Homological Convolutional Neural Networks

• URL: http://arxiv.org/abs/2308.13816v2
• Date: Tue, 14 Nov 2023 09:26:45 GMT
• Title: Homological Convolutional Neural Networks
• Authors: Antonio Briola, Yuanrong Wang, Silvia Bartolucci, Tomaso Aste
• Abstract summary: We propose a novel deep learning architecture that exploits the data structural organization through topologically constrained network representations. We test our model on 18 benchmark datasets against 5 classic machine learning and 3 deep learning models.
• Score: 4.615338063719135
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine learning approaches being often computationally cheaper and equally effective than increasingly complex deep learning architectures. The challenge arises from the fact that, in tabular data, the correlation among features is weaker than the one from spatial or semantic relationships in images or natural language, and the dependency structures need to be modeled without any prior information. In this work, we propose a novel deep learning architecture that exploits the data structural organization through topologically constrained network representations to gain relational information from sparse tabular inputs. The resulting model leverages the power of convolution and is centered on a limited number of concepts from network topology to guarantee: (i) a data-centric and deterministic building pipeline; (ii) a high level of interpretability over the inference process; and (iii) an adequate room for scalability. We test our model on 18 benchmark datasets against 5 classic machine learning and 3 deep learning models, demonstrating that our approach reaches state-of-the-art performances on these challenging datasets. The code to reproduce all our experiments is provided at https://github.com/FinancialComputingUCL/HomologicalCNN.

Related papers

• Escaping the Forest: Sparse Interpretable Neural Networks for Tabular Data [0.0]
  We show that our models, Sparse TABular NET or sTAB-Net with attention mechanisms, are more effective than tree-based models. They achieve better performance than post-hoc methods like SHAP.
  arXiv  Detail & Related papers  (2024-10-23T10:50:07Z)
• How Deep Networks Learn Sparse and Hierarchical Data: the Sparse Random Hierarchy Model [4.215221129670858]
  We show that by introducing sparsity to generative hierarchical models of data, the task acquires insensitivity to spatial transformations that are discrete versions of smooth transformations. We quantify how the sample complexity of CNNs learning the SRHM depends on both the sparsity and hierarchical structure of the task.
  arXiv  Detail & Related papers  (2024-04-16T17:01:27Z)
• On Characterizing the Evolution of Embedding Space of Neural Networks using Algebraic Topology [9.537910170141467]
  We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. We demonstrate that as depth increases, a topologically complicated dataset is transformed into a simple one, resulting in Betti numbers attaining their lowest possible value.
  arXiv  Detail & Related papers  (2023-11-08T10:45:12Z)
• Breaking the Curse of Dimensionality in Deep Neural Networks by Learning Invariant Representations [1.9580473532948401]
  This thesis explores the theoretical foundations of deep learning by studying the relationship between the architecture of these models and the inherent structures found within the data they process. We ask What drives the efficacy of deep learning algorithms and allows them to beat the so-called curse of dimensionality. Our methodology takes an empirical approach to deep learning, combining experimental studies with physics-inspired toy models.
  arXiv  Detail & Related papers  (2023-10-24T19:50:41Z)
• Homological Neural Networks: A Sparse Architecture for Multivariate Complexity [0.0]
  We develop a novel deep neural network unit characterized by a sparse higher-order graphical architecture built over the homological structure of underlying data. Results demonstrate the advantages of this novel design which can tie or overcome the results of state-of-the-art machine learning and deep learning models using only a fraction of parameters.
  arXiv  Detail & Related papers  (2023-06-27T09:46:16Z)
• Towards Robust Dataset Learning [90.2590325441068]
  We propose a principled, tri-level optimization to formulate the robust dataset learning problem. Under an abstraction model that characterizes robust vs. non-robust features, the proposed method provably learns a robust dataset.
  arXiv  Detail & Related papers  (2022-11-19T17:06:10Z)
• Dynamic Latent Separation for Deep Learning [67.62190501599176]
  A core problem in machine learning is to learn expressive latent variables for model prediction on complex data. Here, we develop an approach that improves expressiveness, provides partial interpretation, and is not restricted to specific applications.
  arXiv  Detail & Related papers  (2022-10-07T17:56:53Z)
• Amortized Inference for Causal Structure Learning [72.84105256353801]
  Learning causal structure poses a search problem that typically involves evaluating structures using a score or independence test. We train a variational inference model to predict the causal structure from observational/interventional data. Our models exhibit robust generalization capabilities under substantial distribution shift.
  arXiv  Detail & Related papers  (2022-05-25T17:37:08Z)
• Rethinking Architecture Design for Tackling Data Heterogeneity in Federated Learning [53.73083199055093]
  We show that attention-based architectures (e.g., Transformers) are fairly robust to distribution shifts. Our experiments show that replacing convolutional networks with Transformers can greatly reduce catastrophic forgetting of previous devices.
  arXiv  Detail & Related papers  (2021-06-10T21:04:18Z)
• Model-Based Deep Learning [155.063817656602]
  Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Deep neural networks (DNNs) use generic architectures which learn to operate from data, and demonstrate excellent performance. We are interested in hybrid techniques that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches.
  arXiv  Detail & Related papers  (2020-12-15T16:29:49Z)
• Relation-Guided Representation Learning [53.60351496449232]
  We propose a new representation learning method that explicitly models and leverages sample relations. Our framework well preserves the relations between samples. By seeking to embed samples into subspace, we show that our method can address the large-scale and out-of-sample problem.
  arXiv  Detail & Related papers  (2020-07-11T10:57:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.