Linear Mapping

Linear mapping, the transformation of data using linear functions, is a fundamental operation in numerous fields, with current research focusing on its application and limitations within complex systems. Studies explore the effectiveness of linear mappings compared to deep learning architectures in tasks like language modeling and Bayesian inference, revealing scenarios where simpler linear methods surprisingly outperform more complex alternatives, particularly when computational efficiency or incremental learning is crucial. This research highlights the ongoing interplay between linear and non-linear methods, impacting diverse areas from cognitive science and biological modeling to neural network optimization and efficient model compression.

Papers

October 28, 2024

Learning State Conditioned Linear Mappings for Low-Dimensional Control of Robotic Manipulators
Michael Przystupa, Kerrick Johnstonbaugh, Zichen Zhang, Laura Petrich, Masood Dehghan, Faezeh Haghverd, Martin Jagersand
High Dimensional Action Space State Space Robotic Manipulator Action Representation Action Mapping Linear Mapping

October 5, 2024

Is deeper always better? Replacing linear mappings with deep learning networks in the Discriminative Lexicon Model
Maria Heitmeier, Valeria Schmidt, Hendrik P.A. Lensch, R. Harald Baayen
Deep Learning Model Discriminant Analysis Deep Learning Network Discriminative Deep Linear Mapping

March 12, 2024

Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings
Henrik Häggström, Pedro L. C. Rodrigues, Geoffroy Oudoumanessah, Florence Forbes, Umberto Picchini
Bayesian Inference RSD Difference of Gaussian Posterior Inference Posterior Sampling Simulation Based Inference Intractable Likelihood Sequential Inference Linear Mapping

December 20, 2023

A Minimal Control Family of Dynamical Syetem for Universal Approximation
Yifei Duan, Yongqiang Cai
Dynamical System Optimal Control Universal Approximation Approximation Power Nonlinear Function Linear Mapping

November 26, 2023

Frobenius-Type Norms and Inner Products of Matrices and Linear Maps with Applications to Neural Network Training
Roland Herzog, Frederik Köhne, Leonie Kreis, Anton Schiela
Neural Network External Keyword Matrix Inner Product Linear Mapping Frobenius Norm

August 15, 2023

Ternary Singular Value Decomposition as a Better Parameterized Form in Linear Mapping
Boyu Chen, Hanxuan Chen, Jiao He, Fengyu Sun, Shangling Jui
Parameter Efficient Singular Value Decomposition Ternary Quantization Linear Mapping

May 20, 2023

Vocabulary for Universal Approximation: A Linguistic Perspective of Mapping Compositions
Yongqiang Cai
Language Model Universal Approximation Compositional Model Enhanced Vocabulary Deep Sequence Linguistic Perspective Linear Mapping

May 18, 2023

Revisiting Long-term Time Series Forecasting: An Investigation on Linear Mapping
Zhe Li, Shiyi Qi, Yiduo Li, Zenglin Xu
Time Series Comprehensive Investigation Forecasting Performance Long Term Time Series Forecasting Forecasting Competition Linear Mapping

February 28, 2023

Linear Spaces of Meanings: Compositional Structures in Vision-Language Models
Matthew Trager, Pramuditha Perera, Luca Zancato, Alessandro Achille, Parminder Bhatia, Stefano Soatto
Vision Language Model Jina Embeddings Pre Trained Vision Language Model Multiple Meaning Compositional Structure Linear Mapping

September 30, 2022

Linearly Mapping from Image to Text Space
Jack Merullo, Louis Castricato, Carsten Eickhoff, Ellie Pavlick
Language Model Vision Language Benchmark Conceptual Representation Linear Mapping Text Only Language Model

Linear Mapping

Papers

Learning State Conditioned Linear Mappings for Low-Dimensional Control of Robotic Manipulators

Is deeper always better? Replacing linear mappings with deep learning networks in the Discriminative Lexicon Model

Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings

A Minimal Control Family of Dynamical Syetem for Universal Approximation

Frobenius-Type Norms and Inner Products of Matrices and Linear Maps with Applications to Neural Network Training

Ternary Singular Value Decomposition as a Better Parameterized Form in Linear Mapping

Vocabulary for Universal Approximation: A Linguistic Perspective of Mapping Compositions

Revisiting Long-term Time Series Forecasting: An Investigation on Linear Mapping

Linear Spaces of Meanings: Compositional Structures in Vision-Language Models

Linearly Mapping from Image to Text Space