Dan Rosenbaum

Deborah Levy, Amit Peleg, Naama Pearl et al.

Research on neural radiance fields (NeRFs) for novel view generation is exploding with new models and extensions. However, a question that remains unanswered is what happens in underwater or foggy scenes where the medium strongly influences the appearance of objects. Thus far, NeRF and its variants have ignored these cases. However, since the NeRF framework is based on volumetric rendering, it has inherent capability to account for the medium's effects, once modeled appropriately. We develop a new rendering model for NeRFs in scattering media, which is based on the SeaThru image formation model, and suggest a suitable architecture for learning both scene information and medium parameters. We demonstrate the strength of our method using simulated and real-world scenes, correctly rendering novel photorealistic views underwater. Even more excitingly, we can render clear views of these scenes, removing the medium between the camera and the scene and reconstructing the appearance and depth of far objects, which are severely occluded by the medium. Our code and unique datasets are available on the project's website.

Matthias Bauer, Emilien Dupont, Andy Brock et al.

Neural fields, also known as implicit neural representations, have emerged as a powerful means to represent complex signals of various modalities. Based on this Dupont et al. (2022) introduce a framework that views neural fields as data, termed *functa*, and proposes to do deep learning directly on this dataset of neural fields. In this work, we show that the proposed framework faces limitations when scaling up to even moderately complex datasets such as CIFAR-10. We then propose *spatial functa*, which overcome these limitations by using spatially arranged latent representations of neural fields, thereby allowing us to scale up the approach to ImageNet-1k at 256x256 resolution. We demonstrate competitive performance to Vision Transformers (Steiner et al., 2022) on classification and Latent Diffusion (Rombach et al., 2022) on image generation respectively.

Opher Bar Nathan, Deborah Levy, Tali Treibitz et al.

Underwater image restoration is a challenging task because of water effects that increase dramatically with distance. This is worsened by lack of ground truth data of clean scenes without water. Diffusion priors have emerged as strong image restoration priors. However, they are often trained with a dataset of the desired restored output, which is not available in our case. We also observe that using only color data is insufficient, and therefore augment the prior with a depth channel. We train an unconditional diffusion model prior on the joint space of color and depth, using standard RGBD datasets of natural outdoor scenes in air. Using this prior together with a novel guidance method based on the underwater image formation model, we generate posterior samples of clean images, removing the water effects. Even though our prior did not see any underwater images during training, our method outperforms state-of-the-art baselines for image restoration on very challenging scenes. Our code, models and data are available on the project website.

Azmi Haider, Dan Rosenbaum

The remarkable achievements of both generative models of 2D images and neural field representations for 3D scenes present a compelling opportunity to integrate the strengths of both approaches. In this work, we propose a methodology that combines a NeRF-based representation of 3D scenes with probabilistic modeling and reasoning using diffusion models. We view 3D reconstruction as a perception problem with inherent uncertainty that can thereby benefit from probabilistic inference methods. The core idea is to represent the 3D scene as a stochastic latent variable for which we can learn a prior and use it to perform posterior inference given a set of observations. We formulate posterior sampling using the score-based inference method of diffusion models in conjunction with a likelihood term computed from a reconstruction model that includes volumetric rendering. We train the model using a two-stage process: first we train the reconstruction model while auto-decoding the latent representations for a dataset of 3D scenes, and then we train the prior over the latents using a diffusion model. By using the model to generate samples from the posterior we demonstrate that various 3D reconstruction tasks can be performed, differing by the type of observation used as inputs. We showcase reconstruction from single-view, multi-view, noisy images, sparse pixels, and sparse depth data. These observations vary in the amount of information they provide for the scene and we show that our method can model the varying levels of inherent uncertainty associated with each task. Our experiments illustrate that this approach yields a comprehensive method capable of accurately predicting 3D structure from diverse types of observations.

Emilien Dupont, Hyunjik Kim, S. M. Ali Eslami et al.

It is common practice in deep learning to represent a measurement of the world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying signal represented by these measurements is often continuous, e.g. the scene depicted in an image. A powerful continuous alternative is then to represent these measurements using an implicit neural representation, a neural function trained to output the appropriate measurement value for any input spatial location. In this paper, we take this idea to its next level: what would it take to perform deep learning on these functions instead, treating them as data? In this context we refer to the data as functa, and propose a framework for deep learning on functa. This view presents a number of challenges around efficient conversion from data to functa, compact representation of functa, and effectively solving downstream tasks on functa. We outline a recipe to overcome these challenges and apply it to a wide range of data modalities including images, 3D shapes, neural radiance fields (NeRF) and data on manifolds. We demonstrate that this approach has various compelling properties across data modalities, in particular on the canonical tasks of generative modeling, data imputation, novel view synthesis and classification. Code: https://github.com/deepmind/functa

Richard Hildebrandt, Evangelos Kourlitis, Baran Hashemi et al.

We introduce a new strategy for compositional neural surrogates for radiation-matter interactions, a key task spanning domains from particle physics through nuclear and space engineering to medical physics. Exploiting the locality and the Markov nature of particle interactions, we create a \emph{next-particle prediction} kernel using hybrid discrete-continuous transformer models based on Riemannian Flow Matching on product manifolds. The model generates variable-sized typed sets of particles and radiation side effects that are the result of the interaction of an incident particle with a material volume. The resulting kernel can be composed to simulate unseen large-scale material distributions in a zero-shot manner. Unlike mechanistic simulators, our model is designed to be differentiable, provides tractable likelihoods for future downstream applications. A significant computational speed-up on GPU compared to CPU-bound mechanistic simulation is observed for single-kernel execution. We evaluate the model at the kernel level and demonstrate predictive stability over multi-round autoregressive rollouts. We additionally release a novel 20M-event radiation-matter interaction dataset for further research.

Hussen Abu Hamad, Dan Rosenbaum

Neural processes (NPs) are a class of models that learn stochastic processes directly from data and can be used for inference, sampling and conditional sampling. We introduce a new NP model based on flow matching, a generative modeling paradigm that has demonstrated strong performance on various data modalities. Following the NP training framework, the model provides amortized predictions of conditional distributions over any arbitrary points in the data. Compared to previous NP models, our model is simple to implement and can be used to sample from conditional distributions using an ODE solver, without requiring auxiliary conditioning methods. In addition, the model provides a controllable tradeoff between accuracy and running time via the number of steps in the ODE solver. We show that our model outperforms previous state-of-the-art neural process methods on various benchmarks including synthetic 1D Gaussian processes data, 2D images, and real-world weather data.

Chen Shapira, Dan Rosenbaum

Models that adapt their predictions based on some given contexts, also known as in-context learning, have become ubiquitous in recent years. We propose to study the behavior of such models when data is contaminated by noise. Towards this goal we use the Neural Processes (NP) framework, as a simple and rigorous way to learn a distribution over functions, where predictions are based on a set of context points. Using this framework, we find that the models that perform best on clean data, are different than the models that perform best on noisy data. Specifically, models that process the context using attention, are more severely affected by noise, leading to in-context overfitting. We propose a simple method to train NP models that makes them more robust to noisy data. Experiments on 1D functions and 2D image datasets demonstrate that our method leads to models that outperform all other NP models for all noise levels.

Ori Lifschitz, Tali Treibitz, Dan Rosenbaum

We address the problem of looking into the water from the air, where we seek to remove image distortions caused by refractions at the water surface. Our approach is based on modeling the different water surface structures at various points in time, assuming the underlying image is constant. To this end, we propose a model that consists of two neural-field networks. The first network predicts the height of the water surface at each spatial position and time, and the second network predicts the image color at each position. Using both networks, we reconstruct the observed sequence of images and can therefore use unsupervised training. We show that using implicit neural representations with periodic activation functions (SIREN) leads to effective modeling of the surface height spatio-temporal signal and its derivative, as required for image reconstruction. Using both simulated and real data we show that our method outperforms the latest unsupervised image restoration approach. In addition, it provides an estimate of the water surface.

John F. J. Mellor, Eunbyung Park, Yaroslav Ganin et al.

We investigate using reinforcement learning agents as generative models of images (extending arXiv:1804.01118). A generative agent controls a simulated painting environment, and is trained with rewards provided by a discriminator network simultaneously trained to assess the realism of the agent's samples, either unconditional or reconstructions. Compared to prior work, we make a number of improvements to the architectures of the agents and discriminators that lead to intriguing and at times surprising results. We find that when sufficiently constrained, generative agents can learn to produce images with a degree of visual abstraction, despite having only ever seen real photographs (no human brush strokes). And given enough time with the painting environment, they can produce images with considerable realism. These results show that, under the right circumstances, some aspects of human drawing can emerge from simulated embodiment, without the need for external supervision, imitation or social cues. Finally, we note the framework's potential for use in creative applications.

Hyunjik Kim, Andriy Mnih, Jonathan Schwarz et al.

Neural Processes (NPs) (Garnelo et al 2018a;b) approach regression by learning to map a context set of observed input-output pairs to a distribution over regression functions. Each function models the distribution of the output given an input, conditioned on the context. NPs have the benefit of fitting observed data efficiently with linear complexity in the number of context input-output pairs, and can learn a wide family of conditional distributions; they learn predictive distributions conditioned on context sets of arbitrary size. Nonetheless, we show that NPs suffer a fundamental drawback of underfitting, giving inaccurate predictions at the inputs of the observed data they condition on. We address this issue by incorporating attention into NPs, allowing each input location to attend to the relevant context points for the prediction. We show that this greatly improves the accuracy of predictions, results in noticeably faster training, and expands the range of functions that can be modelled.

Dan Rosenbaum, Frederic Besse, Fabio Viola et al.

We consider learning based methods for visual localization that do not require the construction of explicit maps in the form of point clouds or voxels. The goal is to learn an implicit representation of the environment at a higher, more abstract level. We propose to use a generative approach based on Generative Query Networks (GQNs, Eslami et al. 2018), asking the following questions: 1) Can GQN capture more complex scenes than those it was originally demonstrated on? 2) Can GQN be used for localization in those scenes? To study this approach we consider procedurally generated Minecraft worlds, for which we can generate images of complex 3D scenes along with camera pose coordinates. We first show that GQNs, enhanced with a novel attention mechanism can capture the structure of 3D scenes in Minecraft, as evidenced by their samples. We then apply the models to the localization problem, comparing the results to a discriminative baseline, and comparing the ways each approach captures the task uncertainty.

Marta Garnelo, Jonathan Schwarz, Dan Rosenbaum et al.

A neural network (NN) is a parameterised function that can be tuned via gradient descent to approximate a labelled collection of data with high precision. A Gaussian process (GP), on the other hand, is a probabilistic model that defines a distribution over possible functions, and is updated in light of data via the rules of probabilistic inference. GPs are probabilistic, data-efficient and flexible, however they are also computationally intensive and thus limited in their applicability. We introduce a class of neural latent variable models which we call Neural Processes (NPs), combining the best of both worlds. Like GPs, NPs define distributions over functions, are capable of rapid adaptation to new observations, and can estimate the uncertainty in their predictions. Like NNs, NPs are computationally efficient during training and evaluation but also learn to adapt their priors to data. We demonstrate the performance of NPs on a range of learning tasks, including regression and optimisation, and compare and contrast with related models in the literature.

Marta Garnelo, Dan Rosenbaum, Chris J. Maddison et al.

Deep neural networks excel at function approximation, yet they are typically trained from scratch for each new function. On the other hand, Bayesian methods, such as Gaussian Processes (GPs), exploit prior knowledge to quickly infer the shape of a new function at test time. Yet GPs are computationally expensive, and it can be hard to design appropriate priors. In this paper we propose a family of neural models, Conditional Neural Processes (CNPs), that combine the benefits of both. CNPs are inspired by the flexibility of stochastic processes such as GPs, but are structured as neural networks and trained via gradient descent. CNPs make accurate predictions after observing only a handful of training data points, yet scale to complex functions and large datasets. We demonstrate the performance and versatility of the approach on a range of canonical machine learning tasks, including regression, classification and image completion.

Dan Rosenbaum, Yair Weiss

Cameras that can measure the depth of each pixel in addition to its color have become easily available and are used in many consumer products worldwide. Often the depth channel is captured at lower quality compared to the RGB channels and different algorithms have been proposed to improve the quality of the D channel given the RGB channels. Typically these approaches work by assuming that edges in RGB are correlated with edges in D. In this paper we approach this problem from the standpoint of natural image statistics. We obtain examples of high quality RGBD images from a computer graphics generated movie (MPI-Sintel) and we use these examples to compare different probabilistic generative models of RGBD image patches. We then use the generative models together with a degradation model and obtain a Bayes Least Squares (BLS) estimator of the D channel given the RGB channels. Our results show that learned generative models outperform the state-of-the-art in improving the quality of depth channels given the color channels in natural images even when training is performed on artificially generated images.

Dan Rosenbaum, Yair Weiss

Optical flow is typically estimated by minimizing a "data cost" and an optional regularizer. While there has been much work on different regularizers many modern algorithms still use a data cost that is not very different from the ones used over 30 years ago: a robust version of brightness constancy or gradient constancy. In this paper we leverage the recent availability of ground-truth optical flow databases in order to learn a data cost. Specifically we take a generative approach in which the data cost models the distribution of noise after warping an image according to the flow and we measure the "goodness" of a data cost by how well it matches the true distribution of flow warp error. Consistent with current practice, we find that robust versions of gradient constancy are better models than simple brightness constancy but a learned GMM that models the density of patches of warp error gives a much better fit than any existing assumption of constancy. This significant advantage of the GMM is due to an explicit modeling of the spatial structure of warp errors, a feature which is missing from almost all existing data costs in optical flow. Finally, we show how a good density model of warp error patches can be used for optical flow estimation on whole images. We replace the data cost by the expected patch log-likelihood (EPLL), and show how this cost can be optimized iteratively using an additional step of denoising the warp error image. The results of our experiments are promising and show that patch models with higher likelihood lead to better optical flow estimation.

Alon Gonen, Dan Rosenbaum, Yonina Eldar et al.

The goal of subspace learning is to find a $k$-dimensional subspace of $\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a partial information setting, in which the learner can only observe $r \le d$ attributes from each instance vector. We propose several efficient algorithms for this task, and analyze their sample complexity