# Inference in Deep Networks in High Dimensions

@article{Fletcher2018InferenceID, title={Inference in Deep Networks in High Dimensions}, author={Alyson K. Fletcher and Sundeep Rangan}, journal={2018 IEEE International Symposium on Information Theory (ISIT)}, year={2018}, pages={1884-1888} }

Deep generative networks provide a powerful tool for modeling complex data in a wide range of applications. In inverse problems that use these networks as generative priors on data, one must often perform inference of the inputs of the networks from the outputs. Inference is also required for sampling during stochastic training of these generative models. This paper considers inference in a deep stochastic neural network where the parameters (e.g., weights, biases and activation functions) are…

## 57 Citations

### Inference With Deep Generative Priors in High Dimensions

- Computer ScienceIEEE Journal on Selected Areas in Information Theory
- 2020

This paper shows that the performance of ML-VAMP can be exactly predicted in a certain high-dimensional random limit, and provides a computationally efficient method for multi-layer inference with an exact performance characterization and testable conditions for optimality in the large-system limit.

### Asymptotics of MAP Inference in Deep Networks

- Computer Science2019 IEEE International Symposium on Information Theory (ISIT)
- 2019

This work considers a recently-developed method, multilayer vector approximate message passing (ML-VAMP), to study MAP inference in deep networks and shows that the mean squared error of the ML- VAMP estimate can be exactly and rigorously characterized in a certain high-dimensional random limit.

### Inference in Multi-Layer Networks with Matrix-Valued Unknowns

- Computer ScienceArXiv
- 2020

A unified approximation algorithm for both MAP and MMSE inference is proposed by extending a recently-developed Multi-Layer Vector Approximate Message Passing (ML-VAMP) algorithm to handle matrix-valued unknowns.

### Matrix inference and estimation in multi-layer models

- Computer ScienceNeurIPS
- 2020

It is shown that the performance of the proposed multi-layer matrix vector approximate message passing algorithm can be exactly predicted in a certain random large-system limit, where the dimensions N × d of the unknown quantities grow as N → ∞ with d fixed.

### Additivity of information in multilayer networks via additive Gaussian noise transforms

- Computer Science2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2017

This paper provides a new method for analyzing the fundamental limits of statistical inference in settings where the model is known and has close connections to free probability theory for random matrices.

### Entropy and mutual information in models of deep neural networks

- Computer ScienceNeurIPS
- 2018

It is concluded that, in the proposed setting, the relationship between compression and generalization remains elusive and an experiment framework with generative models of synthetic datasets is proposed, on which deep neural networks are trained with a weight constraint designed so that the assumption in (i) is verified during learning.

### Generalization Error of Generalized Linear Models in High Dimensions

- Computer ScienceICML
- 2020

This work provides a general framework to characterize the asymptotic generalization error for single-layer neural networks (i.e., generalized linear models) with arbitrary non-linearities, making it applicable to regression as well as classification problems.

### Mean-field inference methods for neural networks

- Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2020

A selection of classical mean-field methods and recent progress relevant for inference in neural networks are reviewed, and the principles of derivations of high-temperature expansions, the replica method and message passing algorithms are reminded, highlighting their equivalences and complementarities.

### Inverting Deep Generative models, One layer at a time

- Computer ScienceNeurIPS
- 2019

This paper shows that for the realizable case, single layer inversion can be performed exactly in polynomial time, by solving a linear program, and provides provable error bounds for different norms for reconstructing noisy observations.

### The Spiked Matrix Model With Generative Priors

- Computer ScienceIEEE Transactions on Information Theory
- 2021

A rigorous expression for the performance of the Bayes-optimal estimator in the high-dimensional regime is established, and the statistical threshold for weak-recovery of the spike is identified, and it is shown that linearising the message passing algorithm yields a simple spectral method also achieving the optimal threshold for reconstruction.

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