David W. Romero

Putri A. van der Linden, David W. Romero, Erik J. Bekkers

Neural operations that rely on neighborhood information are much more expensive when deployed on point clouds than on grid data due to the irregular distances between points in a point cloud. In a grid, on the other hand, we can compute the kernel only once and reuse it for all query positions. As a result, operations that rely on neighborhood information scale much worse for point clouds than for grid data, specially for large inputs and large neighborhoods. In this work, we address the scalability issue of point cloud methods by tackling its root cause: the irregularity of the data. We propose learnable gridification as the first step in a point cloud processing pipeline to transform the point cloud into a compact, regular grid. Thanks to gridification, subsequent layers can use operations defined on regular grids, e.g., Conv3D, which scale much better than native point cloud methods. We then extend gridification to point cloud to point cloud tasks, e.g., segmentation, by adding a learnable de-gridification step at the end of the point cloud processing pipeline to map the compact, regular grid back to its original point cloud form. Through theoretical and empirical analysis, we show that gridified networks scale better in terms of memory and time than networks directly applied on raw point cloud data, while being able to achieve competitive results. Our code is publicly available at https://github.com/computri/gridifier.

David M. Knigge, David W. Romero, Albert Gu et al.

Performant Convolutional Neural Network (CNN) architectures must be tailored to specific tasks in order to consider the length, resolution, and dimensionality of the input data. In this work, we tackle the need for problem-specific CNN architectures. We present the Continuous Convolutional Neural Network (CCNN): a single CNN able to process data of arbitrary resolution, dimensionality and length without any structural changes. Its key component are its continuous convolutional kernels which model long-range dependencies at every layer, and thus remove the need of current CNN architectures for task-dependent downsampling and depths. We showcase the generality of our method by using the same architecture for tasks on sequential ($1{\rm D}$), visual ($2{\rm D}$) and point-cloud ($3{\rm D}$) data. Our CCNN matches and often outperforms the current state-of-the-art across all tasks considered.

Stefano Massaroli, Michael Poli, Daniel Y. Fu et al.

Recent advances in attention-free sequence models rely on convolutions as alternatives to the attention operator at the core of Transformers. In particular, long convolution sequence models have achieved state-of-the-art performance in many domains, but incur a significant cost during auto-regressive inference workloads -- naively requiring a full pass (or caching of activations) over the input sequence for each generated token -- similarly to attention-based models. In this paper, we seek to enable $\mathcal O(1)$ compute and memory cost per token in any pre-trained long convolution architecture to reduce memory footprint and increase throughput during generation. Concretely, our methods consist in extracting low-dimensional linear state-space models from each convolution layer, building upon rational interpolation and model-order reduction techniques. We further introduce architectural improvements to convolution-based layers such as Hyena: by weight-tying the filters across channels into heads, we achieve higher pre-training quality and reduce the number of filters to be distilled. The resulting model achieves 10x higher throughput than Transformers and 1.5x higher than Hyena at 1.3B parameters, without any loss in quality after distillation.

David W. Romero, David M. Knigge, Albert Gu et al.

The use of Convolutional Neural Networks (CNNs) is widespread in Deep Learning due to a range of desirable model properties which result in an efficient and effective machine learning framework. However, performant CNN architectures must be tailored to specific tasks in order to incorporate considerations such as the input length, resolution, and dimentionality. In this work, we overcome the need for problem-specific CNN architectures with our Continuous Convolutional Neural Network (CCNN): a single CNN architecture equipped with continuous convolutional kernels that can be used for tasks on data of arbitrary resolution, dimensionality and length without structural changes. Continuous convolutional kernels model long range dependencies at every layer, and remove the need for downsampling layers and task-dependent depths needed in current CNN architectures. We show the generality of our approach by applying the same CCNN to a wide set of tasks on sequential (1$\mathrm{D}$) and visual data (2$\mathrm{D}$). Our CCNN performs competitively and often outperforms the current state-of-the-art across all tasks considered.

Tycho F. A. van der Ouderaa, David W. Romero, Mark van der Wilk

Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing and place symmetry constraints on the functions a neural network can represent. The type of symmetry is typically fixed and has to be chosen in advance. Although some tasks are inherently equivariant, many tasks do not strictly follow such symmetries. In such cases, equivariance constraints can be overly restrictive. In this work, we propose a parameter-efficient relaxation of equivariance that can effectively interpolate between a (i) non-equivariant linear product, (ii) a strict-equivariant convolution, and (iii) a strictly-invariant mapping. The proposed parameterisation can be thought of as a building block to allow adjustable symmetry structure in neural networks. In addition, we demonstrate that the amount of equivariance can be learned from the training data using backpropagation. Gradient-based learning of equivariance achieves similar or improved performance compared to the best value found by cross-validation and outperforms baselines with partial or strict equivariance on CIFAR-10 and CIFAR-100 image classification tasks.

Erik J Bekkers, Sharvaree Vadgama, Rob D Hesselink et al.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions $\mathbb{R}^3$, position and orientations $\mathbb{R}^3 {\times} S^2$, and the group $SE(3)$ itself. Among these, $\mathbb{R}^3 {\times} S^2$ is an optimal choice due to the ability to represent directional information, which $\mathbb{R}^3$ methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full $SE(3)$ group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

David W. Romero, Neil Zeghidour

We present Differentiable Neural Architectures (DNArch), a method that jointly learns the weights and the architecture of Convolutional Neural Networks (CNNs) by backpropagation. In particular, DNArch allows learning (i) the size of convolutional kernels at each layer, (ii) the number of channels at each layer, (iii) the position and values of downsampling layers, and (iv) the depth of the network. To this end, DNArch views neural architectures as continuous multidimensional entities, and uses learnable differentiable masks along each dimension to control their size. Unlike existing methods, DNArch is not limited to a predefined set of possible neural components, but instead it is able to discover entire CNN architectures across all feasible combinations of kernel sizes, widths, depths and downsampling. Empirically, DNArch finds performant CNN architectures for several classification and dense prediction tasks on sequential and image data. When combined with a loss term that controls the network complexity, DNArch constrains its search to architectures that respect a predefined computational budget during training.

Alonso Urbano, David W. Romero

Group equivariance can overly constrain models if the symmetries in the group differ from those observed in data. While common methods address this by determining the appropriate level of symmetry at the dataset level, they are limited to supervised settings and ignore scenarios in which multiple levels of symmetry co-exist in the same dataset. In this paper, we propose a method able to detect the level of symmetry of each input without the need for labels. Our framework is general enough to accommodate different families of both continuous and discrete symmetry distributions, such as arbitrary unimodal, symmetric distributions and discrete groups. We validate the effectiveness of our approach on synthetic datasets with different per-class levels of symmetries, and demonstrate practical applications such as the detection of out-of-distribution symmetries. Our code is publicly available at https://github.com/aurban0/ssl-sym.

David Romero, Ariana Bermudez, Hao Li et al.

Recent models for video generation have achieved remarkable progress and are now deployed in film, social media production, and advertising. Beyond their creative potential, such models also hold promise as world simulators for robotics and embodied decision making. Despite strong advances, however, current approaches still struggle to generate physically plausible object interactions and lack physics-grounded control mechanisms. To address this limitation, we introduce KineMask, an approach for physics-guided video generation that enables realistic rigid body control, interactions, and effects. Given a single image and a specified object velocity, our method generates videos with inferred motions and future object interactions. We propose a two-stage training strategy that gradually removes future motion supervision via object masks. Using this strategy we train video diffusion models (VDMs) on synthetic scenes of simple interactions and demonstrate significant improvements of object interactions in real scenes. Furthermore, KineMask integrates low-level motion control with high-level textual conditioning via predictive scene descriptions, leading to effective support for synthesis of complex dynamical phenomena. Extensive experiments show that KineMask achieves strong improvements over recent models of comparable size. Ablation studies further highlight the complementary roles of low- and high-level conditioning in VDMs. Our code, model, and data will be made publicly available.

David W. Romero, Erik J. Bekkers, Jakub M. Tomczak et al.

Leveraging the symmetries inherent to specific data domains for the construction of equivariant neural networks has lead to remarkable improvements in terms of data efficiency and generalization. However, most existing research focuses on symmetries arising from planar and volumetric data, leaving a crucial data source largely underexplored: time-series. In this work, we fill this gap by leveraging the symmetries inherent to time-series for the construction of equivariant neural network. We identify two core symmetries: *scale and translation*, and construct scale-translation equivariant neural networks for time-series learning. Intriguingly, we find that scale-translation equivariant mappings share strong resemblance with the wavelet transform. Inspired by this resemblance, we term our networks Wavelet Networks, and show that they perform nested non-linear wavelet-like time-frequency transforms. Empirical results show that Wavelet Networks outperform conventional CNNs on raw waveforms, and match strongly engineered spectrogram techniques across several tasks and time-series types, including audio, environmental sounds, and electrical signals. Our code is publicly available at https://github.com/dwromero/wavelet_networks.

Zekun Hao, David W. Romero, Tsung-Yi Lin et al.

Meshes are fundamental representations of 3D surfaces. However, creating high-quality meshes is a labor-intensive task that requires significant time and expertise in 3D modeling. While a delicate object often requires over $10^4$ faces to be accurately modeled, recent attempts at generating artist-like meshes are limited to $1.6$K faces and heavy discretization of vertex coordinates. Hence, scaling both the maximum face count and vertex coordinate resolution is crucial to producing high-quality meshes of realistic, complex 3D objects. We present Meshtron, a novel autoregressive mesh generation model able to generate meshes with up to 64K faces at 1024-level coordinate resolution --over an order of magnitude higher face count and $8{\times}$ higher coordinate resolution than current state-of-the-art methods. Meshtron's scalability is driven by four key components: (1) an hourglass neural architecture, (2) truncated sequence training, (3) sliding window inference, (4) a robust sampling strategy that enforces the order of mesh sequences. This results in over $50{\%}$ less training memory, $2.5{\times}$ faster throughput, and better consistency than existing works. Meshtron generates meshes of detailed, complex 3D objects at unprecedented levels of resolution and fidelity, closely resembling those created by professional artists, and opening the door to more realistic generation of detailed 3D assets for animation, gaming, and virtual environments.

Jerome Ku, Eric Nguyen, David W. Romero et al.

We introduce convolutional multi-hybrid architectures, with a design grounded on two simple observations. First, operators in hybrid models can be tailored to token manipulation tasks such as in-context recall, multi-token recall, and compression, with input-dependent convolutions and attention offering complementary performance. Second, co-designing convolution operators and hardware-aware algorithms enables efficiency gains in regimes where previous alternative architectures struggle to surpass Transformers. At the 40 billion parameter scale, we train end-to-end 1.2 to 2.9 times faster than optimized Transformers, and 1.1 to 1.4 times faster than previous generation hybrids. On H100 GPUs and model width 4096, individual operators in the proposed multi-hybrid StripedHyena 2 architecture achieve two-fold throughput improvement over linear attention and state-space models. Multi-hybrids excel at sequence modeling over byte-tokenized data, as demonstrated by the Evo 2 line of models. We discuss the foundations that enable these results, including architecture design, overlap-add blocked kernels for tensor cores, and dedicated all-to-all and point-to-point context parallelism strategies.

Hermann Kumbong, Xian Liu, Tsung-Yi Lin et al.

Visual Auto-Regressive modeling (VAR) has shown promise in bridging the speed and quality gap between autoregressive image models and diffusion models. VAR reformulates autoregressive modeling by decomposing an image into successive resolution scales. During inference, an image is generated by predicting all the tokens in the next (higher-resolution) scale, conditioned on all tokens in all previous (lower-resolution) scales. However, this formulation suffers from reduced image quality due to the parallel generation of all tokens in a resolution scale; has sequence lengths scaling superlinearly in image resolution; and requires retraining to change the sampling schedule. We introduce Hierarchical Masked Auto-Regressive modeling (HMAR), a new image generation algorithm that alleviates these issues using next-scale prediction and masked prediction to generate high-quality images with fast sampling. HMAR reformulates next-scale prediction as a Markovian process, wherein the prediction of each resolution scale is conditioned only on tokens in its immediate predecessor instead of the tokens in all predecessor resolutions. When predicting a resolution scale, HMAR uses a controllable multi-step masked generation procedure to generate a subset of the tokens in each step. On ImageNet 256x256 and 512x512 benchmarks, HMAR models match or outperform parameter-matched VAR, diffusion, and autoregressive baselines. We develop efficient IO-aware block-sparse attention kernels that allow HMAR to achieve faster training and inference times over VAR by over 2.5x and 1.75x respectively, as well as over 3x lower inference memory footprint. Finally, HMAR yields additional flexibility over VAR; its sampling schedule can be changed without further training, and it can be applied to image editing tasks in a zero-shot manner.

Alonso Urbano, David W. Romero, Max Zimmer et al.

Real world data often exhibits unknown, instance-specific symmetries that rarely exactly match a transformation group $G$ fixed a priori. Class-pose decompositions aim to create disentangled representations by factoring inputs into invariant features and a pose $g\in G$ defined relative to a training-dependent, arbitrary canonical representation. We introduce RECON, a class-pose agnostic $\textit{canonical orientation normalization}$ that corrects arbitrary canonicals via a simple right-multiplication, yielding $\textit{natural}$, data-aligned canonicalizations. This enables (i) unsupervised discovery of instance-specific symmetry distributions, (ii) detection of out-of-distribution poses, and (iii) test-time canonicalization, granting group invariance to pre-trained models without retraining and irrespective of model architecture, improving downstream performance. We demonstrate results on 2D image benchmarks and --for the first time-- extend symmetry discovery to 3D groups.

David M. Knigge, David W. Romero, Erik J. Bekkers

Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular G-CNNs, and show considerable parameter redundancy in group convolution kernels. This finding motivates further weight-tying by sharing convolution kernels over subgroups. To this end, we introduce convolution kernels that are separable over the subgroup and channel dimensions. In order to obtain equivariance to arbitrary affine Lie groups we provide a continuous parameterisation of separable convolution kernels. We evaluate our approach across several vision datasets, and show that our weight sharing leads to improved performance and computational efficiency. In many settings, separable G-CNNs outperform their non-separable counterpart, while only using a fraction of their training time. In addition, thanks to the increase in computational efficiency, we are able to implement G-CNNs equivariant to the $\mathrm{Sim(2)}$ group; the group of dilations, rotations and translations. $\mathrm{Sim(2)}$-equivariance further improves performance on all tasks considered.

David W. Romero, Suhas Lohit

Group Convolutional Neural Networks (G-CNNs) constrain learned features to respect the symmetries in the selected group, and lead to better generalization when these symmetries appear in the data. If this is not the case, however, equivariance leads to overly constrained models and worse performance. Frequently, transformations occurring in data can be better represented by a subset of a group than by a group as a whole, e.g., rotations in $[-90^{\circ}, 90^{\circ}]$. In such cases, a model that respects equivariance $\textit{partially}$ is better suited to represent the data. In addition, relevant transformations may differ for low and high-level features. For instance, full rotation equivariance is useful to describe edge orientations in a face, but partial rotation equivariance is better suited to describe face poses relative to the camera. In other words, the optimal level of equivariance may differ per layer. In this work, we introduce $\textit{Partial G-CNNs}$: G-CNNs able to learn layer-wise levels of partial and full equivariance to discrete, continuous groups and combinations thereof as part of training. Partial G-CNNs retain full equivariance when beneficial, e.g., for rotated MNIST, but adjust it whenever it becomes harmful, e.g., for classification of 6 / 9 digits or natural images. We empirically show that partial G-CNNs pair G-CNNs when full equivariance is advantageous, and outperform them otherwise.

David W. Romero, Robert-Jan Bruintjes, Jakub M. Tomczak et al.

When designing Convolutional Neural Networks (CNNs), one must select the size\break of the convolutional kernels before training. Recent works show CNNs benefit from different kernel sizes at different layers, but exploring all possible combinations is unfeasible in practice. A more efficient approach is to learn the kernel size during training. However, existing works that learn the kernel size have a limited bandwidth. These approaches scale kernels by dilation, and thus the detail they can describe is limited. In this work, we propose FlexConv, a novel convolutional operation with which high bandwidth convolutional kernels of learnable kernel size can be learned at a fixed parameter cost. FlexNets model long-term dependencies without the use of pooling, achieve state-of-the-art performance on several sequential datasets, outperform recent works with learned kernel sizes, and are competitive with much deeper ResNets on image benchmark datasets. Additionally, FlexNets can be deployed at higher resolutions than those seen during training. To avoid aliasing, we propose a novel kernel parameterization with which the frequency of the kernels can be analytically controlled. Our novel kernel parameterization shows higher descriptive power and faster convergence speed than existing parameterizations. This leads to important improvements in classification accuracy.

David W. Romero, Anna Kuzina, Erik J. Bekkers et al.

Conventional neural architectures for sequential data present important limitations. Recurrent networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional networks are unable to handle sequences of unknown size and their memory horizon must be defined a priori. In this work, we show that all these problems can be solved by formulating convolutional kernels in CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) allows us to model arbitrarily long sequences in a parallel manner, within a single operation, and without relying on any form of recurrence. We show that Continuous Kernel Convolutional Networks (CKCNNs) obtain state-of-the-art results in multiple datasets, e.g., permuted MNIST, and, thanks to their continuous nature, are able to handle non-uniformly sampled datasets and irregularly-sampled data natively. CKCNNs match or perform better than neural ODEs designed for these purposes in a faster and simpler manner.

David W. Romero, Jean-Baptiste Cordonnier

We provide a general self-attention formulation to impose group equivariance to arbitrary symmetry groups. This is achieved by defining positional encodings that are invariant to the action of the group considered. Since the group acts on the positional encoding directly, group equivariant self-attention networks (GSA-Nets) are steerable by nature. Our experiments on vision benchmarks demonstrate consistent improvements of GSA-Nets over non-equivariant self-attention networks.

David W. Romero, Erik J. Bekkers, Jakub M. Tomczak et al.

Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we present attentive group equivariant convolutions, a generalization of the group convolution, in which attention is applied during the course of convolution to accentuate meaningful symmetry combinations and suppress non-plausible, misleading ones. We indicate that prior work on visual attention can be described as special cases of our proposed framework and show empirically that our attentive group equivariant convolutional networks consistently outperform conventional group convolutional networks on benchmark image datasets. Simultaneously, we provide interpretability to the learned concepts through the visualization of equivariant attention maps.

David W. Romero, Mark Hoogendoorn

Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never appear (e.g. an upright face with a horizontal nose), current equivariant architectures consider the set of all possible transformations in a transformation group when learning feature representations. Contrarily, the human visual system is able to attend to the set of relevant transformations occurring in the environment and utilizes this information to assist and improve object recognition. Based on this observation, we modify conventional equivariant feature mappings such that they are able to attend to the set of co-occurring transformations in data and generalize this notion to act on groups consisting of multiple symmetries. We show that our proposed co-attentive equivariant neural networks consistently outperform conventional rotation equivariant and rotation & reflection equivariant neural networks on rotated MNIST and CIFAR-10.