Three-dimensional (3D) reconstruction from a single image is an ill-posed problem with inherent ambiguities, i.e. scale. Predicting a 3D scene from text description(s) is similarly ill-posed, i.e. spatial arrangements of objects described. We investigate the question of whether two inherently ambiguous modalities can be used in conjunction to produce metric-scaled reconstructions. To test this, we focus on monocular depth estimation, the problem of predicting a dense depth map from a single image, but with an additional text caption describing the scene. To this end, we begin by encoding the text caption as a mean and standard deviation; using a variational framework, we learn the distribution of the plausible metric reconstructions of 3D scenes corresponding to the text captions as a prior. To "select" a specific reconstruction or depth map, we encode the given image through a conditional sampler that samples from the latent space of the variational text encoder, which is then decoded to the output depth map. Our approach is trained alternatingly between the text and image branches: in one optimization step, we predict the mean and standard deviation from the text description and sample from a standard Gaussian, and in the other, we sample using a (image) conditional sampler. Once trained, we directly predict depth from the encoded text using the conditional sampler. We demonstrate our approach on indoor (NYUv2) and outdoor (KITTI) scenarios, where we show that language can consistently improve performance in both.

We discover the presence of quantization artifacts in Vision Transformers (ViTs), which arise due to the image tokenization step inherent in these architectures. These artifacts result in coarsely quantized features, which negatively impact performance, especially on downstream dense prediction tasks. We present a zero-shot method to improve how pre-trained ViTs handle spatial quantization. In particular, we propose to ensemble the features obtained from perturbing input images via sub-token spatial translations, inspired by Stochastic Resonance, a method traditionally applied to climate dynamics and signal processing. We term our method ``Stochastic Resonance Transformer" (SRT), which we show can effectively super-resolve features of pre-trained ViTs, capturing more of the local fine-grained structures that might otherwise be neglected as a result of tokenization. SRT can be applied at any layer, on any task, and does not require any fine-tuning. The advantage of the former is evident when applied to monocular depth prediction, where we show that ensembling model outputs are detrimental while applying SRT on intermediate ViT features outperforms the baseline models by an average of 4.7% and 14.9% on the RMSE and RMSE-log metrics across three different architectures. When applied to semi-supervised video object segmentation, SRT also improves over the baseline models uniformly across all metrics, and by an average of 2.4% in F&J score. We further show that these quantization artifacts can be attenuated to some extent via self-distillation. On the unsupervised salient region segmentation, SRT improves upon the base model by an average of 2.1% on the maxF metric. Finally, despite operating purely on pixel-level features, SRT generalizes to non-dense prediction tasks such as image retrieval and object discovery, yielding consistent improvements of up to 2.6% and 1.0% respectively.

We introduce a method to segment the visual field into independently moving regions, trained with no ground truth or supervision. It consists of an adversarial conditional encoder-decoder architecture based on Slot Attention, modified to use the image as context to decode optical flow without attempting to reconstruct the image itself. In the resulting multi-modal representation, one modality (flow) feeds the encoder to produce separate latent codes (slots), whereas the other modality (image) conditions the decoder to generate the first (flow) from the slots. This design frees the representation from having to encode complex nuisance variability in the image due to, for instance, illumination and reflectance properties of the scene. Since customary autoencoding based on minimizing the reconstruction error does not preclude the entire flow from being encoded into a single slot, we modify the loss to an adversarial criterion based on Contextual Information Separation. The resulting min-max optimization fosters the separation of objects and their assignment to different attention slots, leading to Divided Attention, or DivA. DivA outperforms recent unsupervised multi-object motion segmentation methods while tripling run-time speed up to 104FPS and reducing the performance gap from supervised methods to 12% or less. DivA can handle different numbers of objects and different image sizes at training and test time, is invariant to permutation of object labels, and does not require explicit regularization.

We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD). We show numerical error (on the order of the smallest floating point bit) induced from floating point arithmetic in training deep nets can be amplified significantly and result in significant test accuracy variance, comparable to the test accuracy variance due to stochasticity in SGD. We show how this is likely traced to instabilities of the optimization dynamics that are restrained, i.e., localized over iterations and regions of the weight tensor space. We do this by presenting a theoretical framework using numerical analysis of partial differential equations (PDE), and analyzing the gradient descent PDE of convolutional neural networks (CNNs). We show that it is stable only under certain conditions on the learning rate and weight decay. We show that rather than blowing up when the conditions are violated, the instability can be restrained. We show this is a consequence of the non-linear PDE associated with the gradient descent of the CNN, whose local linearization changes when over-driving the step size of the discretization, resulting in a stabilizing effect. We link restrained instabilities to the recently discovered Edge of Stability (EoS) phenomena, in which the stable step size predicted by classical theory is exceeded while continuing to optimize the loss and still converging. Because restrained instabilities occur at the EoS, our theory provides new predictions about the EoS, in particular, the role of regularization and the dependence on the network complexity.

We consider the problem of filling in missing spatio-temporal regions of a video. We provide a novel flow-based solution by introducing a generative model of images in relation to the scene (without missing regions) and mappings from the scene to images. We use the model to jointly infer the scene template, a 2D representation of the scene, and the mappings. This ensures consistency of the frame-to-frame flows generated to the underlying scene, reducing geometric distortions in flow based inpainting. The template is mapped to the missing regions in the video by a new L2-L1 interpolation scheme, creating crisp inpaintings and reducing common blur and distortion artifacts. We show on two benchmark datasets that our approach out-performs state-of-the-art quantitatively and in user studies.

We introduce optimization methods for convolutional neural networks that can be used to improve existing gradient-based optimization in terms of generalization error. The method requires only simple processing of existing stochastic gradients, can be used in conjunction with any optimizer, and has only a linear overhead (in the number of parameters) compared to computation of the stochastic gradient. We show that defining the gradients along the output channel direction leads to a performance boost, while other directions can be detrimental. We present the continuum theory of such gradients, its discretization, and application to deep networks. Experiments on benchmark datasets, several networks and baseline optimizers show that optimizers can be improved in generalization error by simply computing the stochastic gradient with respect to output-channel directed metrics. Stochastic gradient descent (SGD) is currently the dominant algorithm for optimizing large-scale convolutional neural networks (CNNs) LeCun et al. (1998); Simonyan & Zisserman (2014); He et al. (2016b). Although there has been large activity in optimization methods seeking to improve performance, SGD still dominates in large-scale CNN optimization in terms of its generalization ability. Despite SGD's dominance, there is still often a gap between training and real-world test accuracy performance in applications, which necessitates research in optimization methods to increase generalization accuracy.