arXiv subjects

Simon Lucey

Publications and source records attributed to Simon Lucey.

At least 73 records · Page 4Linked to original sources

arXiv2022

Evading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions with Superior OOD Generalization

Neural networks trained with SGD were recently shown to rely preferentially on linearly-predictive features and can ignore complex, equally-predictive ones. This simplicity bias can explain their lack of robustness out of distribution (OOD). The more complex the task to learn, the more likely it is that statistical artifacts (i.e. selection biases, spurious correlations) are simpler than the mechanisms to learn. We demonstrate that the simplicity bias can be mitigated and OOD generalization improved. We train a set of similar models to fit the data in different ways using a penalty on the alignment of their input gradients. We show theoretically and empirically that this induces the learning of more complex predictive patterns. OOD generalization fundamentally requires information beyond i.i.d. examples, such as multiple training environments, counterfactual examples, or other side information. Our approach shows that we can defer this requirement to an independent model selection stage. We obtain SOTA results in visual recognition on biased data and generalization across visual domains. The method - the first to evade the simplicity bias - highlights the need for a better understanding and control of inductive biases in deep learning.

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arXiv2022

On Quantizing Implicit Neural Representations

The role of quantization within implicit/coordinate neural networks is still not fully understood. We note that using a canonical fixed quantization scheme during training produces poor performance at low-rates due to the network weight distributions changing over the course of training. In this work, we show that a non-uniform quantization of neural weights can lead to significant improvements. Specifically, we demonstrate that a clustered quantization enables improved reconstruction. Finally, by characterising a trade-off between quantization and network capacity, we demonstrate that it is possible (while memory inefficient) to reconstruct signals using binary neural networks. We demonstrate our findings experimentally on 2D image reconstruction and 3D radiance fields; and show that simple quantization methods and architecture search can achieve compression of NeRF to less than 16kb with minimal loss in performance (323x smaller than the original NeRF).

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arXiv2022

How You Start Matters for Generalization

Characterizing the remarkable generalization properties of over-parameterized neural networks remains an open problem. In this paper, we promote a shift of focus towards initialization rather than neural architecture or (stochastic) gradient descent to explain this implicit regularization. Through a Fourier lens, we derive a general result for the spectral bias of neural networks and show that the generalization of neural networks is heavily tied to their initialization. Further, we empirically solidify the developed theoretical insights using practical, deep networks. Finally, we make a case against the controversial flat-minima conjecture and show that Fourier analysis grants a more reliable framework for understanding the generalization of neural networks.

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arXiv2022

GARF: Gaussian Activated Radiance Fields for High Fidelity Reconstruction and Pose Estimation

Despite Neural Radiance Fields (NeRF) showing compelling results in photorealistic novel views synthesis of real-world scenes, most existing approaches require accurate prior camera poses. Although approaches for jointly recovering the radiance field and camera pose exist (BARF), they rely on a cumbersome coarse-to-fine auxiliary positional embedding to ensure good performance. We present Gaussian Activated neural Radiance Fields (GARF), a new positional embedding-free neural radiance field architecture - employing Gaussian activations - that outperforms the current state-of-the-art in terms of high fidelity reconstruction and pose estimation.

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arXiv2022

Enabling equivariance for arbitrary Lie groups

Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs. Recently, this limitation has motivated a shift in focus from CNNs to Capsule Networks (CapsNets). However, CapsNets suffer from admitting relatively few theoretical guarantees of invariance. We introduce a rigourous mathematical framework to permit invariance to any Lie group of warps, exclusively using convolutions (over Lie groups), without the need for capsules. Previous work on group convolutions has been hampered by strong assumptions about the group, which precludes the application of such techniques to common warps in computer vision such as affine and homographic. Our framework enables the implementation of group convolutions over any finite-dimensional Lie group. We empirically validate our approach on the benchmark affine-invariant classification task, where we achieve 30% improvement in accuracy against conventional CNNs while outperforming most CapsNets. As further illustration of the generality of our framework, we train a homography-convolutional model which achieves superior robustness on a homography-perturbed dataset, where CapsNet results degrade.

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arXiv2022

Long-term Visual Map Sparsification with Heterogeneous GNN

We address the problem of map sparsification for long-term visual localization. For map sparsification, a commonly employed assumption is that the pre-build map and the later captured localization query are consistent. However, this assumption can be easily violated in the dynamic world. Additionally, the map size grows as new data accumulate through time, causing large data overhead in the long term. In this paper, we aim to overcome the environmental changes and reduce the map size at the same time by selecting points that are valuable to future localization. Inspired by the recent progress in Graph Neural Network(GNN), we propose the first work that models SfM maps as heterogeneous graphs and predicts 3D point importance scores with a GNN, which enables us to directly exploit the rich information in the SfM map graph. Two novel supervisions are proposed: 1) a data-fitting term for selecting valuable points to future localization based on training queries; 2) a K-Cover term for selecting sparse points with full map coverage. The experiments show that our method selected map points on stable and widely visible structures and outperformed baselines in localization performance.

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arXiv2022

Learning Positional Embeddings for Coordinate-MLPs

We propose a novel method to enhance the performance of coordinate-MLPs by learning instance-specific positional embeddings. End-to-end optimization of positional embedding parameters along with network weights leads to poor generalization performance. Instead, we develop a generic framework to learn the positional embedding based on the classic graph-Laplacian regularization, which can implicitly balance the trade-off between memorization and generalization. This framework is then used to propose a novel positional embedding scheme, where the hyperparameters are learned per coordinate (i.e, instance) to deliver optimal performance. We show that the proposed embedding achieves better performance with higher stability compared to the well-established random Fourier features (RFF). Further, we demonstrate that the proposed embedding scheme yields stable gradients, enabling seamless integration into deep architectures as intermediate layers.

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arXiv2022

Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs

Coordinate-MLPs are emerging as an effective tool for modeling multidimensional continuous signals, overcoming many drawbacks associated with discrete grid-based approximations. However, coordinate-MLPs with ReLU activations, in their rudimentary form, demonstrate poor performance in representing signals with high fidelity, promoting the need for positional embedding layers. Recently, Sitzmann et al. proposed a sinusoidal activation function that has the capacity to omit positional embedding from coordinate-MLPs while still preserving high signal fidelity. Despite its potential, ReLUs are still dominating the space of coordinate-MLPs; we speculate that this is due to the hyper-sensitivity of networks -- that employ such sinusoidal activations -- to the initialization schemes. In this paper, we attempt to broaden the current understanding of the effect of activations in coordinate-MLPs, and show that there exists a broader class of activations that are suitable for encoding signals. We affirm that sinusoidal activations are only a single example in this class, and propose several non-periodic functions that empirically demonstrate more robust performance against random initializations than sinusoids. Finally, we advocate for a shift towards coordinate-MLPs that employ these non-traditional activation functions due to their high performance and simplicity.

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arXiv2022

On Regularizing Coordinate-MLPs

We show that typical implicit regularization assumptions for deep neural networks (for regression) do not hold for coordinate-MLPs, a family of MLPs that are now ubiquitous in computer vision for representing high-frequency signals. Lack of such implicit bias disrupts smooth interpolations between training samples, and hampers generalizing across signal regions with different spectra. We investigate this behavior through a Fourier lens and uncover that as the bandwidth of a coordinate-MLP is enhanced, lower frequencies tend to get suppressed unless a suitable prior is provided explicitly. Based on these insights, we propose a simple regularization technique that can mitigate the above problem, which can be incorporated into existing networks without any architectural modifications.

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arXiv2022

Reframing Neural Networks: Deep Structure in Overcomplete Representations

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well understood what makes them so effective. To approach this question, we introduce deep frame approximation: a unifying framework for constrained representation learning with structured overcomplete frames. While exact inference requires iterative optimization, it may be approximated by the operations of a feed-forward deep neural network. We indirectly analyze how model capacity relates to frame structures induced by architectural hyperparameters such as depth, width, and skip connections. We quantify these structural differences with the deep frame potential, a data-independent measure of coherence linked to representation uniqueness and stability. As a criterion for model selection, we show correlation with generalization error on a variety of common deep network architectures and datasets. We also demonstrate how recurrent networks implementing iterative optimization algorithms can achieve performance comparable to their feed-forward approximations while improving adversarial robustness. This connection to the established theory of overcomplete representations suggests promising new directions for principled deep network architecture design with less reliance on ad-hoc engineering.

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arXiv2021

Neural Scene Flow Prior

Before the deep learning revolution, many perception algorithms were based on runtime optimization in conjunction with a strong prior/regularization penalty. A prime example of this in computer vision is optical and scene flow. Supervised learning has largely displaced the need for explicit regularization. Instead, they rely on large amounts of labeled data to capture prior statistics, which are not always readily available for many problems. Although optimization is employed to learn the neural network, the weights of this network are frozen at runtime. As a result, these learning solutions are domain-specific and do not generalize well to other statistically different scenarios. This paper revisits the scene flow problem that relies predominantly on runtime optimization and strong regularization. A central innovation here is the inclusion of a neural scene flow prior, which uses the architecture of neural networks as a new type of implicit regularizer. Unlike learning-based scene flow methods, optimization occurs at runtime, and our approach needs no offline datasets -- making it ideal for deployment in new environments such as autonomous driving. We show that an architecture based exclusively on multilayer perceptrons (MLPs) can be used as a scene flow prior. Our method attains competitive -- if not better -- results on scene flow benchmarks. Also, our neural prior's implicit and continuous scene flow representation allows us to estimate dense long-term correspondences across a sequence of point clouds. The dense motion information is represented by scene flow fields where points can be propagated through time by integrating motion vectors. We demonstrate such a capability by accumulating a sequence of lidar point clouds.

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arXiv2021

High Fidelity 3D Reconstructions with Limited Physical Views

Multi-view triangulation is the gold standard for 3D reconstruction from 2D correspondences given known calibration and sufficient views. However in practice, expensive multi-view setups -- involving tens sometimes hundreds of cameras -- are required in order to obtain the high fidelity 3D reconstructions necessary for many modern applications. In this paper we present a novel approach that leverages recent advances in 2D-3D lifting using neural shape priors while also enforcing multi-view equivariance. We show how our method can achieve comparable fidelity to expensive calibrated multi-view rigs using a limited (2-3) number of uncalibrated camera views.

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arXiv2021

Rethinking Positional Encoding

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

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arXiv2021

BARF: Bundle-Adjusting Neural Radiance Fields

Neural Radiance Fields (NeRF) have recently gained a surge of interest within the computer vision community for its power to synthesize photorealistic novel views of real-world scenes. One limitation of NeRF, however, is its requirement of accurate camera poses to learn the scene representations. In this paper, we propose Bundle-Adjusting Neural Radiance Fields (BARF) for training NeRF from imperfect (or even unknown) camera poses -- the joint problem of learning neural 3D representations and registering camera frames. We establish a theoretical connection to classical image alignment and show that coarse-to-fine registration is also applicable to NeRF. Furthermore, we show that naïvely applying positional encoding in NeRF has a negative impact on registration with a synthesis-based objective. Experiments on synthetic and real-world data show that BARF can effectively optimize the neural scene representations and resolve large camera pose misalignment at the same time. This enables view synthesis and localization of video sequences from unknown camera poses, opening up new avenues for visual localization systems (e.g. SLAM) and potential applications for dense 3D mapping and reconstruction.

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arXiv2021

On the Bias Against Inductive Biases

Borrowing from the transformer models that revolutionized the field of natural language processing, self-supervised feature learning for visual tasks has also seen state-of-the-art success using these extremely deep, isotropic networks. However, the typical AI researcher does not have the resources to evaluate, let alone train, a model with several billion parameters and quadratic self-attention activations. To facilitate further research, it is necessary to understand the features of these huge transformer models that can be adequately studied by the typical researcher. One interesting characteristic of these transformer models is that they remove most of the inductive biases present in classical convolutional networks. In this work, we analyze the effect of these and more inductive biases on small to moderately-sized isotropic networks used for unsupervised visual feature learning and show that their removal is not always ideal.

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arXiv2021

Neural Trajectory Fields for Dynamic Novel View Synthesis

Recent approaches to render photorealistic views from a limited set of photographs have pushed the boundaries of our interactions with pictures of static scenes. The ability to recreate moments, that is, time-varying sequences, is perhaps an even more interesting scenario, but it remains largely unsolved. We introduce DCT-NeRF, a coordinatebased neural representation for dynamic scenes. DCTNeRF learns smooth and stable trajectories over the input sequence for each point in space. This allows us to enforce consistency between any two frames in the sequence, which results in high quality reconstruction, particularly in dynamic regions.

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arXiv2021

Deep NRSfM++: Towards Unsupervised 2D-3D Lifting in the Wild

The recovery of 3D shape and pose from 2D landmarks stemming from a large ensemble of images can be viewed as a non-rigid structure from motion (NRSfM) problem. Classical NRSfM approaches, however, are problematic as they rely on heuristic priors on the 3D structure (e.g. low rank) that do not scale well to large datasets. Learning-based methods are showing the potential to reconstruct a much broader set of 3D structures than classical methods -- dramatically expanding the importance of NRSfM to atemporal unsupervised 2D to 3D lifting. Hitherto, these learning approaches have not been able to effectively model perspective cameras or handle missing/occluded points -- limiting their applicability to in-the-wild datasets. In this paper, we present a generalized strategy for improving learning-based NRSfM methods to tackle the above issues. Our approach, Deep NRSfM++, achieves state-of-the-art performance across numerous large-scale benchmarks, outperforming both classical and learning-based 2D-3D lifting methods.

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arXiv2021

PAUL: Procrustean Autoencoder for Unsupervised Lifting

Recent success in casting Non-rigid Structure from Motion (NRSfM) as an unsupervised deep learning problem has raised fundamental questions about what novelty in NRSfM prior could the deep learning offer. In this paper we advocate for a 3D deep auto-encoder framework to be used explicitly as the NRSfM prior. The framework is unique as: (i) it learns the 3D auto-encoder weights solely from 2D projected measurements, and (ii) it is Procrustean in that it jointly resolves the unknown rigid pose for each shape instance. We refer to this architecture as a Procustean Autoencoder for Unsupervised Lifting (PAUL), and demonstrate state-of-the-art performance across a number of benchmarks in comparison to recent innovations such as Deep NRSfM and C3PDO.

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