arXiv subjects

Ian Fischer

Publications and source records attributed to Ian Fischer.

31 records · Page 2Linked to original sources

arXiv2020

Phase Transitions for the Information Bottleneck in Representation Learning

In the Information Bottleneck (IB), when tuning the relative strength between compression and prediction terms, how do the two terms behave, and what's their relationship with the dataset and the learned representation? In this paper, we set out to answer these questions by studying multiple phase transitions in the IB objective: $\text{IB}_β[p(z|x)] = I(X; Z) - βI(Y; Z)$ defined on the encoding distribution p(z|x) for input $X$, target $Y$ and representation $Z$, where sudden jumps of $dI(Y; Z)/d β$ and prediction accuracy are observed with increasing $β$. We introduce a definition for IB phase transitions as a qualitative change of the IB loss landscape, and show that the transitions correspond to the onset of learning new classes. Using second-order calculus of variations, we derive a formula that provides a practical condition for IB phase transitions, and draw its connection with the Fisher information matrix for parameterized models. We provide two perspectives to understand the formula, revealing that each IB phase transition is finding a component of maximum (nonlinear) correlation between $X$ and $Y$ orthogonal to the learned representation, in close analogy with canonical-correlation analysis (CCA) in linear settings. Based on the theory, we present an algorithm for discovering phase transition points. Finally, we verify that our theory and algorithm accurately predict phase transitions in categorical datasets, predict the onset of learning new classes and class difficulty in MNIST, and predict prominent phase transitions in CIFAR10.

cs.LG↗

arXiv2019

Deep Variational Information Bottleneck

We present a variational approximation to the information bottleneck of Tishby et al. (1999). This variational approach allows us to parameterize the information bottleneck model using a neural network and leverage the reparameterization trick for efficient training. We call this method "Deep Variational Information Bottleneck", or Deep VIB. We show that models trained with the VIB objective outperform those that are trained with other forms of regularization, in terms of generalization performance and robustness to adversarial attack.

cs.LG↗

arXiv2019

Learnability for the Information Bottleneck

The Information Bottleneck (IB) method (\cite{tishby2000information}) provides an insightful and principled approach for balancing compression and prediction for representation learning. The IB objective $I(X;Z)-βI(Y;Z)$ employs a Lagrange multiplier $β$ to tune this trade-off. However, in practice, not only is $β$ chosen empirically without theoretical guidance, there is also a lack of theoretical understanding between $β$, learnability, the intrinsic nature of the dataset and model capacity. In this paper, we show that if $β$ is improperly chosen, learning cannot happen -- the trivial representation $P(Z|X)=P(Z)$ becomes the global minimum of the IB objective. We show how this can be avoided, by identifying a sharp phase transition between the unlearnable and the learnable which arises as $β$ is varied. This phase transition defines the concept of IB-Learnability. We prove several sufficient conditions for IB-Learnability, which provides theoretical guidance for choosing a good $β$. We further show that IB-learnability is determined by the largest confident, typical, and imbalanced subset of the examples (the conspicuous subset), and discuss its relation with model capacity. We give practical algorithms to estimate the minimum $β$ for a given dataset. We also empirically demonstrate our theoretical conditions with analyses of synthetic datasets, MNIST, and CIFAR10.

cs.LG↗

arXiv2019

Learning Latent Dynamics for Planning from Pixels

Planning has been very successful for control tasks with known environment dynamics. To leverage planning in unknown environments, the agent needs to learn the dynamics from interactions with the world. However, learning dynamics models that are accurate enough for planning has been a long-standing challenge, especially in image-based domains. We propose the Deep Planning Network (PlaNet), a purely model-based agent that learns the environment dynamics from images and chooses actions through fast online planning in latent space. To achieve high performance, the dynamics model must accurately predict the rewards ahead for multiple time steps. We approach this using a latent dynamics model with both deterministic and stochastic transition components. Moreover, we propose a multi-step variational inference objective that we name latent overshooting. Using only pixel observations, our agent solves continuous control tasks with contact dynamics, partial observability, and sparse rewards, which exceed the difficulty of tasks that were previously solved by planning with learned models. PlaNet uses substantially fewer episodes and reaches final performance close to and sometimes higher than strong model-free algorithms.

cs.LG↗

arXiv2019

Dueling Decoders: Regularizing Variational Autoencoder Latent Spaces

Variational autoencoders learn unsupervised data representations, but these models frequently converge to minima that fail to preserve meaningful semantic information. For example, variational autoencoders with autoregressive decoders often collapse into autodecoders, where they learn to ignore the encoder input. In this work, we demonstrate that adding an auxiliary decoder to regularize the latent space can prevent this collapse, but successful auxiliary decoding tasks are domain dependent. Auxiliary decoders can increase the amount of semantic information encoded in the latent space and visible in the reconstructions. The semantic information in the variational autoencoder's representation is only weakly correlated with its rate, distortion, or evidence lower bound. Compared to other popular strategies that modify the training objective, our regularization of the latent space generally increased the semantic information content.

cs.LG↗

arXiv2019

GILBO: One Metric to Measure Them All

We propose a simple, tractable lower bound on the mutual information contained in the joint generative density of any latent variable generative model: the GILBO (Generative Information Lower BOund). It offers a data-independent measure of the complexity of the learned latent variable description, giving the log of the effective description length. It is well-defined for both VAEs and GANs. We compute the GILBO for 800 GANs and VAEs each trained on four datasets (MNIST, FashionMNIST, CIFAR-10 and CelebA) and discuss the results.

stat.ML↗

arXiv2018

Generative Models of Visually Grounded Imagination

It is easy for people to imagine what a man with pink hair looks like, even if they have never seen such a person before. We call the ability to create images of novel semantic concepts visually grounded imagination. In this paper, we show how we can modify variational auto-encoders to perform this task. Our method uses a novel training objective, and a novel product-of-experts inference network, which can handle partially specified (abstract) concepts in a principled and efficient way. We also propose a set of easy-to-compute evaluation metrics that capture our intuitive notions of what it means to have good visual imagination, namely correctness, coverage, and compositionality (the 3 C's). Finally, we perform a detailed comparison of our method with two existing joint image-attribute VAE methods (the JMVAE method of Suzuki et.al. and the BiVCCA method of Wang et.al.) by applying them to two datasets: the MNIST-with-attributes dataset (which we introduce here), and the CelebA dataset.

cs.LG↗

arXiv2018

TherML: Thermodynamics of Machine Learning

In this work we offer a framework for reasoning about a wide class of existing objectives in machine learning. We develop a formal correspondence between this work and thermodynamics and discuss its implications.

cs.LG↗

arXiv2018

Uncertainty in the Variational Information Bottleneck

We present a simple case study, demonstrating that Variational Information Bottleneck (VIB) can improve a network's classification calibration as well as its ability to detect out-of-distribution data. Without explicitly being designed to do so, VIB gives two natural metrics for handling and quantifying uncertainty.

cs.LG↗

arXiv2018

Fixing a Broken ELBO

Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation is to maximize the evidence lower bound (ELBO) instead. However, maximum likelihood training (whether exact or approximate) does not necessarily result in a good latent representation, as we demonstrate both theoretically and empirically. In particular, we derive variational lower and upper bounds on the mutual information between the input and the latent variable, and use these bounds to derive a rate-distortion curve that characterizes the tradeoff between compression and reconstruction accuracy. Using this framework, we demonstrate that there is a family of models with identical ELBO, but different quantitative and qualitative characteristics. Our framework also suggests a simple new method to ensure that latent variable models with powerful stochastic decoders do not ignore their latent code.

cs.LG↗

arXiv2017

Speed/accuracy trade-offs for modern convolutional object detectors

The goal of this paper is to serve as a guide for selecting a detection architecture that achieves the right speed/memory/accuracy balance for a given application and platform. To this end, we investigate various ways to trade accuracy for speed and memory usage in modern convolutional object detection systems. A number of successful systems have been proposed in recent years, but apples-to-apples comparisons are difficult due to different base feature extractors (e.g., VGG, Residual Networks), different default image resolutions, as well as different hardware and software platforms. We present a unified implementation of the Faster R-CNN [Ren et al., 2015], R-FCN [Dai et al., 2016] and SSD [Liu et al., 2015] systems, which we view as "meta-architectures" and trace out the speed/accuracy trade-off curve created by using alternative feature extractors and varying other critical parameters such as image size within each of these meta-architectures. On one extreme end of this spectrum where speed and memory are critical, we present a detector that achieves real time speeds and can be deployed on a mobile device. On the opposite end in which accuracy is critical, we present a detector that achieves state-of-the-art performance measured on the COCO detection task.

cs.CV↗

arXiv2017

Adversarial Transformation Networks: Learning to Generate Adversarial Examples

Multiple different approaches of generating adversarial examples have been proposed to attack deep neural networks. These approaches involve either directly computing gradients with respect to the image pixels, or directly solving an optimization on the image pixels. In this work, we present a fundamentally new method for generating adversarial examples that is fast to execute and provides exceptional diversity of output. We efficiently train feed-forward neural networks in a self-supervised manner to generate adversarial examples against a target network or set of networks. We call such a network an Adversarial Transformation Network (ATN). ATNs are trained to generate adversarial examples that minimally modify the classifier's outputs given the original input, while constraining the new classification to match an adversarial target class. We present methods to train ATNs and analyze their effectiveness targeting a variety of MNIST classifiers as well as the latest state-of-the-art ImageNet classifier Inception ResNet v2.

cs.NE↗

arXiv2017

Adversarial examples for generative models

We explore methods of producing adversarial examples on deep generative models such as the variational autoencoder (VAE) and the VAE-GAN. Deep learning architectures are known to be vulnerable to adversarial examples, but previous work has focused on the application of adversarial examples to classification tasks. Deep generative models have recently become popular due to their ability to model input data distributions and generate realistic examples from those distributions. We present three classes of attacks on the VAE and VAE-GAN architectures and demonstrate them against networks trained on MNIST, SVHN and CelebA. Our first attack leverages classification-based adversaries by attaching a classifier to the trained encoder of the target generative model, which can then be used to indirectly manipulate the latent representation. Our second attack directly uses the VAE loss function to generate a target reconstruction image from the adversarial example. Our third attack moves beyond relying on classification or the standard loss for the gradient and directly optimizes against differences in source and target latent representations. We also motivate why an attacker might be interested in deploying such techniques against a target generative network.

stat.ML↗