On the Implicit Bias of Initialization Shape: Beyond Infinitesimal Mirror Descent

Recent work has highlighted the role of initialization scale in determining the structure of the solutions that gradient methods converge to. In particular, it was shown that large initialization leads to the neural tangent kernel regime solution, whereas small initialization leads to so called "rich regimes". However, the initialization structure is richer than the overall scale alone and involves relative magnitudes of different weights and layers in the network. Here we show that these relative scales, which we refer to as initialization shape, play an important role in determining the learned model. We develop a novel technique for deriving the inductive bias of gradient-flow and use it to obtain closed-form implicit regularizers for multiple cases of interest.

Towards Understanding Learning in Neural Networks with Linear Teachers

Can a neural network minimizing cross-entropy learn linearly separable data? Despite progress in the theory of deep learning, this question remains unsolved. Here we prove that SGD globally optimizes this learning problem for a two-layer network with Leaky ReLU activations. The learned network can in principle be very complex. However, empirical evidence suggests that it often turns out to be approximately linear. We provide theoretical support for this phenomenon by proving that if network weights converge to two weight clusters, this will imply an approximately linear decision boundary. Finally, we show a condition on the optimization that leads to weight clustering. We provide empirical results that validate our theoretical analysis.

Few-Shot Question Answering by Pretraining Span Selection

In a number of question answering (QA) benchmarks, pretrained models have reached human parity through fine-tuning on an order of 100,000 annotated questions and answers. We explore the more realistic few-shot setting, where only a few hundred training examples are available. We show that standard span selection models perform poorly, highlighting the fact that current pretraining objective are far removed from question answering. To address this, we propose a new pretraining scheme that is more suitable for extractive question answering. Given a passage with multiple sets of recurring spans, we mask in each set all recurring spans but one, and ask the model to select the correct span in the passage for each masked span. Masked spans are replaced with a special token, viewed as a question representation, that is later used during fine-tuning to select the answer span. The resulting model obtains surprisingly good results on multiple benchmarks, e.g., 72.7 F1 with only 128 examples on SQuAD, while maintaining competitive (and sometimes better) performance in the high-resource setting. Our findings indicate that careful design of pretraining schemes and model architecture can have a dramatic effect on performance in the few-shot settings.

Regularizing Towards Permutation Invariance in Recurrent Models

In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order. We show that RNNs can be regularized towards permutation invariance, and that this can result in compact models, as compared to non-recurrent architectures. We implement this idea via a novel form of stochastic regularization. Existing solutions mostly suggest restricting the learning problem to hypothesis classes which are permutation invariant by design. Our approach of enforcing permutation invariance via regularization gives rise to models which are \textit{semi permutation invariant} (e.g. invariant to some permutations and not to others). We show that our method outperforms other permutation invariant approaches on synthetic and real world datasets.

Maximin Optimization for Binary Regression

We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of the gradient ascent-descent method. Such maximin techniques are still poorly understood even in the concave-convex case. The non-convex binary constraints may lead to spurious local minima. Interestingly, we prove that this approach is optimal in linear regression with low noise conditions as well as robust regression with a small number of outliers. Practically, the method also performs well in regression with cross entropy loss, as well as non-convex multi-layer neural networks. Taken together our approach highlights the potential of saddle-point optimization for learning constrained models.

Learning Object Detection from Captions via Textual Scene Attributes

Object detection is a fundamental task in computer vision, requiring large annotated datasets that are difficult to collect, as annotators need to label objects and their bounding boxes. Thus, it is a significant challenge to use cheaper forms of supervision effectively. Recent work has begun to explore image captions as a source for weak supervision, but to date, in the context of object detection, captions have only been used to infer the categories of the objects in the image. In this work, we argue that captions contain much richer information about the image, including attributes of objects and their relations. Namely, the text represents a scene of the image, as described recently in the literature. We present a method that uses the attributes in this "textual scene graph" to train object detectors. We empirically demonstrate that the resulting model achieves state-of-the-art results on several challenging object detection datasets, outperforming recent approaches.

Holdout SGD: Byzantine Tolerant Federated Learning

This work presents a new distributed Byzantine tolerant federated learning algorithm, HoldOut SGD, for Stochastic Gradient Descent (SGD) optimization. HoldOut SGD uses the well known machine learning technique of holdout estimation, in a distributed fashion, in order to select parameter updates that are likely to lead to models with low loss values. This makes it more effective at discarding Byzantine workers inputs than existing methods that eliminate outliers in the parameter-space of the learned model. HoldOut SGD first randomly selects a set of workers that use their private data in order to propose gradient updates. Next, a voting committee of workers is randomly selected, and each voter uses its private data as holdout data, in order to select the best proposals via a voting scheme. We propose two possible mechanisms for the coordination of workers in the distributed computation of HoldOut SGD. The first uses a truthful central server and corresponds to the typical setting of current federated learning. The second is fully distributed and requires no central server, paving the way to fully decentralized federated learning. The fully distributed version implements HoldOut SGD via ideas from the blockchain domain, and specifically the Algorand committee selection and consensus processes. We provide formal guarantees for the HoldOut SGD process in terms of its convergence to the optimal model, and its level of resilience to the fraction of Byzantine workers. Empirical evaluation shows that HoldOut SGD is Byzantine-resilient and efficiently converges to an effectual model for deep-learning tasks, as long as the total number of participating workers is large and the fraction of Byzantine workers is less than half (<1/3 for the fully distributed variant).

Compositional Video Synthesis with Action Graphs

Videos of actions are complex spatio-temporal signals, containing rich compositional structures. Current generative models are limited in their ability to generate examples of object configurations outside the range they were trained on. Towards this end, we introduce a generative model (AG2Vid) based on Action Graphs, a natural and convenient structure that represents the dynamics of actions between objects over time. Our AG2Vid model disentangles appearance and position features, allowing for more accurate generation. AG2Vid is evaluated on the CATER and Something-Something datasets and outperforms other baselines. Finally, we show how Action Graphs can be used for generating novel compositions of unseen actions.

Learning Object Permanence from Video

Object Permanence allows people to reason about the location of non-visible objects, by understanding that they continue to exist even when not perceived directly. Object Permanence is critical for building a model of the world, since objects in natural visual scenes dynamically occlude and contain each-other. Intensive studies in developmental psychology suggest that object permanence is a challenging task that is learned through extensive experience. Here we introduce the setup of learning Object Permanence from data. We explain why this learning problem should be dissected into four components, where objects are (1) visible, (2) occluded, (3) contained by another object and (4) carried by a containing object. The fourth subtask, where a target object is carried by a containing object, is particularly challenging because it requires a system to reason about a moving location of an invisible object. We then present a unified deep architecture that learns to predict object location under these four scenarios. We evaluate the architecture and system on a new dataset based on CATER, and find that it outperforms previous localization methods and various baselines.

On the Inductive Bias of a CNN for Orthogonal Patterns Distributions

Training overparameterized convolutional neural networks with gradient based methods is the most successful learning method for image classification. However, its theoretical properties are far from understood even for very simple learning tasks. In this work, we consider a simplified image classification task where images contain orthogonal patches and are learned with a 3-layer overparameterized convolutional network and stochastic gradient descent. We empirically identify a novel phenomenon where the dot-product between the learned pattern detectors and their detected patterns are governed by the pattern statistics in the training set. We call this phenomenon Pattern Statistics Inductive Bias (PSI) and prove that PSI holds for a simple setup with two points in the training set. Furthermore, we prove that if PSI holds, stochastic gradient descent has sample complexity $O(d^2\log(d))$ where $d$ is the filter dimension. In contrast, we show a VC dimension lower bound in our setting which is exponential in $d$. Taken together, our results provide strong evidence that PSI is a unique inductive bias of stochastic gradient descent, that guarantees good generalization properties.