Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 30 for “"equivariance"”.
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The Neural Processes Family: Translation Equivariance and Output Dependencies
… applications by i) incorporating translation equivariance into the architecture of neural processes rather than requiring the model to learn this inductive bias directly from data and ii) developing methods for neural processes to parametrize rich predictive distributions that can model …
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Single-Model Any-Subgroup Equivariance via Symmetric Positional Encodings
… of symmetries as an inductive bias, known as “equivariance”, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for pre-chosen symmetries, and cannot be applied to datasets with different …
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Equivariance in Tannakian duality and plectic p-adic Hodge theory
For a gerbe G and a finite constant group S acting on it, we use the Grothendieck construction to define a semidirect product gerbe G ⋊ S. We describe such gerbes in terms of Cech cocycles via the cohomology of crossed modules. We characterise a dual form of the Grothendieck construction and show …
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Extracting and learning structures from data
… agents in the system to achieve permutation equivariance. This representation is particularly suitable in a multi-agent setting where the identity of the agents is unknown. We achieve better performance than conventional fully connected deep nets. Lastly, we present a framework on how to …
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Prospects for Quantum Equivariant Neural Networks
… space. Equivariant neural networks guarantee equivariance for arbitrary groups, reducing the system design complexity. Motivated by the theoretical/experimental development of quantum computing, in particular with the quantum advantage derived from other quantum algorithms/subroutines for …
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Real-time Topology-Aware Augmented Reality
… estimations. Mathematical background on group equivariance, including translation equivariance and permutation equivariance, is also introduced to provide theoretical support for the proposed network; 2) Conducted two use cases to demonstrate the capabilities of the proposed methods in …
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Equivariant symmetry breaking sets
… Our approach is general and applicable to equivariance under any group. To achieve this, we introduce the idea of symmetry breaking sets (SBS). Rather than redesign existing networks to output symmetrically degenerate sets, we design sets of symmetry breaking objects which we feed into our …
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Following manifolds in equivariant evolution equations
… and introduce the freezing system based on equivariance with respect to the diffeomorphism group. Furthermore, phase conditions are created that explicitly use the infinite-dimensional setting. These results are then implemented in numerical algorithms, and the thesis concludes with …
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Quantile regression and the duration of unemployment
… for censored regression models on the basis of equivariance of quantiles to monotone transformations. In this thesis, censored quantile regression models are generalized using two-parameter Box-Cox transformation to relax the conventional linear specification of functional form, and the quantile …
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Efficient fixed-radius near neighbors for machine learning
… a replacement for CNNs with goals of invariance, equivariance, interpretability, and computational efficiency that improve upon the abilities of CNNs. This efficient implementation of FRNN is a critical step in making OODL computationally efficient and practical.
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Equivariant Kolmogorov-Arnold-Moser theory
… paper we investigate the additional property of equivariance with a discrete symmetry group, Γ. The setting then becomes Γ-Equivariant, nearly integrable, Hamiltonian, ODEs. In this setting the Diophantine condition is no longer valid as the symmetry constraints imposed by Γ, generically force …
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Contributions to Robust Methods: Modified Rank Covariance Matrix and Spatial-EM Algorithm
… properties of the estimator on orthogonal equivariance under any distribution and affine equivariance under elliptically symmetric distributions have been established. The major robustness properties of the estimator are studied by the <italic> breakdown point </italic> and <italic> …
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Advances in Probabilistic Meta-Learning and the Neural Process Family
… Next, we study the role of translation equivariance in the NPF. Considering the intimate relationship between the NPF and the representation of functions operating on sets, we extend the underlying theory of DeepSets to include translation equivariance. We then develop novel members of …
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Meta-learning and Enforcing Useful Conservation Laws in Sequential Prediction Problems
… neural networks relying on translation equivariance. Automatically discovering such useful symmetries is a promising path to greatly improving the performance of ML systems, but it still remains a challenge. In this work, we focus on sequential prediction problems in real and simulated …
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Convolutional Conditional Neural Processes
… by building in a symmetry called translation equivariance. ConvNPs rely on convolutional neural networks rather than multi-layer perceptrons. Second, we propose Gaussian neural processes (GNPs). GNPs directly parametrise dependencies in the predictions of a neural process. Current approaches …
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Theoretical Properties of Equivariant Neural Networks
… of the thesis concerns the interaction between equivariance and pointwise nonlinearities. We characterize which pairs of group representations and pointwise activations induce non-trivial equivariant nonlinear maps, thereby identifying when standard layer constructions lead to non-degenerate …
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Structuring Representation Geometry in Self-Supervised Learning
… embedding space. To this end, we introduce an equivariance objective and theoretically prove that its minima forces transformations on input space to correspond to rotations on the spherical embedding space. Our proposed method significantly improves performance on downstream tasks, and ensures …
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Numerical Methods in Deep Learning and Computer Vision
… sequences that allow for novel understandings of equivariance and disentanglement. We expect our investigation could pave the way for more in-depth and impactful research at the intersection of numerical methods and deep learning.
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Approximate Inference in Bayesian Neural Networks and Translation Equivariant Neural Processes
… architecture which incorporates translation equivariance into its predictions. We show that when this symmetry is an appropriate assumption, convolutional neural processes outperform their standard multilayer perceptron-based and attentive counterparts on a variety of regression benchmarks.
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Gini Covariance Matrix and its Affine Equivariant Version
… rank function. In order to gain the affine equivariance property for GCM, we utilize the transformation-retransformation (TR) technique and obtain TR version GCM that turns out to be a symmetrized M-functional. Indeed, both GCMs are symmetrized approaches based on the difference of two …
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