arXiv subjects

Yair Weiss

Publications and source records attributed to Yair Weiss.

At least 19 recordsLinked to original sources

arXiv2026

A Theory of Contrastive Learning with Natural Images

Why does contrastive learning with simple images and augmentations yield useful representations for downstream tasks? We address this question by analytically computing the optimal representation in terms of a contrastive loss for a range of basic augmentations and any image dataset with stationary statistics. We show that for certain augmentations the optimum can be attained by a CNN whose first layer filters are sinusoids, followed by a pointwise nonlinearity, global average pooling, and a final linear layer that performs partial whitening. We also show that the optimal weights in such CNNs for more complicated augmentations are still sinusoids. The frequencies of the sinusoids and their weights can be computed using a simple waterfilling algorithm given the dataset's expected power spectrum. Experiments with different image datasets and augmentations show that such CNNs trained with SGD empirically learn sinusoids in their first layer and to perform partial whitening

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arXiv2026

What Color is the Sky (for a non-human) ?

The light of the daytime sky contains a mixture of many colors yet is perceived as blue by human observers. This is largely due to the particular response functions of the human cones. Under these response functions skylight and blue light are metamers: they yield the exact same excitation of the cones. In this paper we ask: is it possible to define the ``color'' of the sky for other visual systems? We present a simple computational method to determine monochromatic metamers to a given input light for arbitrary visual systems. Using published values on spectral sensitivity functions of various species, we use our method to determine the dominant wavelength of monochromatic metamers to skylight. For a wide range of species (bichromats, trichromats and tetrachormats) we find monochromatic metamers to skylight but the dominant wavelength of the metamer can vary drastically between species and be very different from the color perceived by humans.

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arXiv2026

Diffusion Models, Denoiser Architecture and Creativity

The creativity of diffusion models refers to their ability to generate highly realistic images that are different from their training data. Creativity is somewhat surprising since it is known that if the denoiser used in the diffusion model is the Bayes optimal denoiser for a given training set, then the model will simply copy the training samples. In this paper we present empirical and theoretical results that suggest that creativity in diffusion models is due to an interaction between the denoiser architecture and the target distribution. Theoretically, we give explicit forms for the distribution of generated samples as a function of the target distribution and the denoiser architecture for three different denoiser architectures (linear, polynomial, bottleneck). Empirically, we show that small changes in the popular UNET denoiser architecture leads to very different forms of creativity, and these small changes often yield samples that are highly nonrealistic. Taken together, our results show that diffusion models will only be successful if the inductive bias of the denoiser architecture is in strong alignment with the true target distribution.

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arXiv2026

Is the Modality Gap a Bug or a Feature? A Robustness Perspective

Many modern multi-modal models (e.g. CLIP) seek an embedding space in which the two modalities are aligned. Somewhat surprisingly, almost all existing models show a strong modality gap: the distribution of images is well-separated from the distribution of texts in the shared embedding space. Despite a series of recent papers on this topic, it is still not clear why this gap exists nor whether closing the gap in post-processing will lead to better performance on downstream tasks. In this paper we show that under certain conditions, minimizing the contrastive loss yields a representation in which the two modalities are separated by a global gap vector that is orthogonal to their embeddings. We also show that under these conditions the modality gap is monotonically related to robustness: decreasing the gap does not change the clean accuracy of the models but makes it less likely that a model will change its output when the embeddings are perturbed. Our experiments show that for many real-world VLMs we can significantly increase robustness by a simple post-processing step that moves one modality towards the mean of the other modality, without any loss of clean accuracy.

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arXiv2025

Characterizing Nonlinear Dynamics via Smooth Prototype Equivalences

Characterizing the long term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical observations, as well as the variability of possible long-term dynamics. We address this by introducing smooth prototype equivalences (SPE), a framework for matching sparse observations to prototypical behaviors using invertible neural networks which model smooth phase space deformations. SPE can localize the invariant sets describing long-term behavior of the observed dynamics through the learned mapping from prototype space to data space. Furthermore, SPE can classify dynamical regimes by comparing the data residual of the deformed measurements to prototype dynamics. Our method outperforms existing techniques in the classification of oscillatory systems and can efficiently identify invariant structures like limit cycles and fixed points in an equation-free manner, even when only a small, noisy subset of the phase space is observed. SPE further reveals driving genes in synthetic oscillators such as the repressilator regulatory circuit, and traces cyclic biological processes like the cell cycle trajectory directly from experimental high-dimensional single-cell gene expression data.

cs.LG↗

arXiv2024

Lost in Translation: Modern Neural Networks Still Struggle With Small Realistic Image Transformations

Deep neural networks that achieve remarkable performance in image classification have previously been shown to be easily fooled by tiny transformations such as a one pixel translation of the input image. In order to address this problem, two approaches have been proposed in recent years. The first approach suggests using huge datasets together with data augmentation in the hope that a highly varied training set will teach the network to learn to be invariant. The second approach suggests using architectural modifications based on sampling theory to deal explicitly with image translations. In this paper, we show that these approaches still fall short in robustly handling 'natural' image translations that simulate a subtle change in camera orientation. Our findings reveal that a mere one-pixel translation can result in a significant change in the predicted image representation for approximately 40% of the test images in state-of-the-art models (e.g. open-CLIP trained on LAION-2B or DINO-v2) , while models that are explicitly constructed to be robust to cyclic translations can still be fooled with 1 pixel realistic (non-cyclic) translations 11% of the time. We present Robust Inference by Crop Selection: a simple method that can be proven to achieve any desired level of consistency, although with a modest tradeoff with the model's accuracy. Importantly, we demonstrate how employing this method reduces the ability to fool state-of-the-art models with a 1 pixel translation to less than 5% while suffering from only a 1% drop in classification accuracy. Additionally, we show that our method can be easy adjusted to deal with circular shifts as well. In such case we achieve 100% robustness to integer shifts with state-of-the-art accuracy, and with no need for any further training.

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arXiv2024

On adversarial training and the 1 Nearest Neighbor classifier

The ability to fool deep learning classifiers with tiny perturbations of the input has lead to the development of adversarial training in which the loss with respect to adversarial examples is minimized in addition to the training examples. While adversarial training improves the robustness of the learned classifiers, the procedure is computationally expensive, sensitive to hyperparameters and may still leave the classifier vulnerable to other types of small perturbations. In this paper we compare the performance of adversarial training to that of the simple 1 Nearest Neighbor (1NN) classifier. We prove that under reasonable assumptions, the 1NN classifier will be robust to {\em any} small image perturbation of the training images. In experiments with 135 different binary image classification problems taken from CIFAR10, MNIST and Fashion-MNIST we find that 1NN outperforms TRADES (a powerful adversarial training algorithm) in terms of average adversarial accuracy. In additional experiments with 69 robust models taken from the current adversarial robustness leaderboard, we find that 1NN outperforms almost all of them in terms of robustness to perturbations that are only slightly different from those used during training. Taken together, our results suggest that modern adversarial training methods still fall short of the robustness of the simple 1NN classifier. our code can be found at \url{https://github.com/amirhagai/On-Adversarial-Training-And-The-1-Nearest-Neighbor-Classifier} \keywords{Adversarial training}

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arXiv2024

Intriguing Properties of Modern GANs

Modern GANs achieve remarkable performance in terms of generating realistic and diverse samples. This has led many to believe that ``GANs capture the training data manifold''. In this work we show that this interpretation is wrong. We empirically show that the manifold learned by modern GANs does not fit the training distribution: specifically the manifold does not pass through the training examples and passes closer to out-of-distribution images than to in-distribution images. We also investigate the distribution over images implied by the prior over the latent codes and study whether modern GANs learn a density that approximates the training distribution. Surprisingly, we find that the learned density is very far from the data distribution and that GANs tend to assign higher density to out-of-distribution images. Finally, we demonstrate that the set of images used to train modern GANs are often not part of the typical set described by the GANs' distribution.

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arXiv2022

Generating natural images with direct Patch Distributions Matching

Many traditional computer vision algorithms generate realistic images by requiring that each patch in the generated image be similar to a patch in a training image and vice versa. Recently, this classical approach has been replaced by adversarial training with a patch discriminator. The adversarial approach avoids the computational burden of finding nearest neighbors of patches but often requires very long training times and may fail to match the distribution of patches. In this paper we leverage the recently developed Sliced Wasserstein Distance and develop an algorithm that explicitly and efficiently minimizes the distance between patch distributions in two images. Our method is conceptually simple, requires no training and can be implemented in a few lines of codes. On a number of image generation tasks we show that our results are often superior to single-image-GANs, require no training, and can generate high quality images in a few seconds. Our implementation is available at https://github.com/ariel415el/GPDM

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arXiv2022

What do CNNs Learn in the First Layer and Why? A Linear Systems Perspective

It has previously been reported that the representation that is learned in the first layer of deep Convolutional Neural Networks (CNNs) is highly consistent across initializations and architectures. In this work, we quantify this consistency by considering the first layer as a filter bank and measuring its energy distribution. We find that the energy distribution is very different from that of the initial weights and is remarkably consistent across random initializations, datasets, architectures and even when the CNNs are trained with random labels. In order to explain this consistency, we derive an analytical formula for the energy profile of linear CNNs and show that this profile is mostly dictated by the second order statistics of image patches in the training set and it will approach a whitening transformation when the number of iterations goes to infinity. Finally, we show that this formula for linear CNNs also gives an excellent fit for the energy profiles learned by commonly used nonlinear CNNs such as ResNet and VGG, and that the first layer of these CNNs indeed perform approximate whitening of their inputs.

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arXiv2021

Posterior Sampling for Image Restoration using Explicit Patch Priors

Almost all existing methods for image restoration are based on optimizing the mean squared error (MSE), even though it is known that the best estimate in terms of MSE may yield a highly atypical image due to the fact that there are many plausible restorations for a given noisy image. In this paper, we show how to combine explicit priors on patches of natural images in order to sample from the posterior probability of a full image given a degraded image. We prove that our algorithm generates correct samples from the distribution $p(x|y) \propto \exp(-E(x|y))$ where $E(x|y)$ is the cost function minimized in previous patch-based approaches that compute a single restoration. Unlike previous approaches that computed a single restoration using MAP or MMSE, our method makes explicit the uncertainty in the restored images and guarantees that all patches in the restored images will be typical given the patch prior. Unlike previous approaches that used implicit priors on fixed-size images, our approach can be used with images of any size. Our experimental results show that posterior sampling using patch priors yields images of high perceptual quality and high PSNR on a range of challenging image restoration problems.

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arXiv2021

A Bayes-Optimal View on Adversarial Examples

Since the discovery of adversarial examples - the ability to fool modern CNN classifiers with tiny perturbations of the input, there has been much discussion whether they are a "bug" that is specific to current neural architectures and training methods or an inevitable "feature" of high dimensional geometry. In this paper, we argue for examining adversarial examples from the perspective of Bayes-Optimal classification. We construct realistic image datasets for which the Bayes-Optimal classifier can be efficiently computed and derive analytic conditions on the distributions under which these classifiers are provably robust against any adversarial attack even in high dimensions. Our results show that even when these "gold standard" optimal classifiers are robust, CNNs trained on the same datasets consistently learn a vulnerable classifier, indicating that adversarial examples are often an avoidable "bug". We further show that RBF SVMs trained on the same data consistently learn a robust classifier. The same trend is observed in experiments with real images in different datasets.

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arXiv2020

The Surprising Effectiveness of Linear Unsupervised Image-to-Image Translation

Unsupervised image-to-image translation is an inherently ill-posed problem. Recent methods based on deep encoder-decoder architectures have shown impressive results, but we show that they only succeed due to a strong locality bias, and they fail to learn very simple nonlocal transformations (e.g. mapping upside down faces to upright faces). When the locality bias is removed, the methods are too powerful and may fail to learn simple local transformations. In this paper we introduce linear encoder-decoder architectures for unsupervised image to image translation. We show that learning is much easier and faster with these architectures and yet the results are surprisingly effective. In particular, we show a number of local problems for which the results of the linear methods are comparable to those of state-of-the-art architectures but with a fraction of the training time, and a number of nonlocal problems for which the state-of-the-art fails while linear methods succeed.

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arXiv2019

Why do deep convolutional networks generalize so poorly to small image transformations?

Convolutional Neural Networks (CNNs) are commonly assumed to be invariant to small image transformations: either because of the convolutional architecture or because they were trained using data augmentation. Recently, several authors have shown that this is not the case: small translations or rescalings of the input image can drastically change the network's prediction. In this paper, we quantify this phenomena and ask why neither the convolutional architecture nor data augmentation are sufficient to achieve the desired invariance. Specifically, we show that the convolutional architecture does not give invariance since architectures ignore the classical sampling theorem, and data augmentation does not give invariance because the CNNs learn to be invariant to transformations only for images that are very similar to typical images from the training set. We discuss two possible solutions to this problem: (1) antialiasing the intermediate representations and (2) increasing data augmentation and show that they provide only a partial solution at best. Taken together, our results indicate that the problem of insuring invariance to small image transformations in neural networks while preserving high accuracy remains unsolved.

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arXiv2019

Cheating with (Recursive) Models

To what extent can agents with misspecified subjective models predict false correlations? We study an "analyst" who utilizes models that take the form of a recursive system of linear regression equations. The analyst fits each equation to minimize the sum of squared errors against an arbitrarily large sample. We characterize the maximal pairwise correlation that the analyst can predict given a generic objective covariance matrix, subject to the constraint that the estimated model does not distort the mean and variance of individual variables. We show that as the number of variables in the model grows, the false pairwise correlation can become arbitrarily close to one, regardless of the true correlation.

econ.TH↗

arXiv2019

Weak lensing shear estimation beyond the shape-noise limit: a machine learning approach

Weak lensing shear estimation typically results in per galaxy statistical errors significantly larger than the sought after gravitational signal of only a few percent. These statistical errors are mostly a result of shape-noise -- an estimation error due to the diverse (and a-priori unknown) morphology of individual background galaxies. These errors are inversely proportional to the limiting angular resolution at which localized objects, such as galaxy clusters, can be probed with weak lensing shear. In this work we report on our initial attempt to reduce statistical errors in weak lensing shear estimation using a machine learning approach -- training a multi-layered convolutional neural network to directly estimate the shear given an observed background galaxy image. We train, calibrate and evaluate the performance and stability of our estimator using simulated galaxy images designed to mimic the distribution of HST observations of lensed background sources in the CLASH galaxy cluster survey. Using the trained estimator, we produce weak lensing shear maps of the cores of 20 galaxy clusters in the CLASH survey, demonstrating an RMS scatter reduced by approximately 26% when compared to maps produced with a commonly used shape estimator. This is equivalent to a survey speed enhancement of approximately 60%. However, given the non-transparent nature of the machine learning approach, this result requires further testing and validation. We provide python code to train and test this estimator on both simulated and real galaxy cluster observations. We also provide updated weak lensing catalogues for the 20 CLASH galaxy clusters studied.

astro-ph.CO↗

arXiv2018

On GANs and GMMs

A longstanding problem in machine learning is to find unsupervised methods that can learn the statistical structure of high dimensional signals. In recent years, GANs have gained much attention as a possible solution to the problem, and in particular have shown the ability to generate remarkably realistic high resolution sampled images. At the same time, many authors have pointed out that GANs may fail to model the full distribution ("mode collapse") and that using the learned models for anything other than generating samples may be very difficult. In this paper, we examine the utility of GANs in learning statistical models of images by comparing them to perhaps the simplest statistical model, the Gaussian Mixture Model. First, we present a simple method to evaluate generative models based on relative proportions of samples that fall into predetermined bins. Unlike previous automatic methods for evaluating models, our method does not rely on an additional neural network nor does it require approximating intractable computations. Second, we compare the performance of GANs to GMMs trained on the same datasets. While GMMs have previously been shown to be successful in modeling small patches of images, we show how to train them on full sized images despite the high dimensionality. Our results show that GMMs can generate realistic samples (although less sharp than those of GANs) but also capture the full distribution, which GANs fail to do. Furthermore, GMMs allow efficient inference and explicit representation of the underlying statistical structure. Finally, we discuss how GMMs can be used to generate sharp images.

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arXiv2017

Reflection Separation Using Guided Annotation

Photographs taken through a glass surface often contain an approximately linear superposition of reflected and transmitted layers. Decomposing an image into these layers is generally an ill-posed task and the use of an additional image prior and user provided cues is presently necessary in order to obtain good results. Current annotation approaches rely on a strong sparsity assumption. For images with significant texture this assumption does not typically hold, thus rendering the annotation process unviable. In this paper we show that using a Gaussian Mixture Model patch prior, the correct local decomposition can almost always be found as one of 100 likely modes of the posterior. Thus, the user need only choose one of these modes in a sparse set of patches and the decomposition may then be completed automatically. We demonstrate the performance of our method using synthesized and real reflection images.

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