The goal of this work is to shed light on the remarkable phenomenon of transition to linearity of certain neural networks as their width approaches infinity. We show that the transition to linearity'' of the model and, equivalently, constancy of the (neural) tangent kernel (NTK) result from the scaling properties of the norm of the Hessian matrix of the network as a function of the network width. We present a general framework for understanding the constancy of the tangent kernel via Hessian scaling applicable to the standard classes of neural networks. Our analysis provides a new perspective on the phenomenon of constant tangent kernel, which is different from the widely accepted lazy training''. Furthermore, we show that the transition to linearity is not a general property of wide neural networks and does not hold when the last layer of the network is non-linear. It is also not necessary for successful optimization by gradient descent.

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The goal of this work is to shed light on the remarkable phenomenon of "transition to linearity" of certain neural networks as their width approaches infinity.

We thank all reviewers for the insightful and encouraging comments. Theorem 3.2 and results in Appendix G has been proved previously (e.g., [1]). Our Hessian analysis results, including Theorem 3.2 and Theorem 3.1, are new. This can perhaps cause confusion. The paper mostly focuses on squared loss while widely applied NNs use softmax-cross entropy loss.

Color constancy estimates illuminant chromaticity to correct color-biased images. Recently, Deep Neural Network-driven Color Constancy (DNNCC) models have made substantial advancements. Nevertheless, the potential risks in DNNCC due to the vulnerability of deep neural networks have not yet been explored. In this paper, we conduct the first investigation into the impact of a key factor in color constancy-brightness-on DNNCC from a robustness perspective. Our evaluation reveals that several mainstream DNNCC models exhibit high sensitivity to brightness despite their focus on chromaticity estimation. This sheds light on a potential limitation of existing DNNCC models: their sensitivity to brightness may hinder performance given the widespread brightness variations in real-world datasets. From the insights of our analysis, we propose a simple yet effective brightness robustness enhancement strategy for DNNCC models, termed BRE. The core of BRE is built upon the adaptive step-size adversarial brightness augmentation technique, which identifies high-risk brightness variation and generates augmented images via explicit brightness adjustment. Subsequently, BRE develops a brightness-robustness-aware model optimization strategy that integrates adversarial brightness training and brightness contrastive loss, significantly bolstering the brightness robustness of DNNCC models. BRE is hyperparameter-free and can be integrated into existing DNNCC models, without incurring additional overhead during the testing phase. Experiments on two public color constancy datasets-ColorChecker and Cube+-demonstrate that the proposed BRE consistently enhances the illuminant estimation performance of existing DNNCC models, reducing the estimation error by an average of 5.04% across six mainstream DNNCC models, underscoring the critical role of enhancing brightness robustness in these models.

Perceptual constancy is the ability to maintain stable perceptions of objects despite changes in sensory input, such as variations in distance, angle, or lighting. This ability is crucial for recognizing visual information in a dynamic world, making it essential for Vision-Language Models (VLMs). However, whether VLMs are currently and theoretically capable of mastering this ability remains underexplored. In this study, we evaluated 33 VLMs using 253 experiments across three domains: color, size, and shape constancy. The experiments included single-image and video adaptations of classic cognitive tasks, along with novel tasks in in-the-wild conditions, to evaluate the models' recognition of object properties under varying conditions. We found significant variability in VLM performance, with models performance in shape constancy clearly dissociated from that of color and size constancy.

The goal of this work is to shed light on the remarkable phenomenon of "transition to linearity" of certain neural networks as their width approaches infinity. We show that the "transition to linearity'' of the model and, equivalently, constancy of the (neural) tangent kernel (NTK) result from the scaling properties of the norm of the Hessian matrix of the network as a function of the network width. We present a general framework for understanding the constancy of the tangent kernel via Hessian scaling applicable to the standard classes of neural networks. Our analysis provides a new perspective on the phenomenon of constant tangent kernel, which is different from the widely accepted "lazy training''. Furthermore, we show that the "transition to linearity" is not a general property of wide neural networks and does not hold when the last layer of the network is non-linear.

Color constancy is the recovery of true surface color from observed color, and requires estimating the chromaticity of scene illumination to correct for the bias it induces. In this paper, we show that the per-pixel color statistics of natural scenes--without any spatial or semantic context--can by themselves be a powerful cue for color constancy. Specifically, we describe an illuminant estimation method that is built around a "classifier" for identifying the true chromaticity of a pixel given its luminance (absolute brightness across color channels). During inference, each pixel's observed color restricts its true chromaticity to those values that can be explained by one of a candidate set of illuminants, and applying the classifier over these values yields a distribution over the corresponding illuminants. A global estimate for the scene illuminant is computed through a simple aggregation of these distributions across all pixels.

Contrastive learning is a paradigm for learning representations from unlabelled data that has been highly successful for image and text data. Several recent works have examined contrastive losses to claim that contrastive models effectively learn spectral embeddings, while few works show relations between (wide) contrastive models and kernel principal component analysis (PCA). However, it is not known if trained contrastive models indeed correspond to kernel methods or PCA. In this work, we analyze the training dynamics of two-layer contrastive models, with non-linear activation, and answer when these models are close to PCA or kernel methods. It is well known in the supervised setting that neural networks are equivalent to neural tangent kernel (NTK) machines, and that the NTK of infinitely wide networks remains constant during training. We provide the first convergence results of NTK for contrastive losses, and present a nuanced picture: NTK of wide networks remains almost constant for cosine similarity based contrastive losses, but not for losses based on dot product similarity. We further study the training dynamics of contrastive models with orthogonality constraints on output layer, which is implicitly assumed in works relating contrastive learning to spectral embedding. Our deviation bounds suggest that representations learned by contrastive models are close to the principal components of a certain matrix computed from random features. We empirically show that our theoretical results possibly hold beyond two-layer networks.

A neural network model of 3-D lightness perception is presented which builds upon the FACADE Theory Boundary Contour Sys(cid:173) tem/Feature Contour System of Grossberg and colleagues. Early ratio encoding by retinal ganglion neurons as well as psychophysi(cid:173) cal results on constancy across different backgrounds (background constancy) are used to provide functional constraints to the theory and suggest a contrast negation hypothesis which states that ratio measures between coplanar regions are given more weight in the determination of lightness of the respective regions.