This paper shows how to train only the implicit layer of overparameterized implicit neural networks.
problem Understanding how the implicit layer contributes to the training of overparameterized implicit neural networks.
method Restricting training to only the implicit layer and analyzing the generalization error for ReLU-activated networks.
result Global convergence is guaranteed even if only the implicit layer is trained, and gradient flow with proper random initialization can achieve small generalization errors.
Paper studies the theoretical equivalence between implicit and explicit neural networks in high dimensions.
problem Lack of theoretical analysis of implicit and explicit neural networks.
method Examined high-dimensional implicit neural networks and established their equivalence to explicit networks.
result Equivalence between implicit and explicit neural networks in high dimensions.
Gradient matching method estimates implicit regularization in complex deep learning systems.
problem Estimating implicit regularization in modern deep learning systems with complex modifications.
method Gradient matching methods to empirically estimate implicit regularization.
result Empirical estimation of implicit regularization in arbitrary networks, including dropout.
Continuous semi-implicit models enable faster training and better performance in generative modeling.
problem Slow convergence in hierarchical semi-implicit models during training.
method CoSIM, a continuous semi-implicit model that incorporates a continuous transition kernel for efficient training.
result CoSIM achieves superior performance on image generation tasks compared to existing methods.
Gradient descent converges to a global minimum in nonlinear ReLU implicit networks with linear width.
problem Understanding convergence of gradient methods in nonlinear, infinitely deep ReLU networks.
method Introduced a scaling constant to ensure well-posedness of the equilibrium equation, proving convergence to a global minimum for linear width networks.
result Gradient descent converges to a global minimum at a linear rate for nonlinear ReLU implicit networks with linear width.
Study finds implicit government guarantee improves municipal investment bond ratings.
problem Questioning the objectivity of municipal investment bond ratings due to implicit government guarantee.
method Text mining of policy documents and PMC index model for implicit guarantee strength calculation.
result Implicit government guarantee boosts municipal investment bond ratings, especially in less developed regions.
Study shows SGD's generalization is not explained by implicit bias.
problem Explaining the generalization ability of overparameterized learning algorithms.
method Revisited Stochastic Convex Optimization with SGD, demonstrating limitations of implicit bias.
result No distribution-independent or distribution-dependent implicit regularizer can explain SGD's generalization.
This paper measures the intensity of implicit government guarantees using PMC index model.
problem Excessive local government debt due to implicit government guarantees.
method Text mining of policy documents related to municipal investment bonds, PMC index model.
result Recent policies have reduced the intensity of implicit government guarantees.
The paper explains implicit regularization in hierarchical tensor factorization and deep CNNs.
problem Understanding implicit regularization in complex neural network architectures.
method Theoretical analysis using dynamical systems to overcome challenges in hierarchy.
result Established implicit regularization towards low hierarchical tensor rank, equivalent to locality in CNNs.
In this paper, we describe the "implicit autoencoder" (IAE), a generative autoencoder in which both the generative path and the recognition path are parametrized by implicit distributions. We use two generative adversarial networks to define the reconstruction and the regularization cost functions of the implicit autoe…
Implicit discourse relation classification is of great challenge due to the lack of connectives as strong linguistic cues, which motivates the use of annotated implicit connectives to improve the recognition. We propose a feature imitation framework in which an implicit relation network is driven to learn from another …
Deep tensor factorization benefits from implicit regularization with polynomial growth.
problem Tensor factorization's implicit regularization effect in deep networks is not well understood.
method Investigated the implicit regularization in deep tensor factorization, showing polynomial growth.
result Implicit regularization in deep tensor factorization grows polynomially with depth, improving estimation accuracy and convergence.
Gradient descent on ReLU networks with square loss implicitly favors balanced weights.
problem Understanding implicit regularization in nonlinear neural networks with regression losses.
method Analyzing gradient descent dynamics on ReLU networks with square loss.
result It is impossible to characterize the implicit regularization of ReLU networks with square loss by any explicit function of model parameters.
New insights into how deep models generalize, focusing on matrix factorization.
problem Understanding how deep models generalize and why they work well.
method Using Morse functions and dynamical systems to study implicit regularization.
result Solved a conjecture on implicit regularization in matrix factorization.
We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference …
Deep equilibrium models converge globally without explicit computation.
problem Global convergence of deep learning models with implicit layers.
method Analysis of gradient dynamics and proof of convergence rate.
result Deep equilibrium models converge to global optimum at a linear rate.
Sayer uses implicit feedback to optimize system policies.
problem Leveraging implicit feedback to improve system policies is difficult due to bias and incompleteness.
method Sayer combines randomized exploration and unbiased counterfactual estimators to evaluate and train new policies using implicit feedback.
result Sayer can accurately evaluate and train new policies that outperform existing ones.
Proposes efficient, modular method for implicit differentiation.
problem Implicit differentiation of optimization problems.
method Automatic implicit differentiation using autodiff and implicit function theorem.
result Automatic differentiation of optimization problems is made easier and more modular.
This paper analyzes implicit bias in Deep Linear Discriminant Analysis.
problem The implicit bias of Deep Linear Discriminant Analysis.
method Analyzing gradient flow on a L-layer diagonal linear network.
result Under balanced initialization, the network transforms additive updates into multiplicative updates, conserving the (2/L) quasi-norm.
The paper analyzes implicit regularization in tensor factorization using neural networks.
problem Understanding implicit regularization in tensor factorization.
method Dynamical systems perspective and gradient descent analysis.
result Gradient descent induces a form of greedy low tensor rank search.
This paper proves SGD converges to global minimum for over-parameterized ReLU networks.
problem Theoretical understanding of implicit neural networks is limited.
method Gradient flow analysis of ReLU activated implicit neural networks.
result Randomly initialized gradient descent converges to global minimum at a linear rate for square loss function in over-parameterized ReLU networks.
Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational posterior. However, existing methods on implicit posteriors still face challenges of…
Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of implicit models remains limited due to challenges in specifying complex latent stru…
IDAC improves reinforcement learning efficiency by modeling implicit distributions.
problem Improving sample efficiency in reinforcement learning algorithms.
method IDAC uses two DGNs for a distributional critic and a semi-implicit actor to model implicit policy distributions.
result IDAC outperforms state-of-the-art algorithms on OpenAI Gym environments.
Global implicit function theorem for Fréchet spaces, solving derivative loss problems.
problem Solving initial value problems with derivative loss in Fréchet spaces.
method Global implicit function theorems for Keller's Cc1-mappings in Fréchet spaces, applied through submersions and transversality. result Global existence and uniqueness of solutions to initial value problems with derivative loss.
Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit regularization of gradient descent over deep linear neural networks for matrix completion …
New proof shows norms can't explain deep learning's implicit regularization.
problem Understanding the implicit regularization in deep learning.
method Mathematical proof on matrix factorization problems.
result Implicit regularization drives norms towards infinity, suggesting rank minimization is key.
We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological vector spaces to Banach spaces.
The study provides a generalization bound for a family of implicit networks.
problem Theoretical understanding of implicit networks' generalization is limited.
method A generalization bound is derived for a family of implicit networks using a covering number argument for Rademacher complexity.
result A theoretical generalization bound is established for implicit networks.
The paper classifies deformations of curves with inflections and vertices.
problem Deforming implicit curves with inflections and vertices.
method Classification of deformations for curves with 2 parameters.
result Generically, inflections and vertices emerge from singularities during deformations.
The study analyzes implicit biases in neural networks using backward error analysis.
problem Analyzing implicit biases in multitask and continual learning settings.
method Backward error analysis to compute implicit training biases, deriving modified losses with three terms.
result The conflict term, measuring gradient alignment, is a new quantity in continual learning.
Semi-Implicit Variational Inference (SIVI) is improved with SIVI-SM using score matching.
problem Intractable densities in variational distributions hinder SIVI training.
method SIVI-SM uses score matching to handle intractable densities in a minimax formulation.
result SIVI-SM outperforms ELBO-based SIVI methods in Bayesian inference tasks.
Improved MUSE boosts performance and reduces error in Bayesian inference.
problem Hierarchical Bayesian inference problems
method Implicit differentiation applied to MUSE algorithm
result Significant speedup and improved accuracy compared to Hamiltonian Monte Carlo
Novel approach finds implicit regularisation in two-player games using BEA.
problem Understanding implicit regularisation in two-player games.
method Using backward error analysis to construct continuous-time flows with gradient-eligible vector fields.
result Identifies new implicit regularisation effects in two-player games.
SINDy-PI robustly identifies implicit dynamics from noisy data.
problem Accurately modeling nonlinear dynamics from noisy data.
method Parallel, implicit SINDy algorithm with multiple optimization algorithms and model selection.
result Significantly more noise robust than previous SINDy approaches.
In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can be obtained from the Hamilton-Pontryagin principle, by making use of an anholonom…
New TD method stabilizes average-reward learning.
problem Stability issues in average-reward TD learning.
method Implicit fixed point update for average-reward TD(λ). result Improved numerical stability and broader step-size range.
New algorithm expands FTRL framework with improved worst-case regret bounds.
problem Online learning with improved worst-case regret bounds.
method Generalized implicit Follow-The-Regularized-Leader (FTRL) algorithm.
result Unified framework for designing updates improving worst-case regret bounds.
Survey on why deep learning works despite having more parameters than data.
problem Understanding why deep learning algorithms generalize well despite having more parameters than training data.
method Explains the concept of implicit bias and reviews recent research findings.
result Implicit bias is a key factor in deep learning's ability to generalize.
New insights into network generalization show learning rate affects both norm and sharpness.
problem Understanding the generalization of overparameterized networks.
method Empirical analysis and theoretical proof of the trade-off between norm and sharpness.
result Learning rate influences both norm and sharpness, neither alone minimizes generalization error.
For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the well known singularities of generic vector fields on the plane and the singularit…
Novel framework optimizes experiments for implicit models using mutual information.
problem Optimizing experiments for intractable implicit models.
method Sequential Bayesian Experimental Design using Mutual Information.
result Framework efficiently estimates parameters with few iterations.
New method learns robot skills from data, matching or outperforming existing methods.
problem Learning robot skills from fixed datasets.
method Offline Reinforcement Learning via Supervised Learning using implicit models.
result Implicit models can match or outperform explicit models in acquiring robotic skills.
Kernel semi-implicit variational inference improves variational inference without additional optimization.
problem Intractability of hierarchical semi-implicit distributions in variational inference.
method Kernel semi-implicit variational inference (KSIVI) using kernel methods to eliminate lower-level optimization.
result KSIVI reduces variational inference to kernel Stein discrepancy (KSD) optimization, improving expressiveness and tractability.
New framework improves robustness of implicit neural networks.
problem Ill-posedness and convergence instability in implicit neural networks.
method NEMON framework based on contraction theory for ℓ∞ norm, including well-posedness condition, average iteration, and input-output Lipschitz constant regularization. result Improved accuracy and robustness of implicit models with smaller input-output Lipschitz bounds.
Improves BED scalability for implicit models.
problem Designing experiments for implicit models with intractable data distributions.
method Hybrid gradient approach combining variational MI estimator, ES, and SGA.
result Significantly improves scalability of BED for implicit models.
SIS-RNN improves model flexibility for sequential data.
problem Limited expressive power of existing stochastic RNNs.
method Semi-implicit variational inference for implicit latent representations.
result SIS-RNN outperforms existing methods in various tasks.
New method for high-fidelity shape representations from raw data.
problem Creating accurate shape representations from raw data.
method A simple loss function encouraging neural network to vanish on input point cloud and have unit norm gradient.
result Our method produces high-fidelity, smooth, and natural zero level set surfaces.