Sameera Ramasinghe

Sameera Ramasinghe, Hemanth Saratchandran, Violetta Shevchenko et al. · amazon-science

Modelling dynamical systems is an integral component for understanding the natural world. To this end, neural networks are becoming an increasingly popular candidate owing to their ability to learn complex functions from large amounts of data. Despite this recent progress, there has not been an adequate discussion on the architectural regularization that neural networks offer when learning such systems, hindering their efficient usage. In this paper, we initiate a discussion in this direction using coordinate networks as a test bed. We interpret dynamical systems and coordinate networks from a signal processing lens, and show that simple coordinate networks with few layers can be used to solve multiple problems in modelling dynamical systems, without any explicit regularizers.

Jianqiao Zheng, Sameera Ramasinghe, Xueqian Li et al.

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 mainly 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. In addition, we argue that employing a more complex positional encoding -- that scales exponentially with the number of modes -- requires only a linear (rather than deep) coordinate function to achieve comparable performance. Counter-intuitively, we demonstrate that trading positional embedding complexity for network deepness is orders of magnitude faster than current state-of-the-art; despite the additional embedding complexity. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice.

Townim Chowdhury, Ali Cheraghian, Sameera Ramasinghe et al.

Few-shot class-incremental learning (FSCIL) aims to incrementally fine-tune a model (trained on base classes) for a novel set of classes using a few examples without forgetting the previous training. Recent efforts address this problem primarily on 2D images. However, due to the advancement of camera technology, 3D point cloud data has become more available than ever, which warrants considering FSCIL on 3D data. This paper addresses FSCIL in the 3D domain. In addition to well-known issues of catastrophic forgetting of past knowledge and overfitting of few-shot data, 3D FSCIL can bring newer challenges. For example, base classes may contain many synthetic instances in a realistic scenario. In contrast, only a few real-scanned samples (from RGBD sensors) of novel classes are available in incremental steps. Due to the data variation from synthetic to real, FSCIL endures additional challenges, degrading performance in later incremental steps. We attempt to solve this problem using Microshapes (orthogonal basis vectors) by describing any 3D objects using a pre-defined set of rules. It supports incremental training with few-shot examples minimizing synthetic to real data variation. We propose new test protocols for 3D FSCIL using popular synthetic datasets (ModelNet and ShapeNet) and 3D real-scanned datasets (ScanObjectNN and CO3D). By comparing state-of-the-art methods, we establish the effectiveness of our approach in the 3D domain.

Yanshuo Wang, Ali Cheraghian, Zeeshan Hayder et al.

Real-world systems often encounter new data over time, which leads to experiencing target domain shifts. Existing Test-Time Adaptation (TTA) methods tend to apply computationally heavy and memory-intensive backpropagation-based approaches to handle this. Here, we propose a novel method that uses a backpropagation-free approach for TTA for the specific case of 3D data. Our model uses a two-stream architecture to maintain knowledge about the source domain as well as complementary target-domain-specific information. The backpropagation-free property of our model helps address the well-known forgetting problem and mitigates the error accumulation issue. The proposed method also eliminates the need for the usually noisy process of pseudo-labeling and reliance on costly self-supervised training. Moreover, our method leverages subspace learning, effectively reducing the distribution variance between the two domains. Furthermore, the source-domain-specific and the target-domain-specific streams are aligned using a novel entropy-based adaptive fusion strategy. Extensive experiments on popular benchmarks demonstrate the effectiveness of our method. The code will be available at \url{https://github.com/abie-e/BFTT3D}.

Hamidreza Dastmalchi, Aijun An, Ali Cheraghian et al.

Test-time adaptation (TTA) of 3D point clouds is crucial for mitigating discrepancies between training and testing samples in real-world scenarios, particularly when handling corrupted point clouds. LiDAR data, for instance, can be affected by sensor failures or environmental factors, causing domain gaps. Adapting models to these distribution shifts online is crucial, as training for every possible variation is impractical. Existing methods often focus on fine-tuning pre-trained models based on self-supervised learning or pseudo-labeling, which can lead to forgetting valuable source domain knowledge over time and reduce generalization on future tests. In this paper, we introduce a novel 3D test-time adaptation method, termed 3DD-TTA, which stands for 3D Denoising Diffusion Test-Time Adaptation. This method uses a diffusion strategy that adapts input point cloud samples to the source domain while keeping the source model parameters intact. The approach uses a Variational Autoencoder (VAE) to encode the corrupted point cloud into a shape latent and latent points. These latent points are corrupted with Gaussian noise and subjected to a denoising diffusion process. During this process, both the shape latent and latent points are updated to preserve fidelity, guiding the denoising toward generating consistent samples that align more closely with the source domain. We conduct extensive experiments on the ShapeNet dataset and investigate its generalizability on ModelNet40 and ScanObjectNN, achieving state-of-the-art results. The code has been released at \url{https://github.com/hamidreza-dastmalchi/3DD-TTA}.

Vishagar Arunan, Saeedha Nazar, Hashiru Pramuditha et al.

Splatting-based 3D reconstruction methods have gained popularity with the advent of 3D Gaussian Splatting, efficiently synthesizing high-quality novel views. These methods commonly resort to using exponential family functions, such as the Gaussian function, as reconstruction kernels due to their anisotropic nature, ease of projection, and differentiability in rasterization. However, the field remains restricted to variations within the exponential family, leaving generalized reconstruction kernels largely underexplored, partly due to the lack of easy integrability in 3D to 2D projections. In this light, we show that a class of decaying anisotropic radial basis functions (DARBFs), which are non-negative functions of the Mahalanobis distance, supports splatting by approximating the Gaussian function's closed-form integration advantage. With this fresh perspective, we demonstrate up to 34% faster convergence during training and a 45% reduction in memory consumption across various DARB reconstruction kernels, while maintaining comparable PSNR, SSIM, and LPIPS results. We will make the code available.

Jianqiao Zheng, Sameera Ramasinghe, Simon Lucey

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.

Sameera Ramasinghe, Moshiur Farazi, Salman Khan et al.

Conditional GANs (cGAN), in their rudimentary form, suffer from critical drawbacks such as the lack of diversity in generated outputs and distortion between the latent and output manifolds. Although efforts have been made to improve results, they can suffer from unpleasant side-effects such as the topology mismatch between latent and output spaces. In contrast, we tackle this problem from a geometrical perspective and propose a novel training mechanism that increases both the diversity and the visual quality of a vanilla cGAN, by systematically encouraging a bi-lipschitz mapping between the latent and the output manifolds. We validate the efficacy of our solution on a baseline cGAN (i.e., Pix2Pix) which lacks diversity, and show that by only modifying its training mechanism (i.e., with our proposed Pix2Pix-Geo), one can achieve more diverse and realistic outputs on a broad set of image-to-image translation tasks. Codes are available at https://github.com/samgregoost/Rethinking-CGANs.

Hemanth Saratchandran, Sameera Ramasinghe, Simon Lucey

In the realm of computer vision, Neural Fields have gained prominence as a contemporary tool harnessing neural networks for signal representation. Despite the remarkable progress in adapting these networks to solve a variety of problems, the field still lacks a comprehensive theoretical framework. This article aims to address this gap by delving into the intricate interplay between initialization and activation, providing a foundational basis for the robust optimization of Neural Fields. Our theoretical insights reveal a deep-seated connection among network initialization, architectural choices, and the optimization process, emphasizing the need for a holistic approach when designing cutting-edge Neural Fields.

Jianqiao Zheng, Xueqian Li, Sameera Ramasinghe et al.

End-to-end trained per-point embeddings are an essential ingredient of any state-of-the-art 3D point cloud processing such as detection or alignment. Methods like PointNet, or the more recent point cloud transformer -- and its variants -- all employ learned per-point embeddings. Despite impressive performance, such approaches are sensitive to out-of-distribution (OOD) noise and outliers. In this paper, we explore the role of an analytical per-point embedding based on the criterion of bandwidth. The concept of bandwidth enables us to draw connections with an alternate per-point embedding -- positional embedding, particularly random Fourier features. We present compelling robust results across downstream tasks such as point cloud classification and registration with several categories of OOD noise.

Sameera Ramasinghe, Simon Lucey

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.

Sameera Ramasinghe, Simon Lucey

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.

Lachlan Ewen MacDonald, Sameera Ramasinghe, Simon Lucey

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.

Sameera Ramasinghe, Kasun Fernando, Salman Khan et al.

Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these initial errors, leading to poor generalizations. This paper proposes a framework to construct Normalizing Flows (NF), which demonstrates higher robustness against such initial errors. To this end, we utilize Bernstein-type polynomials inspired by the optimal stability of the Bernstein basis. Further, compared to the existing NF frameworks, our method provides compelling advantages like theoretical upper bounds for the approximation error, higher interpretability, suitability for compactly supported densities, and the ability to employ higher degree polynomials without training instability. We conduct a thorough theoretical analysis and empirically demonstrate the efficacy of the proposed technique using experiments on both real-world and synthetic datasets.

Sameera Ramasinghe, Salman Khan, Nick Barnes et al.

Point-clouds are a popular choice for vision and graphics tasks due to their accurate shape description and direct acquisition from range-scanners. This demands the ability to synthesize and reconstruct high-quality point-clouds. Current deep generative models for 3D data generally work on simplified representations (e.g., voxelized objects) and cannot deal with the inherent redundancy and irregularity in point-clouds. A few recent efforts on 3D point-cloud generation offer limited resolution and their complexity grows with the increase in output resolution. In this paper, we develop a principled approach to synthesize 3D point-clouds using a spectral-domain Generative Adversarial Network (GAN). Our spectral representation is highly structured and allows us to disentangle various frequency bands such that the learning task is simplified for a GAN model. As compared to spatial-domain generative approaches, our formulation allows us to generate arbitrary number of points high-resolution point-clouds with minimal computational overhead. Furthermore, we propose a fully differentiable block to transform from {the} spectral to the spatial domain and back, thereby allowing us to integrate knowledge from well-established spatial models. We demonstrate that Spectral-GAN performs well for point-cloud generation task. Additionally, it can learn {a} highly discriminative representation in an unsupervised fashion and can be used to accurately reconstruct 3D objects.

Sameera Ramasinghe, Salman Khan, Nick Barnes et al.

Convolution is an integral operation that defines how the shape of one function is modified by another function. This powerful concept forms the basis of hierarchical feature learning in deep neural networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other topological spaces---such as a sphere ($\mathbb{S}^2$) or a unit ball ($\mathbb{B}^3$)---entails unique challenges. In this work, we propose a novel `\emph{volumetric convolution}' operation that can effectively model and convolve arbitrary functions in $\mathbb{B}^3$. We develop a theoretical framework for \emph{volumetric convolution} based on Zernike polynomials and efficiently implement it as a differentiable and an easily pluggable layer in deep networks. By construction, our formulation leads to the derivation of a novel formula to measure the symmetry of a function in $\mathbb{B}^3$ around an arbitrary axis, that is useful in function analysis tasks. We demonstrate the efficacy of proposed volumetric convolution operation on one viable use case i.e., 3D object recognition.

Sameera Ramasinghe, Salman Khan, Nick Barnes et al.

Existing networks directly learn feature representations on 3D point clouds for shape analysis. We argue that 3D point clouds are highly redundant and hold irregular (permutation-invariant) structure, which makes it difficult to achieve inter-class discrimination efficiently. In this paper, we propose a two-faceted solution to this problem that is seamlessly integrated in a single `Blended Convolution and Synthesis' layer. This fully differentiable layer performs two critical tasks in succession. In the first step, it projects the input 3D point clouds into a latent 3D space to synthesize a highly compact and more inter-class discriminative point cloud representation. Since, 3D point clouds do not follow a Euclidean topology, standard 2/3D Convolutional Neural Networks offer limited representation capability. Therefore, in the second step, it uses a novel 3D convolution operator functioning inside the unit ball ($\mathbb{B}^3$) to extract useful volumetric features. We extensively derive formulae to achieve both translation and rotation of our novel convolution kernels. Finally, using the proposed techniques we present an extremely light-weight, end-to-end architecture that achieves compelling results on 3D shape recognition and retrieval.

Sameera Ramasinghe, Salman Khan, Nick Barnes

Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other topological spaces---such as a sphere ($\mathbb{S}^2$) or a unit ball ($\mathbb{B}^3$)---entails unique challenges. In this work, we propose a novel `\emph{volumetric convolution}' operation that can effectively convolve arbitrary functions in $\mathbb{B}^3$. We develop a theoretical framework for \emph{volumetric convolution} based on Zernike polynomials and efficiently implement it as a differentiable and an easily pluggable layer for deep networks. Furthermore, our formulation leads to derivation of a novel formula to measure the symmetry of a function in $\mathbb{B}^3$ around an arbitrary axis, that is useful in 3D shape analysis tasks. We demonstrate the efficacy of proposed volumetric convolution operation on a possible use-case i.e., 3D object recognition task.

Sameera Ramasinghe, C. D. Athuralya, Salman Khan

Recently proposed Capsule Network is a brain inspired architecture that brings a new paradigm to deep learning by modelling input domain variations through vector based representations. Despite being a seminal contribution, CapsNet does not explicitly model structured relationships between the detected entities and among the capsule features for related inputs. Motivated by the working of cortical network in human visual system, we seek to resolve CapsNet limitations by proposing several intuitive modifications to the CapsNet architecture. We introduce, (1) a novel routing weight initialization technique, (2) an improved CapsNet design that exploits semantic relationships between the primary capsule activations using a densely connected Conditional Random Field and (3) a Cholesky transformation based correlation module to learn a general priority scheme. Our proposed design allows CapsNet to scale better to more complex problems, such as the multi-label classification task, where semantically related categories co-exist with various interdependencies. We present theoretical bases for our extensions and demonstrate significant improvements on ADE20K scene dataset.