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 varying performances across selected DARB reconstruction kernels, achieving comparable training convergence and memory footprints, with on-par PSNR, SSIM, and LPIPS results.

Implicit Neural Representations (INRs) are a versatile and powerful tool for encoding various forms of data, including images, videos, sound, and 3D shapes. A critical factor in the success of INRs is the initialization of the network, which can significantly impact the convergence and accuracy of the learned model. Unfortunately, commonly used neural network initializations are not widely applicable for many activation functions, especially those used by INRs. In this paper, we improve upon previous initialization methods by deriving an initialization that has stable variance across layers, and applies to any activation function. We show that this generalizes many previous initialization methods, and has even better stability for well studied activations. We also show that our initialization leads to improved results with INR activation functions in multiple signal modalities. Our approach is particularly effective for Gaussian INRs, where we demonstrate that the theory of our initialization matches with task performance in multiple experiments, allowing us to achieve improvements in image, audio, and 3D surface reconstruction.

Pipeline Parallelism (PP) enables large neural network training on small, interconnected devices by splitting the model into multiple stages. To maximize pipeline utilization, asynchronous optimization is appealing as it offers 100% pipeline utilization by construction. However, it is inherently challenging as the weights and gradients are no longer synchronized, leading to *stale (or delayed) gradients*. To alleviate this, we introduce a variant of Nesterov Accelerated Gradient (NAG) for asynchronous optimization in PP. Specifically, we modify the look-ahead step in NAG to effectively address the staleness in gradients. We theoretically prove that our approach converges at a sublinear rate in the presence of fixed delay in gradients. Our experiments on large-scale language modelling tasks using decoder-only architectures with up to **1B parameters**, demonstrate that our approach significantly outperforms existing asynchronous methods, even surpassing the synchronous baseline.

Composed Image Retrieval (CIR) is the task of retrieving images matching a reference image augmented with a text, where the text describes changes to the reference image in natural language. Traditionally, models designed for CIR have relied on triplet data containing a reference image, reformulation text, and a target image. However, curating such triplet data often necessitates human intervention, leading to prohibitive costs. This challenge has hindered the scalability of CIR model training even with the availability of abundant unlabeled data. With the recent advances in foundational models, we advocate a shift in the CIR training paradigm where human annotations can be efficiently replaced by large language models (LLMs). Specifically, we demonstrate the capability of large captioning and language models in efficiently generating data for CIR only relying on unannotated image collections. Additionally, we introduce an embedding reformulation architecture that effectively combines image and text modalities. Our model, named InstructCIR, outperforms state-of-the-art methods in zero-shot composed image retrieval on CIRR and FashionIQ datasets. Furthermore, we demonstrate that by increasing the amount of generated data, our zero-shot model gets closer to the performance of supervised baselines.

We consider a decentralized setup in which the participants collaboratively train and serve a large neural network, and where each participant only processes a subset of the model. In this setup, we explore the possibility of unmaterializable weights, where a full weight set is never available to any one participant. We introduce Unextractable Protocol Models (UPMs): a training and inference framework that leverages the sharded model setup to ensure model shards (i.e.,, subsets) held by participants are incompatible at different time steps. UPMs periodically inject time-varying, random, invertible transforms at participant boundaries; preserving the overall network function yet rendering cross-time assemblies incoherent. On Qwen-2.5-0.5B and Llama-3.2-1B, 10 000 transforms leave FP32 perplexity unchanged ($\Delta$PPL$< 0.01$; Jensen–Shannon drift $<4 \times 10^{-5}$), and we show how to control growth for lower precision datatypes. Applying a transform every 30s adds 3% latency, 0.1% bandwidth, and 10% GPU-memory overhead at inference, while training overhead falls to 1.6% time and < 1% memory. We consider several attacks, showing that the requirements of direct attacks are impractical and easy to defend against, and that gradient-based fine-tuning of stitched partitions consumes $\geq 60\%$ of the tokens required to train from scratch. By enabling models to be collaboratively trained yet not extracted, UPMs make it practical to embed programmatic incentive mechanisms in community-driven decentralized training.

Scaling models has led to significant advancements in deep learning, but training these models in decentralized settings remains challenging due to communication bottlenecks. While existing compression techniques are effective in data-parallel, they do not extend to model parallelism. Unlike data-parallel training, where weight gradients are exchanged, model-parallel requires compressing activations and activation gradients as they propagate through layers, accumulating compression errors. We propose a novel compression algorithm that compresses both forward and backward passes, enabling up to 99% compression with no convergence degradation with negligible memory/compute overhead. By leveraging a recursive structure in transformer networks, we predefine a low-dimensional subspace to confine the activations and gradients, allowing full reconstruction in subsequent layers. Our method achieves up to 100x improvement in communication efficiency and enables training billion-parameter-scale models over low-end GPUs connected via consumer-grade internet speeds as low as 80Mbps, matching the convergence of centralized datacenter systems with 100Gbps connections with model parallel.

Pretraining language models with extended context windows enhances their ability to leverage rich information during generation. Existing methods split input sequences into chunks, broadcast them across multiple devices, and compute attention block by block which incurs significant communication overhead. While feasible in high-speed clusters, these methods are impractical for decentralized training over low-bandwidth connections. We propose a compression method for communication-efficient context parallelism in decentralized settings, achieving a remarkable compression rate of over 95% with negligible overhead and no loss in convergence. Our key insight is to exploit the intrinsic low-rank structure of activation outputs by dynamically constraining them to learned mixtures of subspaces via efficient reparameterizations. We demonstrate scaling billion-parameter decentralized models to context lengths exceeding 100K tokens on networks as slow as 300Mbps, matching the wall-clock convergence speed of centralized models on 100Gbps interconnects.

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 https://github.com/hamidreza-dastmalchi/3DD-Tta.

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 [17], or the more recent point cloud transformer [7]—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.

Inferring the 3D structure of a non-rigid dynamic scene from a single moving camera is an under-constrained problem. Inspired by the remarkable progress of neural radiance fields (NeRFs) in photo-realistic novel view synthesis of static scenes, it has also been extended to dynamic settings. Such methods heavily rely on implicit neural priors to regularize the problem. In this work, we take a step back and investigate how current implementations may entail deleterious effects including limited expressiveness, entanglement of light and density fields, and sub-optimal motion localization. Further, we devise a factorisation-based framework that represents the scene as a composition of bandlimited, high-dimensional signals. We demonstrate compelling results across complex dynamic scenes that involve changes in lighting, texture and long-range dynamics.

Recent advancements in machine learning have spotlighted the potential of hyperbolic spaces as they effectively learn hierarchical feature representations. While there has been progress in leveraging hyperbolic spaces in single-modality contexts, its exploration in multimodal settings remains under explored. A recent work has sought to transpose Euclidean multimodal learning techniques to hyperbolic spaces, by adopting a geodesic distance based contrastive loss. However, we show both theoretically and empirically that such spatial proximity based contrastive loss significantly disrupts hierarchies in the latent space. To remedy this, we advocate that the cross-modal representations should accept the inherent modality gap between text and images, and introduce a novel approach to measure cross-modal similarity that does not enforce spatial proximity. Our approach shows remarkable capabilities in preserving unimodal hierarchies while aligning the two modalities. Our experiments on a series of downstream tasks demonstrate that a better latent structure emerges with our objective function while being superior in text-to-image and image-to-text retrieval tasks.

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.

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 prob-lem and mitigates the error accumulation issue. The pro-posed method also eliminates the need for the usually noisy process of pseudo-labeling and reliance on costly self-supervised training. Moreover, our method leverages sub-space learning, effectively reducing the distribution vari-ance between the two domains. Furthermore, the source-domain-specific and the target-domain-specific streams are aligned using a novel entropy-based adaptive fusion strat-egy. Extensive experiments on popular benchmarks demon-strate the effectiveness of our method. The code will be available at https://github.com/abie-e/BFTT3D.

Novel-view synthesis through diffusion models has demonstrated remarkable potential for generating diverse and high-quality images. Yet, the independent process of image generation in these prevailing methods leads to challenges in maintaining multiple view consistency. To address this, we introduce ViewFusion, a novel, training-free algorithm that can be seamlessly integrated into existing pre-trained diffusion models. Our approach adopts an auto-regressive method that implicitly leverages previously generated views as context for next view generation, ensuring robust multi-view consistency during the novel-view generation process. Through a diffusion process that fuses known-view information via interpolated denoising, our framework successfully extends single-view conditioned models to work in multiple-view conditional settings without any additional fine-tuning. Extensive experimental results demonstrate the effectiveness of View Fusion in generating consistent and detailed novel views.

Synthesizing novel views for dynamic scenes from a collection of RGB inputs poses significant challenges due to the inherent under-constrained nature of the problem. To mitigate this ill-posedness, practitioners in the field of neural radiance fields (NeRF) often resort to the adoption of intricate geometric regularization techniques, including scene flow, depth estimation, or learned perceptual similarity. While these geometric cues have demonstrated their effectiveness, their incorporation leads to evaluation of computationally expensive off-the-shelf models, introducing substantial computational overhead into the pipeline. Moreover, seamlessly integrating such modules into diverse dynamic NeRF models can be a non-trivial task, hindering their utilization in an architecture-agnostic manner. In this paper, we propose a theoretically grounded, lightweight regularizer by treating the dynamics of a time-varying scene as a low-frequency change of a probability distribution of the light intensity. We constrain the dynamics of this distribution using optimal transport (OT) and provide error bounds under reasonable assumptions. Our regularization is learning-free, architecture agnostic, and can be implemented with just a few lines of code. Finally, we demonstrate the practical efficacy of our regularizer across state-of-the-art architectures.

Implicit Neural Representations (INRs) have gained popularity for encoding signals as compact, differentiable entities. While commonly using techniques like Fourier positional encodings or non-traditional activation functions (e.g., Gaussian, sinusoid, or wavelets) to capture high-frequency content, their properties lack exploration within a unified theoretical framework. Addressing this gap, we conduct a comprehensive analysis of these activations from a sampling theory perspective. Our investigation reveals that, especially in shallow INRs, $\mathrm{sinc}$ activations—previously unused in conjunction with INRs—are theoretically optimal for signal encoding. Additionally, we establish a connection between dynamical systems and INRs, leveraging sampling theory to bridge these two paradigms.

Implicit neural representations (INRs) have proven effective in various tasks including image, shape, audio, and video reconstruction. These INRs typically learn the implicit field from sampled input points. This is often done using a single network for the entire domain, imposing many global constraints on a single function. In this paper, we propose a mixture of experts (MoE) implicit neural representation approach that enables learning local piece-wise continuous functions that simultaneously learns to subdivide the domain and fit it locally. We show that incorporating a mixture of experts architecture into existing INR formulations provides a boost in speed, accuracy, and memory requirements. Additionally, we introduce novel conditioning and pretraining methods for the gating network that improves convergence to the desired solution. We evaluate the effectiveness of our approach on multiple reconstruction tasks, including surface reconstruction, image reconstruction, and audio signal reconstruction and show improved performance compared to non-MoE methods. Code is available at our project page https://sitzikbs.github.io/neural-experts-projectpage/ .

We propose a novel method to enhance the performance of coordinate-MLPs (also referred to as neural fields) 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.

Coordinate networks are widely used in computer vision due to their ability to represent signals as compressed, continuous entities. However, training these networks with first-order optimizers can be slow, hindering their use in real-time applications. Recent works have opted for shallow voxel-based representations to achieve faster training, but this sacrifices memory efficiency. This work proposes a solution that leverages second-order optimization methods to significantly reduce training times for coordinate networks while maintaining their compressibility. Experiments demonstrate the effectiveness of this approach on various signal modalities, such as audio, images, videos, shape and neural radiance fields (NeRF).

Characterizing the remarkable generalization properties of over-parameterized neural networks remains an open problem. A growing body of recent literature shows that the bias of stochastic gradient descent (SGD) and architecture choice implicitly leads to better generalization. In this paper, we show on the contrary that, independently of architecture, SGD can itself be the cause of poor generalization if one does not ensure good initialization. Specifically, we prove that *any* differentiably parameterized model, trained under gradient flow, obeys a weak spectral bias law which states that sufficiently high frequencies train arbitrarily slowly. This implies that very high frequencies present at initialization will remain after training, and hamper generalization. Further, we empirically test the developed theoretical insights using practical, deep networks. Finally, we contrast our framework with that supplied by the *flat-minima* conjecture and show that Fourier analysis grants a more reliable framework for understanding the generalization of neural networks.

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 infocus 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.

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.

Few-shot class incremental learning (FSCIL) aims to incrementally add sets of novel classes to a well-trained base model in multiple training sessions with the restriction that only a few novel instances are available per class. While learning novel classes, FSCIL methods gradually forget base (old) class training and overfit to a few novel class samples. Existing approaches have addressed this problem by computing the class prototypes from the visual or semantic word vector domain. In this paper, we propose addressing this problem using a mixture of subspaces. Subspaces define the cluster structure of the visual domain and help to describe the visual and semantic domain considering the overall distribution of the data. Additionally, we propose to employ a variational autoencoder (VAE) to generate synthesized visual samples for augmenting pseudo-feature while learning novel classes incrementally. The combined effect of the mixture of subspaces and synthesized features reduces the forgetting and overfitting problem of FSCIL. Extensive experiments on three image classification datasets show that our proposed method achieves competitive results compared to state-of-the-art methods.

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.

Convolution is an effective technique that can be used to obtain abstract feature representations using hierarchical layers in deep networks. However, performing convolution in non-Euclidean topological spaces such as the unit ball (B 3 ) is still an under-explored problem. In this paper, we propose a light-weight experimental architecture for 3D object classification, that operates in B 3 . The proposed network utilizes both hand-crafted and learned features, and uses capsules in the penultimate layer to disentangle 3D shape features through pose and view equivariance. It simultaneously maintains an intrinsic co-ordinate frame, where mutual relationships between object parts are preserved. Furthermore, we show that the optimal view angles for extracting patterns from 3D objects depend on its shape and achieve compelling results with a relatively shallow network, compared to the state-of-the-art.

Point-clouds are a popular choice for robotics and computer vision 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 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. Our codes are available at https://github.com/samgregoost/Spectral-GAN/.

Existing models for shape analysis directly learn feature representations on 3D point clouds. 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-pronged 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 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, we propose a novel 3D convolution operator functioning inside the unit ball to extract useful volumetric features. We 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.

Activity recognition in videos in a deep-learning setting-or otherwise-uses both static and pre-computed motion components. The method of combining the two components, while keeping the burden on the deep network less, still remains uninvestigated. Moreover, it is not clear what the level of contribution of individual components is, and how to control the contribution. In this paper, we use a combination of convolutional-neural-network-generated static features and motion features in the form of motion tubes. We propose three schemas for combining static and motion components: based on a variance ratio, principal components, and Cholesky decomposition. The Cholesky-decomposition-based method allows the control of contributions. The ratio given by variance analysis of static and motion features matches well with the experimental optimal ratio used in the Cholesky decomposition-based method. The resulting activity recognition system is better or on par with the existing state-of-the-art when tested with three popular data sets. The findings also enable us to characterize a data set with respect to its richness in motion information.