Related papers: Learning Functions on Multiple Sets using Multi-Se…
Learning functions on point clouds has applications in many fields, including computer vision, computer graphics, physics, and chemistry. Recently, there has been a growing interest in neural architectures that are invariant or equivariant…
This study compares various superlearner and deep learning architectures (machine-learning-based and neural-network-based) for classification problems across several simulated and industrial datasets to assess performance and computational…
Despite the widespread adoption of Transformer models for NLP tasks, the expressive power of these models is not well-understood. In this paper, we establish that Transformer models are universal approximators of continuous permutation…
Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine…
Existing deep methods produce highly accurate 3D reconstructions in stereo and multiview stereo settings, i.e., when cameras are both internally and externally calibrated. Nevertheless, the challenge of simultaneous recovery of camera poses…
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus…
In this paper, we develop a theory about the relationship between $G$-invariant/equivariant functions and deep neural networks for finite group $G$. Especially, for a given $G$-invariant/equivariant function, we construct its universal…
Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…
Permutation-invariant, -equivariant, and -covariant functions and anti-symmetric functions are important in quantum physics, computer vision, and other disciplines. Applications often require most or all of the following properties: (a) a…
We propose a permutation-invariant neural architecture for indoor localization using RSSI scans from Wi-Fi access points. Each scan is modeled as an unordered set of (BSSID, RSSI) pairs, where BSSIDs are mapped to learned embeddings and…
Recent work has proven that training large language models with self-supervised tasks and fine-tuning these models to complete new tasks in a transfer learning setting is a powerful idea, enabling the creation of models with many…
We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…
Most set prediction models in deep learning use set-equivariant operations, but they actually operate on multisets. We show that set-equivariant functions cannot represent certain functions on multisets, so we introduce the more appropriate…
Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…
We study the approximation of shift-invariant or equivariant functions by deep fully convolutional networks from the dynamical systems perspective. We prove that deep residual fully convolutional networks and their continuous-layer…
Deep neural networks have been widely used as universal approximators for functions with inherent physical structures, including permutation symmetry. In this paper, we construct symmetric deep neural networks to approximate symmetric…
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be…
Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often…
With the emergence of deep learning, metric learning has gained significant popularity in numerous machine learning tasks dealing with complex and large-scale datasets, such as information retrieval, object recognition and recommendation…
Precise load forecasting in buildings could increase the bill savings potential and facilitate optimized strategies for power generation planning. With the rapid evolution of computer science, data-driven techniques, in particular the Deep…