arXiv subjects

David Jacobs

Publications and source records attributed to David Jacobs.

At least 37 records · Page 2Linked to original sources

arXiv2022

Poisons that are learned faster are more effective

Imperceptible poisoning attacks on entire datasets have recently been touted as methods for protecting data privacy. However, among a number of defenses preventing the practical use of these techniques, early-stopping stands out as a simple, yet effective defense. To gauge poisons' vulnerability to early-stopping, we benchmark error-minimizing, error-maximizing, and synthetic poisons in terms of peak test accuracy over 100 epochs and make a number of surprising observations. First, we find that poisons that reach a low training loss faster have lower peak test accuracy. Second, we find that a current state-of-the-art error-maximizing poison is 7 times less effective when poison training is stopped at epoch 8. Third, we find that stronger, more transferable adversarial attacks do not make stronger poisons. We advocate for evaluating poisons in terms of peak test accuracy.

cs.LG↗

arXiv2022

On the Spectral Bias of Convolutional Neural Tangent and Gaussian Process Kernels

We study the properties of various over-parametrized convolutional neural architectures through their respective Gaussian process and neural tangent kernels. We prove that, with normalized multi-channel input and ReLU activation, the eigenfunctions of these kernels with the uniform measure are formed by products of spherical harmonics, defined over the channels of the different pixels. We next use hierarchical factorizable kernels to bound their respective eigenvalues. We show that the eigenvalues decay polynomially, quantify the rate of decay, and derive measures that reflect the composition of hierarchical features in these networks. Our results provide concrete quantitative characterization of over-parameterized convolutional network architectures.

cs.LG↗

arXiv2022

Robust Contrastive Learning Using Negative Samples with Diminished Semantics

Unsupervised learning has recently made exceptional progress because of the development of more effective contrastive learning methods. However, CNNs are prone to depend on low-level features that humans deem non-semantic. This dependency has been conjectured to induce a lack of robustness to image perturbations or domain shift. In this paper, we show that by generating carefully designed negative samples, contrastive learning can learn more robust representations with less dependence on such features. Contrastive learning utilizes positive pairs that preserve semantic information while perturbing superficial features in the training images. Similarly, we propose to generate negative samples in a reversed way, where only the superfluous instead of the semantic features are preserved. We develop two methods, texture-based and patch-based augmentations, to generate negative samples. These samples achieve better generalization, especially under out-of-domain settings. We also analyze our method and the generated texture-based samples, showing that texture features are indispensable in classifying particular ImageNet classes and especially finer classes. We also show that model bias favors texture and shape features differently under different test settings. Our code, trained models, and ImageNet-Texture dataset can be found at https://github.com/SongweiGe/Contrastive-Learning-with-Non-Semantic-Negatives.

cs.CV↗

arXiv2021

Shift Invariance Can Reduce Adversarial Robustness

Shift invariance is a critical property of CNNs that improves performance on classification. However, we show that invariance to circular shifts can also lead to greater sensitivity to adversarial attacks. We first characterize the margin between classes when a shift-invariant linear classifier is used. We show that the margin can only depend on the DC component of the signals. Then, using results about infinitely wide networks, we show that in some simple cases, fully connected and shift-invariant neural networks produce linear decision boundaries. Using this, we prove that shift invariance in neural networks produces adversarial examples for the simple case of two classes, each consisting of a single image with a black or white dot on a gray background. This is more than a curiosity; we show empirically that with real datasets and realistic architectures, shift invariance reduces adversarial robustness. Finally, we describe initial experiments using synthetic data to probe the source of this connection.

cs.LG↗

arXiv2021

Maneuver Identification Challenge

AI algorithms that identify maneuvers from trajectory data could play an important role in improving flight safety and pilot training. AI challenges allow diverse teams to work together to solve hard problems and are an effective tool for developing AI solutions. AI challenges are also a key driver of AI computational requirements. The Maneuver Identification Challenge hosted at maneuver-id.mit.edu provides thousands of trajectories collected from pilots practicing in flight simulators, descriptions of maneuvers, and examples of these maneuvers performed by experienced pilots. Each trajectory consists of positions, velocities, and aircraft orientations normalized to a common coordinate system. Construction of the data set required significant data architecture to transform flight simulator logs into AI ready data, which included using a supercomputer for deduplication and data conditioning. There are three proposed challenges. The first challenge is separating physically plausible (good) trajectories from unfeasible (bad) trajectories. Human labeled good and bad trajectories are provided to aid in this task. Subsequent challenges are to label trajectories with their intended maneuvers and to assess the quality of those maneuvers.

cs.AI↗

arXiv2021

Low Curvature Activations Reduce Overfitting in Adversarial Training

Adversarial training is one of the most effective defenses against adversarial attacks. Previous works suggest that overfitting is a dominant phenomenon in adversarial training leading to a large generalization gap between test and train accuracy in neural networks. In this work, we show that the observed generalization gap is closely related to the choice of the activation function. In particular, we show that using activation functions with low (exact or approximate) curvature values has a regularization effect that significantly reduces both the standard and robust generalization gaps in adversarial training. We observe this effect for both differentiable/smooth activations such as SiLU as well as non-differentiable/non-smooth activations such as LeakyReLU. In the latter case, the "approximate" curvature of the activation is low. Finally, we show that for activation functions with low curvature, the double descent phenomenon for adversarially trained models does not occur.

cs.LG↗

arXiv2020

On the Similarity between the Laplace and Neural Tangent Kernels

Recent theoretical work has shown that massively overparameterized neural networks are equivalent to kernel regressors that use Neural Tangent Kernels(NTK). Experiments show that these kernel methods perform similarly to real neural networks. Here we show that NTK for fully connected networks is closely related to the standard Laplace kernel. We show theoretically that for normalized data on the hypersphere both kernels have the same eigenfunctions and their eigenvalues decay polynomially at the same rate, implying that their Reproducing Kernel Hilbert Spaces (RKHS) include the same sets of functions. This means that both kernels give rise to classes of functions with the same smoothness properties. The two kernels differ for data off the hypersphere, but experiments indicate that when data is properly normalized these differences are not significant. Finally, we provide experiments on real data comparing NTK and the Laplace kernel, along with a larger class ofγ-exponential kernels. We show that these perform almost identically. Our results suggest that much insight about neural networks can be obtained from analysis of the well-known Laplace kernel, which has a simple closed-form.

cs.LG↗

arXiv2020

SharinGAN: Combining Synthetic and Real Data for Unsupervised Geometry Estimation

We propose a novel method for combining synthetic and real images when training networks to determine geometric information from a single image. We suggest a method for mapping both image types into a single, shared domain. This is connected to a primary network for end-to-end training. Ideally, this results in images from two domains that present shared information to the primary network. Our experiments demonstrate significant improvements over the state-of-the-art in two important domains, surface normal estimation of human faces and monocular depth estimation for outdoor scenes, both in an unsupervised setting.

cs.CV↗

arXiv2020

Towards Automatic Generation of Questions from Long Answers

Automatic question generation (AQG) has broad applicability in domains such as tutoring systems, conversational agents, healthcare literacy, and information retrieval. Existing efforts at AQG have been limited to short answer lengths of up to two or three sentences. However, several real-world applications require question generation from answers that span several sentences. Therefore, we propose a novel evaluation benchmark to assess the performance of existing AQG systems for long-text answers. We leverage the large-scale open-source Google Natural Questions dataset to create the aforementioned long-answer AQG benchmark. We empirically demonstrate that the performance of existing AQG methods significantly degrades as the length of the answer increases. Transformer-based methods outperform other existing AQG methods on long answers in terms of automatic as well as human evaluation. However, we still observe degradation in the performance of our best performing models with increasing sentence length, suggesting that long answer QA is a challenging benchmark task for future research.

cs.CL↗

arXiv2020

Frequency Bias in Neural Networks for Input of Non-Uniform Density

Recent works have partly attributed the generalization ability of over-parameterized neural networks to frequency bias -- networks trained with gradient descent on data drawn from a uniform distribution find a low frequency fit before high frequency ones. As realistic training sets are not drawn from a uniform distribution, we here use the Neural Tangent Kernel (NTK) model to explore the effect of variable density on training dynamics. Our results, which combine analytic and empirical observations, show that when learning a pure harmonic function of frequency $κ$, convergence at a point $\x \in \Sphere^{d-1}$ occurs in time $O(κ^d/p(\x))$ where $p(\x)$ denotes the local density at $\x$. Specifically, for data in $\Sphere^1$ we analytically derive the eigenfunctions of the kernel associated with the NTK for two-layer networks. We further prove convergence results for deep, fully connected networks with respect to the spectral decomposition of the NTK. Our empirical study highlights similarities and differences between deep and shallow networks in this model.

cs.LG↗

arXiv2020

Adversarially robust transfer learning

Transfer learning, in which a network is trained on one task and re-purposed on another, is often used to produce neural network classifiers when data is scarce or full-scale training is too costly. When the goal is to produce a model that is not only accurate but also adversarially robust, data scarcity and computational limitations become even more cumbersome. We consider robust transfer learning, in which we transfer not only performance but also robustness from a source model to a target domain. We start by observing that robust networks contain robust feature extractors. By training classifiers on top of these feature extractors, we produce new models that inherit the robustness of their parent networks. We then consider the case of fine tuning a network by re-training end-to-end in the target domain. When using lifelong learning strategies, this process preserves the robustness of the source network while achieving high accuracy. By using such strategies, it is possible to produce accurate and robust models with little data, and without the cost of adversarial training. Additionally, we can improve the generalization of adversarially trained models, while maintaining their robustness.

cs.LG↗

arXiv2019

The Convergence Rate of Neural Networks for Learned Functions of Different Frequencies

We study the relationship between the frequency of a function and the speed at which a neural network learns it. We build on recent results that show that the dynamics of overparameterized neural networks trained with gradient descent can be well approximated by a linear system. When normalized training data is uniformly distributed on a hypersphere, the eigenfunctions of this linear system are spherical harmonic functions. We derive the corresponding eigenvalues for each frequency after introducing a bias term in the model. This bias term had been omitted from the linear network model without significantly affecting previous theoretical results. However, we show theoretically and experimentally that a shallow neural network without bias cannot represent or learn simple, low frequency functions with odd frequencies. Our results lead to specific predictions of the time it will take a network to learn functions of varying frequency. These predictions match the empirical behavior of both shallow and deep networks.

cs.LG↗

arXiv2019

Understanding the (un)interpretability of natural image distributions using generative models

Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and high-dimensional image distributions. More recent generative models leverage the power of neural networks to implicitly learn and represent probability models over complex images. We describe methods to extract explicit probability density estimates from GANs, and explore the properties of these image density functions. We perform sanity check experiments to provide evidence that these probabilities are reasonable. However, we also show that density functions of natural images are difficult to interpret and thus limited in use. We study reasons for this lack of interpretability, and show that we can get interpretability back by doing density estimation on latent representations of images.

cs.LG↗

arXiv2018

SfSNet: Learning Shape, Reflectance and Illuminance of Faces in the Wild

We present SfSNet, an end-to-end learning framework for producing an accurate decomposition of an unconstrained human face image into shape, reflectance and illuminance. SfSNet is designed to reflect a physical lambertian rendering model. SfSNet learns from a mixture of labeled synthetic and unlabeled real world images. This allows the network to capture low frequency variations from synthetic and high frequency details from real images through the photometric reconstruction loss. SfSNet consists of a new decomposition architecture with residual blocks that learns a complete separation of albedo and normal. This is used along with the original image to predict lighting. SfSNet produces significantly better quantitative and qualitative results than state-of-the-art methods for inverse rendering and independent normal and illumination estimation.

cs.CV↗

arXiv2018

Stabilizing Adversarial Nets With Prediction Methods

Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not minimizers, of the loss function. The alternating stochastic gradient methods typically used for such problems do not reliably converge to saddle points, and when convergence does happen it is often highly sensitive to learning rates. We propose a simple modification of stochastic gradient descent that stabilizes adversarial networks. We show, both in theory and practice, that the proposed method reliably converges to saddle points, and is stable with a wider range of training parameters than a non-prediction method. This makes adversarial networks less likely to "collapse," and enables faster training with larger learning rates.

cs.LG↗

arXiv2017

3D Menagerie: Modeling the 3D shape and pose of animals

There has been significant work on learning realistic, articulated, 3D models of the human body. In contrast, there are few such models of animals, despite many applications. The main challenge is that animals are much less cooperative than humans. The best human body models are learned from thousands of 3D scans of people in specific poses, which is infeasible with live animals. Consequently, we learn our model from a small set of 3D scans of toy figurines in arbitrary poses. We employ a novel part-based shape model to compute an initial registration to the scans. We then normalize their pose, learn a statistical shape model, and refine the registrations and the model together. In this way, we accurately align animal scans from different quadruped families with very different shapes and poses. With the registration to a common template we learn a shape space representing animals including lions, cats, dogs, horses, cows and hippos. Animal shapes can be sampled from the model, posed, animated, and fit to data. We demonstrate generalization by fitting it to images of real animals including species not seen in training.

cs.CV↗

arXiv2017

Big Batch SGD: Automated Inference using Adaptive Batch Sizes

Classical stochastic gradient methods for optimization rely on noisy gradient approximations that become progressively less accurate as iterates approach a solution. The large noise and small signal in the resulting gradients makes it difficult to use them for adaptive stepsize selection and automatic stopping. We propose alternative "big batch" SGD schemes that adaptively grow the batch size over time to maintain a nearly constant signal-to-noise ratio in the gradient approximation. The resulting methods have similar convergence rates to classical SGD, and do not require convexity of the objective. The high fidelity gradients enable automated learning rate selection and do not require stepsize decay. Big batch methods are thus easily automated and can run with little or no oversight.

cs.LG↗

arXiv2016

Biconvex Relaxation for Semidefinite Programming in Computer Vision

Semidefinite programming is an indispensable tool in computer vision, but general-purpose solvers for semidefinite programs are often too slow and memory intensive for large-scale problems. We propose a general framework to approximately solve large-scale semidefinite problems (SDPs) at low complexity. Our approach, referred to as biconvex relaxation (BCR), transforms a general SDP into a specific biconvex optimization problem, which can then be solved in the original, low-dimensional variable space at low complexity. The resulting biconvex problem is solved using an efficient alternating minimization (AM) procedure. Since AM has the potential to get stuck in local minima, we propose a general initialization scheme that enables BCR to start close to a global optimum - this is key for our algorithm to quickly converge to optimal or near-optimal solutions. We showcase the efficacy of our approach on three applications in computer vision, namely segmentation, co-segmentation, and manifold metric learning. BCR achieves solution quality comparable to state-of-the-art SDP methods with speedups between 4X and 35X. At the same time, BCR handles a more general set of SDPs than previous approaches, which are more specialized.

cs.CV↗