Implicit models can match or exceed explicit models with more test-time compute.
problem Understanding the expressive power and scaling of implicit models.
method Nonparametric analysis of expressive power, mathematical characterization of implicit operators, and test-time scaling experiments.
result Implicit models can progressively express more complex mappings through iteration, matching a richer function class with test-time compute.
Gradient descent promotes low-rank solutions in tensor completion.
problem Implicit regularization in tensor factorization using gradient descent.
method Introduced deep Tucker and TensorTrain (TT) unconstrained factorization to address tensor completion.
result Gradient descent promotes solutions with low-rank.
Bayesian model predicts mental health symptoms from IAT data, improving accuracy over D-score.
problem Limited predictive performance of D-score method for mental health assessment.
method Sparse hierarchical Bayesian model leveraging multi-modal data.
result AUCs of 0.73 (E-IAT) and 0.76 (PSY-IAT) in best modality configurations, significant after FDR correction.
New model leads to optimal test loss in sparse linear regression.
problem Sparse linear regression with low test loss despite interpolating training data.
method Developed a new parametrization of the model that combines benefits of ℓ1 and ℓ2 norms.
result Training via gradient descent leads to an interpolator with near-optimal test loss.
Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base measure, and are learned end-to-end using stochastic optimization. One strategy…
SGD with large learning rates can achieve better test accuracy than expected.
problem SGD with large learning rates often outperforms expected convergence bounds.
method Proved that SGD with small learning rates stays close to gradient flow path on modified loss.
result Explicitly adding an implicit regularizer to the loss improves test accuracy.
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.
The paper challenges the belief that more inner iterations at test time improve performance in implicit deep learning.
problem The performance improvement of implicit deep learning models with increased inner iterations at test time.
method Theoretical analysis of a simple setting, validation on implicit deep learning problems.
result Overparametrization plays a key role; increasing the number of iterations at test time does not improve performance for overparametrized networks.
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…
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
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.
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.
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that those objects can be naturally associated to systems with constraints -- we recall…
Gradient descent implicitly regularizes neural networks by penalizing large loss gradients.
problem How to optimize deep neural networks without explicit regularization.
method Backward error analysis to calculate implicit gradient regularization and demonstrate its effectiveness empirically.
result Implicit gradient regularization biases gradient descent toward flat minima, improving model robustness and test errors.
Black-box optimization is primarily important for many compute-intensive applications, including reinforcement learning (RL), robot control, etc. This paper presents a novel theoretical framework for black-box optimization, in which our method performs stochastic update with the implicit natural gradient of an exponent…
Neural networks used for image classification tasks in critical applications must be tested with sufficient realistic data to assure their correctness. To effectively test an image classification neural network, one must obtain realistic test data adequate enough to inspire confidence that differences between the impli…
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.
Large batch training with DP-SGD reduces model performance due to implicit bias.
problem Large batch training with DP-SGD reduces model performance.
method The study analyzes the phenomenon of implicit bias in Noisy-SGD (DP-SGD without clipping) and its theoretical solutions for linear models.
result The implicit bias in large batch training with DP-SGD is amplified by additional noise, similar to SGD.
This paper is devoted to the characterization of differentially flat nonlinear systems in implicit representation, after elimination of the input variables, in the differential geometric framework of manifolds of jets of infinite order. We extend the notion of Lie-Bäcklund equivalence, introduced in Fliess et al. (1999…
Neural networks learn the support of the target function through SGD's implicit regularization effect.
problem Learning the support of the target function in neural networks.
method Investigation of mini-batch SGD's ability to learn the support in the first layer of a neural network.
result Mini-batch SGD effectively learns the support in the first layer by shrinking irrelevant weights, while vanilla GD requires an explicit regularization term.
Progress in probabilistic generative models has accelerated, developing richer models with neural architectures, implicit densities, and with scalable algorithms for their Bayesian inference. However, there has been limited progress in models that capture causal relationships, for example, how individual genetic factor…
Studying Binomial and Gaussian return dynamics in discrete time, we show how excess volatility can be traded to create growth. We test our results on real world data to confirm the observed model phenomena while also highlighting implicit risks.
Proposes LDIDPs for efficient sequential data generation from latent dynamical models.
problem Challenges in generating high-fidelity sequential samples from latent dynamical models.
method Utilizes implicit diffusion processes to sample from latent dynamical processes.
result Demonstrates accurate learning of dynamics and efficient generation of high-quality sequential data.
Gradient descent in tensor factorization favors low-rank solutions.
problem Tackling implicit regularization in tensor factorization problems.
method Gradient descent with small random initialization for overparametrized tensor factorization.
result Gradient descent leads to implicit regularization towards low tubal rank solutions.
Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF model with P features, N data points, and a ridge λ, we show that the avera…
This work shows how exploiting gradient alignment can improve distributed and federated learning performance.
problem Misalignment of gradients across clients in distributed and federated learning.
method Utilizing implicit regularization through a novel GradAlign algorithm that induces gradient alignment with large mini-batches.
result Improvements in test accuracies and generalization performance.
Understanding users' context is essential for successful recommendations, especially for Online-to-Offline (O2O) recommendation, such as Yelp, Groupon, and Koubei. Different from traditional recommendation where individual preference is mostly static, O2O recommendation should be dynamic to capture variation of users' …
We present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted …
We present an approach of computing the intersection curve C of two rational parametric surface §1(u,s) and §2(v,t), one being projectable and hence can easily be implicitized. Plugging the parametric surface to the implicit surface yields a plane algebraic curve G(v,t)=0. By analyzing the topology …
Improved Fréchet regression tackles noise and multicollinearity.
problem Addressing noise and multicollinearity in multi-label regression.
method Implicit regularization framework for explicit modeling of relationships.
result Effective modeling of complex dependencies without introducing biases.
Adapts CNN for robust medical image segmentation across different scanners and protocols.
problem Performance degradation of CNNs in medical image segmentation due to mismatch between training and test images.
method Designs a segmentation CNN as a concatenation of a shallow normalization CNN and a deep CNN. At test time, adapts the normalization sub-network for each test image using a denoising autoencoder.
result Consistently improves performance on multi-center MRI datasets of brain, heart, and prostate.
Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible, this task is particularly difficult and therefore largely unexplored. This is mai…
DINo forecasts PDEs with flexible extrapolation and adaptability.
problem Fixed discretizations limit real-world PDE forecasting.
method DINo uses implicit neural representations for continuous-time dynamics.
result DINo outperforms other neural PDE forecasters.
Gradient flow with infinitesimal initialization converges to Greedy Low-Rank Learning for matrix factorization.
problem Understanding implicit regularization in gradient descent for matrix factorization.
method Theoretical and empirical analysis of gradient flow with infinitesimal initialization and Greedy Low-Rank Learning.
result Gradient flow with infinitesimal initialization is mathematically equivalent to Greedy Low-Rank Learning for depth-2 matrix factorization under reasonable assumptions.
REALFIN benchmarks financial reasoning by removing implicit assumptions, revealing model weaknesses.
problem Models struggle when implicit assumptions are missing, leading to incorrect answers.
method Developed a bilingual benchmark that systematically removes essential premises from financial questions.
result General-purpose models over-commit, while finance-specialized models fail to identify missing premises.
Paper proposes a new method to assess synthetic data generators.
problem Assessing the quality of implicit generative models.
method Kernelised Stein Statistic (KSD) test based on non-parametric Stein operator.
result Improved power performance compared to existing approaches.
This paper studies how gradient descent in control systems can perform well on unseen data.
problem The extent of a learned controller's ability to extrapolate to unseen initial states.
method Theoretical study of policy gradient in Linear Quadratic Regulator (LQR) problems, focusing on the role of exploration.
result The performance of a learned controller on unseen initial states depends on the degree of exploration induced by the system.
Generative adversarial networks (GANs) provide an algorithmic framework for constructing generative models with several appealing properties: they do not require a likelihood function to be specified, only a generating procedure; they provide samples that are sharp and compelling; and they allow us to harness our knowl…
New KNN test improves association analysis of high-dimensional sequencing data.
problem Challenges in using neural networks for high-dimensional sequencing data analysis.
method Kernel-based neural network (KNN) test for complex association analysis.
result KNN test outperforms SKAT in detecting non-linear and interaction effects.
SAM improves deep learning tasks by promoting balancedness, reducing outlier impact.
problem Improving generalization in deep learning tasks, especially with scale-invariant problems.
method Introduces balancedness as a new concept to depict global behaviors of SAM, focusing on the difference between squared norms of two variables.
result SAM promotes balancedness and is data-responsive, outperforming SGD in outlier scenarios.
A test for neural networks identifies genetic associations.
problem Testing complex associations in neural networks.
method Sieve quasi-likelihood ratio test for neural networks with one hidden layer.
result The test statistic has an asymptotic chi-squared distribution.
Paper shows how gradient concentration helps in learning from inexact data.
problem Learning from inexact and stochastic training data.
method Combines probabilistic gradient concentration with inexact optimization techniques.
result Derives sharp test error guarantees for learning.
New Hamiltonian Monte Carlo method for non-canonical dynamics.
problem Incompatibility of canonical symplectic structure with non-canonical dynamics.
method Developed a framework for Hamiltonian Monte Carlo using non-canonical symplectic structures with implicit integration.
result Non-canonical Hamiltonian Monte Carlo provides sampling advantages.
Second generation sequencing technologies are being increasingly used for genetic association studies, where the main research interest is to identify sets of genetic variants that contribute to various phenotype. The phenotype can be univariate disease status, multivariate responses and even high-dimensional outcomes.…
RL struggles with generalization due to implicit partial observability.
problem Generalization in RL is difficult due to implicit partial observability.
method Re-cast RL problem as solving epistemic POMDPs and propose ensemble-based techniques.
result Simple ensemble-based technique achieves significant generalization gains.
Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being intelligently desi…
Power of network tests degrades when vertices are misaligned.
problem Power loss in network hypothesis testing due to vertex shuffling.
method Theoretical analysis and simulations of Frobenius norm differences in random dot product and stochastic block models.
result Shuffling vertices can significantly reduce the power of network tests.
Study uses neural fields to improve geophysical inversions by reducing artifacts.
problem Improving geophysical inversions by reducing artifacts and improving model recovery.
method Employing neural fields for test-time learning in geophysical inversions.
result Test-time learning with neural fields eliminates unwanted artifacts in recovered models.