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Found 22 papers, 7 papers with code
Position Paper: Challenges and Opportunities in Topological Deep Learning
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models.
TopoX: A Suite of Python Packages for Machine Learning on Topological Domains
We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes.
Connecting the Dots: Is Mode-Connectedness the Key to Feasible Sample-Based Inference in Bayesian Neural Networks?
A major challenge in sample-based inference (SBI) for Bayesian neural networks is the size and structure of the networks' parameter space.
Position Paper: Bayesian Deep Learning in the Age of Large-Scale AI
In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets.
Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs
In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e. g., to develop a spectral theory.
Model-agnostic variable importance for predictive uncertainty: an entropy-based approach
In particular, by adapting permutation feature importance, partial dependence plots, and individual conditional expectation plots, we demonstrate that novel insights into model behaviour may be obtained and that these methods can be used to measure the impact of features on both the entropy of the predictive distribution and the log-likelihood of the ground truth labels under that distribution.
ICML 2023 Topological Deep Learning Challenge : Design and Results
This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning.
Towards Efficient MCMC Sampling in Bayesian Neural Networks by Exploiting Symmetry
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape.
Approximate blocked Gibbs sampling for Bayesian neural networks
It is also possible to alleviate vanishing acceptance rates for increasing depth by reducing the proposal variance in deeper layers.
Topological Deep Learning: Going Beyond Graph Data
Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations.
Probability-Generating Function Kernels for Spherical Data
Probability-generating function (PGF) kernels are introduced, which constitute a class of kernels supported on the unit hypersphere, for the purposes of spherical data analysis.
A Random Persistence Diagram Generator
Topological data analysis (TDA) studies the shape patterns of data.
Simplicial Complex Representation Learning
In this work, we propose a method for simplicial complex-level representation learning that embeds a simplicial complex to a universal embedding space in a way that complex-to-complex proximity is preserved.
Hidden Markov models are recurrent neural networks: A disease progression modeling application
To allow for this, we formulate a special case of recurrent neural networks (RNNs), which we name hidden Markov recurrent neural networks (HMRNNs), and prove that each HMRNN has the same likelihood function as a corresponding discrete-observation HMM.
Bayesian neural networks and dimensionality reduction
We attempt to solve these problems by deploying Markov chain Monte Carlo sampling algorithms (MCMC) for Bayesian inference in ANN models with latent variables.
Hidden Markov models as recurrent neural networks: an application to Alzheimer's disease
Hidden Markov models (HMMs) are commonly used for disease progression modeling when the true patient health state is not fully known.
Depth-2 Neural Networks Under a Data-Poisoning Attack
In this class of networks, we attempt to learn the network weights in the presence of a malicious oracle doing stochastic, bounded and additive adversarial distortions on the true output during training.
Automated detection of corrosion in used nuclear fuel dry storage canisters using residual neural networks
The results demonstrate that such a deep learning approach allows to detect the locus of corrosion via smaller tiles, and at the same time to infer with high accuracy whether an image comes from a corroded canister.
Wide Neural Networks with Bottlenecks are Deep Gaussian Processes
There has recently been much work on the "wide limit" of neural networks, where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process (GP) as all hidden layers are sent to infinite width.
Challenges in Markov chain Monte Carlo for Bayesian neural networks
Nevertheless, this paper shows that a non-converged Markov chain, generated via MCMC sampling from the parameter space of a neural network, can yield via Bayesian marginalization a valuable posterior predictive distribution of the output of the neural network.
Geometric adaptive Monte Carlo in random environment
This paper analyzes the computational complexity of manifold Langevin Monte Carlo and proposes a geometric adaptive Monte Carlo sampler aimed at balancing the benefits of exploiting local geometry with computational cost to achieve a high effective sample size for a given computational cost.
Forward-Mode Automatic Differentiation in Julia
We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++.
Mathematical Software
