail preservation, low-frequency noise removal, and temporal stability on a variety of production and academic datasets.

Denoising with kernel prediction and asymmetric loss functions

Recent years have seen increasing attention and significant progress in many-light rendering, a class of methods for the efficient computation of global illumination. The many-light formulation offers a unified mathematical framework for the problem reducing the full lighting transport simulation to the calculation of the direct illumination from many virtual light sources. These methods are unrivaled in their scalability: they are able to produce artifact-free images in a fraction of a second but also converge to the full solution over time. In this state-of-the-art report, we have three goals: give an easy-to-follow, introductory tutorial of many-light theory; provide a comprehensive, unified survey of the topic with a comparison of the main algorithms; and present a vision to motivate and guide future research. We will cover both the fundamental concepts as well as improvements, extensions, and applications of many-light rendering.

Scalable Realistic Rendering with Many-Light Methods.

We present a robust, unbiased technique for intelligent light-path construction in path-tracing algorithms. Inspired by existing path-guiding algorithms, our method learns an approximate representation of the scene's spatio-directional radiance field in an unbiased and iterative manner. To that end, we propose an adaptive spatio-directional hybrid data structure, referred to as SD-tree, for storing and sampling incident radiance. The SD-tree consists of an upper part-a binary tree that partitions the 3D spatial domain of the light field-and a lower part-a quadtree that partitions the 2D directional domain. We further present a principled way to automatically budget training and rendering computations to minimize the variance of the final image. Our method does not require tuning hyperparameters, although we allow limiting the memory footprint of the SD-tree. The aforementioned properties, its ease of implementation, and its stable performance make our method compatible with production environments. We demonstrate the merits of our method on scenes with difficult visibility, detailed geometry, and complex specular-glossy light transport, achieving better performance than previous state-of-the-art algorithms.

Jan Novák

Papers

Kernel-predicting convolutional networks for denoising Monte Carlo renderings

Neural Importance Sampling

Denoising with kernel prediction and asymmetric loss functions

Scalable Realistic Rendering with Many-Light Methods.

Practical Path Guiding for Efficient Light-Transport Simulation