Toward an Over-parameterized Direct-Fit Model of Visual Perception

• URL: http://arxiv.org/abs/2210.03850v2
• Date: Tue, 11 Oct 2022 15:37:43 GMT
• Title: Toward an Over-parameterized Direct-Fit Model of Visual Perception
• Authors: Xin Li
• Abstract summary: In this paper, we highlight the difference in parallel and sequential binding mechanisms between simple and complex cells. A new proposal for abstracting them into space partitioning and composition is developed. We show how it leads to a dynamic programming (DP)-like approximate nearest-neighbor search based on $ell_infty$-optimization.
• Score: 5.4823225815317125
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: In this paper, we revisit the problem of computational modeling of simple and complex cells for an over-parameterized and direct-fit model of visual perception. Unlike conventional wisdom, we highlight the difference in parallel and sequential binding mechanisms between simple and complex cells. A new proposal for abstracting them into space partitioning and composition is developed as the foundation of our new hierarchical construction. Our construction can be interpreted as a product topology-based generalization of the existing k-d tree, making it suitable for brute-force direct-fit in a high-dimensional space. The constructed model has been applied to several classical experiments in neuroscience and psychology. We provide an anti-sparse coding interpretation of the constructed vision model and show how it leads to a dynamic programming (DP)-like approximate nearest-neighbor search based on $\ell_{\infty}$-optimization. We also briefly discuss two possible implementations based on asymmetrical (decoder matters more) auto-encoder and spiking neural networks (SNN), respectively.

Related papers

• Topological Deep Learning with State-Space Models: A Mamba Approach for Simplicial Complexes [4.787059527893628]
  We propose a novel architecture designed to operate with simplicial complexes, utilizing the Mamba state-space model as its backbone. Our approach generates sequences for the nodes based on the neighboring cells, enabling direct communication between all higher-order structures, regardless of their rank.
  arXiv  Detail & Related papers  (2024-09-18T14:49:25Z)
• Learnable & Interpretable Model Combination in Dynamic Systems Modeling [0.0]
  We discuss which types of models are usually combined and propose a model interface that is capable of expressing a variety of mixed equation based models. We propose a new wildcard topology, that is capable of describing the generic connection between two combined models in an easy to interpret fashion. The contributions of this paper are highlighted at a proof of concept: Different connection topologies between two models are learned, interpreted and compared.
  arXiv  Detail & Related papers  (2024-06-12T11:17:11Z)
• DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion [66.21290235237808]
  We introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks.
  arXiv  Detail & Related papers  (2023-01-23T15:18:54Z)
• Low-Rank Constraints for Fast Inference in Structured Models [110.38427965904266]
  This work demonstrates a simple approach to reduce the computational and memory complexity of a large class of structured models. Experiments with neural parameterized structured models for language modeling, polyphonic music modeling, unsupervised grammar induction, and video modeling show that our approach matches the accuracy of standard models at large state spaces.
  arXiv  Detail & Related papers  (2022-01-08T00:47:50Z)
• Dist2Cycle: A Simplicial Neural Network for Homology Localization [66.15805004725809]
  Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations. We propose a graph convolutional model for learning functions parametrized by the $k$-homological features of simplicial complexes.
  arXiv  Detail & Related papers  (2021-10-28T14:59:41Z)
• Redefining Neural Architecture Search of Heterogeneous Multi-Network Models by Characterizing Variation Operators and Model Components [71.03032589756434]
  We investigate the effect of different variation operators in a complex domain, that of multi-network heterogeneous neural models. We characterize both the variation operators, according to their effect on the complexity and performance of the model; and the models, relying on diverse metrics which estimate the quality of the different parts composing it.
  arXiv  Detail & Related papers  (2021-06-16T17:12:26Z)
• Structured Reordering for Modeling Latent Alignments in Sequence Transduction [86.94309120789396]
  We present an efficient dynamic programming algorithm performing exact marginal inference of separable permutations. The resulting seq2seq model exhibits better systematic generalization than standard models on synthetic problems and NLP tasks.
  arXiv  Detail & Related papers  (2021-06-06T21:53:54Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• Generalising Recursive Neural Models by Tensor Decomposition [12.069862650316262]
  We introduce a general approach to model aggregation of structural context leveraging a tensor-based formulation. We show how the exponential growth in the size of the parameter space can be controlled through an approximation based on the Tucker decomposition. By this means, we can effectively regulate the trade-off between expressivity of the encoding, controlled by the hidden size, computational complexity and model generalisation.
  arXiv  Detail & Related papers  (2020-06-17T17:28:19Z)
• Collegial Ensembles [11.64359837358763]
  We show that collegial ensembles can be efficiently implemented in practical architectures using group convolutions and block diagonal layers. We also show how our framework can be used to analytically derive optimal group convolution modules without having to train a single model.
  arXiv  Detail & Related papers  (2020-06-13T16:40:26Z)
• Segmentation and Recovery of Superquadric Models using Convolutional Neural Networks [2.454342521577328]
  We present a (two-stage) approach built around convolutional neural networks (CNNs) In the first stage, our approach uses a Mask RCNN model to identify superquadric-like structures in depth scenes. We are able to describe complex structures with a small number of interpretable parameters.
  arXiv  Detail & Related papers  (2020-01-28T18:17:48Z)

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.