Improved standard parameterization yields well-defined neural tangent kernel.
problem Extrapolation of standard parameterization to infinite width is problematic.
method Proposed an improved extrapolation of the standard parameterization.
result Improved standard parameterization yields similar accuracy to NTK parameterization but with better correspondence to finite width networks.
Machine learning models emulate and approximate complex mappings in model physics.
problem Developing and ensuring accurate physical parameterizations.
method Machine learning tools to emulate and approximate mappings.
result ML can improve parameterizations and enforce physical constraints.
Revisits PPO design choices, exposing failure modes and proposing alternatives.
problem Failure modes of standard PPO in new environments.
method Revisits standard PPO design choices, exposes failure modes, and proposes alternative approaches.
result Alternative design choices prevent failure modes in new environments.
Recently, over-parameterized neural networks have been extensively analyzed in the literature. However, the previous studies cannot satisfactorily explain why fully trained neural networks are successful in practice. In this paper, we present a new theoretical framework for analyzing over-parameterized neural networks …
Least squares regression shows unexpected double descent in under-parameterized models.
problem Understanding the generalization of under-parameterized models in regression.
method Analyzing the spectrum and eigenvectors of the sample covariance matrix.
result Least squares regression can exhibit a peak in generalization in the under-parameterized regime, contrary to previous explanations.
Traditionally, neural networks are parameterized using optimization procedures such as stochastic gradient descent, RMSProp and ADAM. These procedures tend to drive the parameters of the network toward a local minimum. In this article, we employ alternative "sampling" algorithms (referred to here as "thermodynamic para…
Exact expressions for double descent and implicit regularization in over-parameterized models.
problem Understanding the generalization error of over-parameterized models like deep neural networks.
method Surrogate random design to replace standard i.i.d. design, leading to exact expressions for mean squared error and implicit regularization.
result Exact non-asymptotic expressions for double descent and implicit regularization in over-parameterized models.
Compact parameterization improves Bayesian neural network performance.
problem Improving performance of Bayesian neural networks using variational methods.
method Restricting variational distribution to a k-tied Normal distribution with low-rank factorization.
result Compact parameterization improves signal-to-noise ratio and convergence speed.
The combination of the re-parameterization trick with the use of variational auto-encoders has caused a sensation in Bayesian deep learning, allowing the training of realistic generative models of images and has considerably increased our ability to use scalable latent variable models. The re-parameterization trick is …
New neural operators learn structured patterns efficiently.
problem Learning and representing complex, structured patterns in data.
method Sparse autoencoder neural operators (SAE-NOs) parameterize concepts as functions, enabling efficient and structured representation.
result SAE-FNOs learn localized patterns and generalize across different scales and discretizations.
FP-UCB algorithm achieves bounded regret for finitely parameterized multi-armed bandits.
problem Finitely parameterized multi-armed bandits with unknown but known parameter set.
method FP-UCB algorithm using structural information about the parameter set.
result FP-UCB achieves bounded regret under structural condition, logarithmic otherwise.
Solves parameter non-identifiability in Bayesian LTI system identification.
problem Parameter non-identifiability in standard Bayesian approaches for LTI system identification.
method Embedding canonical forms of LTI systems within the Bayesian framework.
result Unlocking the use of meaningful priors and robust uncertainty estimates.
We prove generic regularity and Uhlenbeck-type compactification theorems for the moduli spaces of PU(2)-monopoles. Generic regularity is NOT obtained in the usual way (by applying Sard theorem to a smooth parameterized moduli space), since the parameterized moduli space can be a priori singular. We explain why, using t…
Proof of learning rate transfer in MLPs with μP parameterization.
problem Understanding and optimizing learning rates in neural networks with different parameterizations.
method Theoretical analysis and empirical validation of learning rate transfer in MLPs with μP, SP, and NTP parameterizations. result The optimal learning rate converges to a non-zero constant as width goes to infinity under μP, explaining learning rate transfer. Numerous methods for computing conformal mesh paramterizations has been developed due to the vast applications in the field of geometry processing. Spectral conformal parameterization (SCP) is one of these methods to computing a quality conformal parameterization based on the spectral technique. SCP focus on a generali…
New insights into optimization and generalization for linear models.
problem Understanding the implicit regularization of optimization methods for linear models.
method Investigating the norms minimized by interpolating solutions and using projections to move between solutions.
result Proving that for over-parameterized linear classification, projections onto the data-span enable the use of under-parameterized techniques.
New framework analyzes deep neural networks using feature probabilities.
problem Degenerate situation in over-parameterized DNNs.
method Mean-field framework representing DNNs by feature probabilities and functions.
result Global convergence proof for over-parameterized Res-Net training.
Large learning rates work surprisingly well in standard parameterization, contrary to theory.
problem Theoretical limits of large learning rates do not match practical network behavior.
method Fine-grained analysis of learning rates and network behavior under cross-entropy loss.
result There are two distinct sub-regimes of unstable learning rates, with a controlled divergence regime where features continue to evolve.
Standard neural network architectures are non-linear only by virtue of a simple element-wise activation function, making them both brittle and excessively large. In this paper, we consider methods for making the feed-forward layer more flexible while preserving its basic structure. We develop simple drop-in replacement…
Data-driven optimization improves mean-variance portfolios by penalizing norms.
problem Estimation error in mean-variance optimization.
method Augment MVO with norm penalties, use neural networks for optimization, and compute derivatives implicitly.
result Data-driven optimization reduces portfolio risk compared to standard MVO.
OPT framework improves neural network generalization by learning an orthogonal transformation.
problem Improving neural network generalization.
method Orthogonal over-parameterized training (OPT) framework that minimizes hyperspherical energy.
result OPT framework provably minimizes hyperspherical energy and improves empirical generalization.
New parameterization of neural networks with Lipschitz bounds for robustness.
problem Developing robust neural networks with Lipschitz bounds.
method Introducing a new parameterization that admits a Lipschitz bound during training without requiring projections or barrier functions.
result The new parameterization improves robustness to adversarial attacks in image classification.
Pruning improves model generalization in over-parameterized models, contradicting traditional theories.
problem Pruning's effect on generalization in over-parameterized models.
method Empirical study on standard pruning algorithms and additional regularization effects.
result Pruning leads to better training and regularization, improving generalization.
This paper optimizes learning from data with over-parameterization.
problem Learning an unknown function from data with various model assumptions.
method Solving a discrete over-parameterized optimization problem with a penalty term.
result Near optimal approximation of the function f can be found. LipKernel adds robustness to CNNs by enforcing Lipschitz bounds.
problem Improving robustness of CNNs in real-time applications.
method Dissipative layers parameterized by LMIs and 2-D Roesser model.
result Orders of magnitude faster run-time compared to state-of-the-art methods.
Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized that even without training, convolutional networks can function as concise imag…
Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, while a second algorithm makes use of a neural network parameterization of option prices. The accuracy of the two methods is es…
One-hot encoding is a labelling system that embeds classes as standard basis vectors in a label space. Despite seeing near-universal use in supervised categorical classification tasks, the scheme is problematic in its geometric implication that, as all classes are equally distant, all classes are equally different. Thi…
Linear models can overfit without harming OOD generalization under certain conditions.
problem Understanding how overparameterized linear models generalize to out-of-distribution data.
method Analyzing overparameterized linear models under covariate shift, providing guarantees for OOD generalization.
result Benign overfitting occurs in standard ridge regression under OOD conditions, with specific structural conditions on target covariance.
We use parameterized Morse theory on the pages of an open book decomposition to efficiently encode the contact topology in terms of a labelled graph on a disjoint union of tori (one per binding component). This construction allows us to generalize the notion of the front projection of a Legendrian knot from the standar…
UDM reparameterization improves language model generation.
problem Mismatch between UDM training objective and denoising posterior.
method Leave-one-out denoising and absorbing state reformulation.
result Improved UDM generation through leave-one-out parameterization.
New insights into model robustness for random features and NTK models.
problem Understanding and distinguishing robustness in machine learning models.
method Analyzing empirical risk minimization in random features and NTK models.
result Random features models are not robust under any degree of over-parameterization, even when satisfying the universal law of robustness.
Wide hypernetworks don't guarantee convergence under gradient descent.
problem Theoretical guarantees for wide hypernetworks in over-parameterized settings.
method Analyzing infinitely wide hypernetworks and their convergence properties.
result Infinitely wide hypernetworks do not guarantee convergence to a global minimum under gradient descent.
This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified framework for parameter estimation that encompasses both on-line learning, where the model is c…
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient gradient computation that enables gradient-based optimization procedures, including…
Paper analyzes adversarial training's performance in binary classification.
problem Understanding the generalization performance of adversarial training.
method Derives precise theoretical predictions for adversarial training performance.
result Provides exact asymptotics for test errors of adversarial training.
The paper introduces various canonical parameterizations for 2D-curved shapes.
problem Comparing unparameterized simple curves in the plane.
method Proposes diverse canonical parameterizations, including arc-length and curvature-based.
result Natural parameterizations correspond to physical movements and are geometric invariants.
Agent57 beats human average on all Atari games.
problem Atari game benchmark's poor performance in challenging games.
method Trained neural network with adaptive policy selection and novel architecture.
result First deep RL agent to outperform human average on all 57 Atari games.
New method μP2 improves neural network training by scaling perturbations layerwise.
problem Improving neural network performance as models scale up.
method Layerwise perturbation scaling in the infinite-width limit of neural networks.
result Layerwise perturbation scaling ensures all layers are effectively perturbed in the limit.
We identify a class of over-parameterized deep neural networks with standard activation functions and cross-entropy loss which provably have no bad local valley, in the sense that from any point in parameter space there exists a continuous path on which the cross-entropy loss is non-increasing and gets arbitrarily clos…
The recent liberalization of the electricity and gas markets has resulted in the growth of energy exchanges and modelling problems. In this paper, we modelize jointly gas and electricity spot prices using a mean-reverting model which fits the correlations structures for the two commodities. The dynamics are based on Or…
Rényi Neural Processes replace KL divergence with Rényi divergence to improve NP performance.
problem Parameterization coupling in Neural Processes leads to prior misspecification.
method Propose Rényi Neural Processes (RNP) by replacing KL divergence with Rényi divergence.
result Significant performance improvements in real-world problems, including better log-likelihoods.
Deep learning models generalize by extending decision boundaries outside the convex hull of training data.
problem Understanding how deep learning models generalize beyond their training data.
method Investigation of decision boundaries inside and outside the convex hull of training sets, using various neural network architectures and training regimes.
result Over-parameterization is necessary for deep learning models to extend decision boundaries outside the convex hull of their training data.
Study proves convergence of subgradients for optimal transport-based objectives.
problem Ensuring statistical consistency and optimization stability in transport-based models.
method Proves graphical convergence of subdifferentials to the subdifferential of the population objective.
result Standard subgradient methods consistently approach stationary points of the population-level problem.
Paper introduces NICc for fast cluster-based validation of prediction models.
problem Validation of prediction models on clustered data.
method Derived NICc to approximate leave-one-cluster-out deviance for standard regression models.
result NICc provides more accurate model size and variable selection, especially with strong clustering.
Paper explores why overfitted DNNs in adversarial training can generalize.
problem Understanding why overfitted DNNs in adversarial training can generalize despite poor robust generalization.
method An approximation viewpoint to analyze the robust overfitting of over-parameterized DNNs.
result Existence of infinitely many overfitted DNNs that achieve good robust generalization under certain conditions.
New parameterization for (1,1)-knots simplifies their study.
problem Parameterizing (1,1)-knots in a novel way. method From minimal-length representatives of arcs in the multipunctured plane.
result Introduced parameterization is essentially unique for satellite (1,1)-knots. ResRep prunes CNNs without losing accuracy by separating remembering and forgetting.
problem Pruning CNNs to reduce FLOPs without sacrificing accuracy.
method Decoupling remembering and forgetting in CNNs, using SGD for remembering and a novel update rule for forgetting.
result Achieved lossless pruning with high compression ratio (76.15% accuracy on ImageNet with 45% FLOPs reduction).