Symmetry in loss functions constrains model parameters, leading to specific learning outcomes.
problem Understanding and leveraging symmetries in neural networks to improve learning outcomes.
method Analyzing the impact of loss function symmetries on model parameters and learning behavior.
result Mirror-reflection symmetries in loss functions lead to constraints on model parameters, influencing learning outcomes.
This paper finds ReLU restores symmetry in SCL under class imbalances.
problem Symmetry break in SCL under class imbalances.
method Analytical proof and experiments with ReLU activation and batch selection.
result ReLU restores symmetry in SCL-learned representations without loss in test accuracy.
Unified framework connects different neural network models.
problem Understanding the geometry of neural network loss landscapes.
method Unified framework capturing four symmetry classes.
result First discovery of low- and zero-barrier linear interpolation paths.
New method approximates curvature from symmetries in deep networks.
problem Hard to approximate curvature in large deep networks.
method Analytically averaging over group actions that leave the loss invariant to construct structured Hessian approximations.
result Structured Hessian approximations from single gradients can be estimated, stored, and inverted.
Data symmetries in neural networks can generate conserved quantities.
problem Conservation laws in neural networks
method Using tensorizable networks
result Data augmentation can induce conserved quantities
Study reveals different types of critical points in shallow neural networks.
problem Optimization challenges in two-layer ReLU networks with symmetry.
method Symmetry analysis, bifurcation theory, and geometric group actions.
result Different types of spurious minima have distinct loss behavior.
This work tackles Bayesian neural networks by addressing loss landscape symmetries.
problem Understanding and optimizing the loss landscape of Bayesian neural networks.
method The approach involves extending marginalized loss barrier formalism to BNNs, proposing a matching algorithm to search for linearly connected solutions using permutation matrices and combinatorial optimization.
result Nearly zero marginalized loss barriers for linearly connected solutions were found.
Symmetry-regularized Neural ODEs improve model stability and interpretability.
problem Improving the stability and physical interpretability of Neural ODEs.
method Integrating Lie symmetries and conservation laws into the loss function.
result Symmetry-regularized Neural ODEs enhance model stability and interpretability.
Continuous symmetries and their breaking play a prominent role in contemporary physics. Effective low-energy field theories around symmetry breaking states explain diverse phenomena such as superconductivity, magnetism, and the mass of nucleons. We show that such field theories can also be a useful tool in machine lear…
Noise balance theory explains SGD's behavior in neural networks.
problem Understanding SGD's navigation in neural network loss landscapes.
method Analyzes minibatch noise and loss function symmetries.
result Derives the stationary distribution of SGD for deep networks.
Proposes neuron alignment to optimize mode connectivity in neural networks.
problem Understanding and optimizing mode connectivity in deep neural networks.
method Introduces neuron alignment to approximate optimal weight permutations and improve mode connectivity.
result Neuron alignment significantly alleviates robust loss barriers and improves model robustness and accuracy.
Develops SymGCP for tensor decompositions with general symmetry.
problem Handling symmetry in tensor decompositions for better model accuracy.
method Introduces SymGCP, a generalized CP decomposition that accounts for any subset of tensor modes' symmetry.
result SymGCP enables efficient and scalable tensor decomposition with improved model robustness and accuracy.
Many loss functions in representation learning are invariant under a continuous symmetry transformation. For example, the loss function of word embeddings (Mikolov et al., 2013) remains unchanged if we simultaneously rotate all word and context embedding vectors. We show that representation learning models for time ser…
Method discovers symmetries in data with neural networks.
problem Discovering symmetries in high-dimensional data.
method Fully connected neural networks trained with a loss function for symmetry.
result Generators for symmetries in latent space.
We consider the optimization problem associated with fitting two-layer ReLU networks with respect to the squared loss, where labels are assumed to be generated by a target network. Focusing first on standard Gaussian inputs, we show that the structure of spurious local minima detected by stochastic gradient descent (SG…
TRS-ODENs learn dynamics with time-reversal symmetry for more efficient learning.
problem Learning dynamics with time-reversal symmetry for more efficient learning.
method Proposed a loss function and a new framework (TRS-ODENs) to learn dynamics efficiently.
result TRS-ODENs can learn dynamics from noisy and complex trajectories efficiently.
Symmetrizes loss functions to improve neural network robustness against noisy labels.
problem Designing robust loss functions for noisy labels in neural networks.
method Symmetrization of multi-class loss functions, focusing on cross-entropy and unhinged loss.
result The multi-class unhinged loss is the unique convex symmetric loss under suitable assumptions.
Paper analyzes CycleGAN solutions and symmetries.
problem CycleGAN image translation without paired data.
method Theoretical analysis of exact and approximate solutions.
result Exact solution space is invariant to automorphisms.
We propose to impose symmetry in neural network parameters to improve parameter usage and make use of dedicated convolution and matrix multiplication routines. Due to significant reduction in the number of parameters as a result of the symmetry constraints, one would expect a dramatic drop in accuracy. Surprisingly, we…
Modified Jones-Faddy skew t-distribution captures asymmetry in stock returns.
problem Negative skew and positive mean in stock returns due to broken symmetry of stochastic volatility.
method Modified Jones-Faddy skew t-distribution applied to split gains and losses, using stochastic differential equations for stock returns and volatility.
result The modified distribution effectively captures the asymmetry in daily S&P500 returns, including its tails.
A new optimizer DDC improves deep learning models by respecting symmetries.
problem Deep networks' loss is invariant to continuous symmetries, leading to optimization issues.
method DDC builds a Dead-Direction Conditioner that lifts a base optimizer into a G-equivariant one, preserving the quotient geometry.
result DDCAdam and DDCMuon outperform standard optimizers in various tasks, improving validation-train loss gaps and learning dynamics.
Remove symmetries to improve model optimization and performance.
problem Symmetries in loss functions trap models in low-capacity states, hindering training and optimization.
method Proposes syre, a simple algorithm to remove symmetries in neural networks.
result Removing symmetries correlates well with improved optimization and performance.
Symmetry proven for positive solutions of a weighted p-Laplace operator inequality.
problem Proving symmetry of positive solutions to a specific type of inequality.
method Analyzing positive critical points of Caffarelli-Kohn-Nirenberg inequalities with a weighted p-Laplace operator.
result Complete classification and symmetry result for positive solutions in a range of parameters.
Automatically learns flexible symmetry constraints in neural networks using gradients.
problem Fixed hard constraints on neural network functions that cannot be adapted.
method Improves parameterisations of soft equivariance and optimizes marginal likelihood using differentiable Laplace approximations.
result Achieves equivalent or improved performance on image classification tasks compared to baselines with hard-coded symmetry.
Empirical study shows removing neural parameter symmetries impacts model performance.
problem Understanding the impact of neural parameter symmetries on model performance.
method Developed two methods to reduce parameter space symmetries in neural networks.
result Removing parameter symmetries can lead to faster and more effective Bayesian neural network training.
Tests for equivariance in non-parametric regression models.
problem Detecting false assumptions of symmetry in regression models.
method Develops tests for G-equivariance independent of the model. result Confidence in using equivariant models when symmetry is unknown.
This work refines claims about neural network connectivity, showing that simultaneous linear connectivity is possible under certain conditions.
problem Neural networks' loss landscapes are non-convex due to permutation symmetries, leading to high loss barriers between permuted networks.
method The authors introduce and analyze three claims of increasing strength regarding the connectivity of neural networks, focusing on permutations that align networks.
result The authors provide evidence that strong linear connectivity may be possible under certain conditions, specifically when interpolating among three networks of increasing width.
This work relaxes GNN symmetries to approximate automorphisms, improving model performance.
problem Improving graph neural network performance on asymmetric graphs.
method Formalizing approximate symmetries via graph coarsening, introducing a bias-variance formula.
result Best generalization performance achieved by choosing a larger symmetry group than automorphisms but smaller than permutations.
In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular target object. We present a general kernel framework for learning conditional rankings from various types of relational da…
The paper explores how symmetries and noise in SGD influence parameter dynamics.
problem Understanding the dynamics of parameter updates in SGD with symmetries.
method Proved the existence of noise equilibria and showed their role in balancing gradient noise.
result Gradient noise creates a systematic motion of parameters to a unique fixed point, called noise equilibria.
Noether's framework reveals symmetry-breaking in neural networks.
problem Understanding the role of symmetry breaking in neural networks.
method Developed a theoretical framework using Lagrangian mechanics.
result Identified 'kinetic symmetry breaking' and its effect on learning dynamics.
We study the problem of nonparametric dependence detection. Many existing methods may suffer severe power loss due to non-uniform consistency, which we illustrate with a paradox. To avoid such power loss, we approach the nonparametric test of independence through the new framework of binary expansion statistics (BEStat…
The paper studies minimal resistance dynamics in radial fields, finding unique solutions for incompressible flows.
problem Nonlinear dynamics of minimal resistance in radial fields.
method Analysis of two non-equilibrium scenarios: scale-invariant free expansion and incompressible source flow.
result Incompressible flow acts as a structural regularizer, admitting unique, smooth, and strictly concave solutions.
GE-autoencoder identifies spontaneous symmetry breaking in systems.
problem Locating phase boundaries and identifying spontaneously broken symmetries in systems.
method Group-equivariant autoencoder using group theory to constrain parameters and learn invariant order parameters.
result GE-autoencoder accurately determines spontaneous symmetry breaking and estimates critical temperatures more efficiently.
The permutation symmetry of neurons in each layer of a deep neural network gives rise not only to multiple equivalent global minima of the loss function, but also to first-order saddle points located on the path between the global minima. In a network of d−1 hidden layers with nk neurons in layers $k = 1, \ldots, …
The paper connects flatness to generalization in learning multi-index models with neural networks.
problem Understanding the generalization of non-convex neural networks using flatness measures.
method Analyzes 2-layer non-convex homogeneous neural networks and their connection to multi-index models.
result Flattest interpolators achieve small population loss and generalize well, establishing a direct link between flatness and generalization.
Toy model study shows resampling/reweighting can improve feature learning in imbalanced classification.
problem Improving feature learning in imbalanced classification problems.
method High-dimensional toy model with replica method, class-wise resampling/reweighting, and simplified model.
result No resampling/reweighting can sometimes give best feature learning performance.
New deep learning method preserves orientation in shape matching.
problem Symmetry issues in shape matching.
method Orientation-aware functional maps using complex functional representations and DiffusionNet.
result Stable correspondence predictions with robust orientation preservation.
This paper bounds min-entropy leakage for Blowfish privacy using graph symmetries.
problem Bounding min-entropy leakage for Blowfish privacy mechanisms.
method Organizing analysis over symmetrical partitions corresponding to orbits of graph automorphism groups.
result Demonstrates a construction meeting the bound with asymptotic equality, showing tightness.
Improves convergence speed in compressive sensing with a new probabilistic approach.
problem Efficiently solving the best subset selection problem in compressive sensing.
method Smooth probabilistic reformulation of ℓ0 regularized regression. result Empirically outperforms existing compressive sensing algorithms across various settings.
New optimizer designs respect symmetry, improving deep learning models.
problem Optimizers lack respect for symmetry in neural networks.
method Introduce symmetry-compatible principle for optimizer design.
result Symmetry-compatible optimizers improve model performance.
Proposes new loss functions for GANs to improve estimation accuracy and robustness.
problem Improving the training of GANs to achieve more accurate and robust models.
method Introduces Hellinger-type loss functions and analyzes their statistical properties.
result Demonstrates improved estimation accuracy and robustness of the proposed loss functions.
New method extends invariant reduction to rescaled geometric structures.
problem Computing invariant geometric structures under symmetries.
method Extends invariant reduction to rescaled structures using shift rule.
result Emergence and loss of invariance in reductions.
The paper uncovers symmetries in large language models through layer-peeled optimization.
problem Understanding geometric structure in large language model weights and context embeddings.
method Constrained layer-peeled optimization program to analyze symmetries in next-token distributions.
result Symmetries in target next-token distributions are transferred to optimal model weights and context embeddings.
Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork, mapping a latent vector into high-performance (low-loss) weight vectors, general…
Analyzes the Hessian of ReLU networks, proving skewed eigenvalue distribution.
problem Characterizing the Hessian at spurious minima in shallow ReLU models.
method Symmetry breaking and representation theory techniques.
result Proves skewed eigenvalue distribution of Hessian at spurious minima.
Group averaging boosts model accuracy without training cost.
problem Challenging training of equivariant models in physics.
method Group averaging at test time, improving accuracy.
result Improves model accuracy by up to 37% in continuous dynamics.
Analyzes multi-day stock returns, showing linear volatility and mean dependence.
problem Linear dependence of volatility and mean in accumulated stock returns.
method Modified Jones-Faddy skew t-distribution analysis.
result Linear dependence of volatility and mean on the number of days of accumulation.