Autoencoders discover and accelerate molecular dynamics simulations.
problem Efficient sampling of macromolecular folding landscapes with high free energy barriers.
method Employing auto-associative artificial neural networks to learn nonlinear collective variables (CVs) that are explicit and differentiable functions of atomic coordinates.
result Substantial speedups in exploration of configurational space and discovery of data-driven CVs.
Study of phase separation and geometry on a closed elastic curve, including dynamics and free energy minimization.
problem Free energy and dynamics of a closed elastic filament coupled to a scalar concentration field.
method Analytical and numerical simulations of coupled Willmore flow and Cahn--Hilliard gradient flow on differential geometry.
result Qualitative changes in free energy landscape due to closure constraint, leading to metastable and stable multi-domain morphologies.
Unified framework for sampling and approximating high-dimensional energy landscapes.
problem Sampling and approximating complex energy landscapes in physical systems with constraints and energy barriers.
method Formulates a minimax optimization problem that jointly adapts surrogate approximation and adaptive sampling.
result Demonstrates effectiveness in biomolecular systems with up to 30 collective variables.
IDM learns clustered representations for complex FELs.
problem Learning meaningful representations for complex free energy landscapes.
method Information Distilling of Metastability (IDM) method.
result IDM achieves physically meaningful representations of FELs.
Deep neural networks undergo hierarchical free-energy landscape transitions with increasing data size.
problem Understanding the design space and dynamics of deep neural networks.
method Statistical mechanical approach based on replica method.
result Hierarchical free-energy landscape transitions with ultrametricity, leading to simpler configurations in deeper layers.
Bayesian inference learns free energy landscapes from experimental data.
problem Characterize the free energy landscape of classical many-body systems from experimental data.
method Combines non-parametric Bayesian inference with physically-motivated constraints to automate the construction of approximate free energy functionals.
result Inference algorithms yield a probability distribution over free energy functionals, leading to highly accurate analytic expressions.
GMVAE improves clustering in molecular simulations data.
problem Clustering metastable states in multi-basin free-energy landscapes.
method Gaussian mixture variational autoencoder (GMVAE) for dimensionality reduction and clustering.
result Enhanced clustering of metastable states compared to standard VAEs.
Experimental fractal landscape dynamics observed in emulsions.
problem Understanding anomalous motions in soft glassy materials.
method Quantitative analysis of oil droplet trajectories in dense emulsions.
result Experimental fractal geometry matches computational model of soft glassy dynamics.
New sampler tackles complex discrete energy landscapes efficiently.
problem Stagnation in gradient-based discrete samplers for non-convex settings.
method DREXEL sampler with Replica Exchange and Adjusted Metropolis.
result Proves samplers satisfy detailed balance and converge to target distribution.
We reveal connections between RBMs and Bosons, explaining symmetry breaking in their energy landscapes.
problem Understanding the relationships among different deep generative models and their learning mechanisms.
method Introducing a reciprocal space formulation to RBMs, revealing connections to diffusion processes and Bosons.
result Symmetry breaking in RBM energy landscapes is characterized by singular values and weight matrix eigenvectors.
Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide complete and accurate description of the…
Neural networks' energy landscape is surprisingly flat, suggesting minimal structural changes between minima.
problem Understanding the structure of neural network energy landscapes.
method Constructing continuous paths between minima of recent neural network architectures on CIFAR10 and CIFAR100.
result Paths between minima are essentially flat in both training and test landscapes, implying minimal structural changes.
Study shows TAP free energy minimization provides better posterior inference in high-dimensional linear models.
problem Deviation from true posterior mean and underestimation of posterior uncertainty in variational inference.
method Minimization of TAP free energy in a high-dimensional asymptotic framework, showing geometric and statistical properties.
result Local minimizer of TAP free energy provides consistent estimate of posterior marginals and correctly calibrated posterior inference.
Enhanced diffusion sampling improves rare event sampling in biomolecular simulations.
problem Efficiently sampling rare transition events in biomolecular systems.
method Quantitative steering protocols to generate biased ensembles and exact reweighting.
result Fast, accurate, and scalable estimation of equilibrium properties.
Enhanced diffusion sampling tackles rare event sampling in biomolecular simulations.
problem Efficiently sampling rare transition events in biomolecular simulations.
method Quantitative steering protocols to generate biased ensembles, followed by exact reweighting.
result Fast, accurate, and scalable estimation of equilibrium properties for folding free energies.
Study energy landscapes in glass models, focusing on Gaussian and spiked-tensor functions.
problem Characterize statistical properties and phase transitions of high-dimensional energy landscapes.
method Developed a Kac-Rice method framework to compute landscape complexity and analyze phase transitions rigorously.
result Characterized the ruggedness and arrangements of local minima in energy landscapes.
Paper connects free-energy and low-degree hardness in high-dimensional statistics.
problem High-dimensional statistical inference problems are computationally hard.
method Defines a free-energy criterion and connects it to low-degree hardness.
result Establishes connection between free-energy and low-degree hardness for Gaussian models.
ELS framework improves safety alignment by dynamically steering LLMs towards helpful responses.
problem Over-Refusal in Aligned Large Language Models
method Fine-tuning free framework using an Energy-Based Model (EBM) to dynamically steer LLMs during inference.
result Extensive experiments show a significant reduction in false refusals (from 57.3% to 82.6%) while maintaining safety performance.
New theory shows predictive coding makes learning landscape easier to navigate.
problem Understanding the impact of predictive coding's inference procedure on learning efficiency.
method Analyzed the geometry of the energy landscape of deep linear networks, proving many non-strict saddles become strict in the equilibrated energy.
result All highly degenerate (non-strict) saddles of the loss become strict in the equilibrated energy, suggesting a more robust learning landscape.
Enhances diffusion-based sampling for molecular systems.
problem Inefficiency and thermodynamic mode miss in diffusion-based samplers for molecular systems.
method Introduces a sequential bias along collective variables (CVs) to encourage exploration and increase temperature in the projected space.
result Improves efficiency, mode discovery, and free energy estimation; first to demonstrate reactive sampling.
In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \emph{Energy Landscape Maps} (ELMs) which characterize and visualize an energy function with a tree structure, in which each leaf node re…
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular pot…
We explore the energy landscape of a simple neural network. In particular, we expand upon previous work demonstrating that the empirical complexity of fitted neural networks is vastly less than a naive parameter count would suggest and that this implicit regularization is actually beneficial for generalization from fit…
Study of Willmore energy on sphere sublevel sets and flow singularities.
problem Understanding the Willmore energy landscape and singularities of the Willmore flow.
method Gluing different instances of the Willmore flow and using an invariant for triple-point-free spheres.
result Classification of initial surfaces with energy at most 12π leading to unavoidable singularities.
SGD with machine learning noise converges to global minimum exponentially fast.
problem Optimizing machine learning models with stochastic gradient descent.
method Analysis of SGD with machine learning noise, focusing on energy landscapes and gradient noise.
result SGD converges to the global minimum exponentially fast under certain conditions.
Improved Langevin Monte Carlo reduces energy barriers for faster optimization.
problem Optimizing functions with high energy barriers.
method Proposes a modified landscape for Langevin Monte Carlo.
result Polynomial dependence on energy barrier in Log-Sobolev constant.
Sparse neural networks training is difficult due to optimization failures and energy landscape issues.
problem Training sparse neural networks leads to suboptimal solutions and optimization failures.
method Investigated optimization dynamics and energy landscape in sparse neural networks.
result Sparse neural networks have a linear path with a monotonically decreasing objective from initialization to a good solution, but not from a bad solution.
This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenval…
iDEM generates samples from Boltzmann densities without data.
problem Generating statistically independent samples from unnormalized distributions.
method Iterative algorithm using energy and gradient for diffusion-based sampler training.
result iDEM achieves state-of-the-art performance and trains faster than existing methods.
Proposes a method to sample from flat basins of posterior distributions in Bayesian deep learning.
problem Sampling from multi-modal posterior distributions leads to overfitting due to trapping in bad modes.
method Introduces an auxiliary guiding variable to bias MCMC sampling towards flat basins of the energy landscape.
result The method converges faster and outperforms existing methods in sampling from flat basins of the posterior.
Deep neural networks are optimizable due to their multilayered structure.
problem Understanding why deep neural networks are easily optimizable despite their non-convex loss functions.
method Analysis of a spin glass model of deep neural networks using random matrix theory and algebraic geometry.
result The multilayered structure of deep neural networks leads to fewer stationary points, more clustered minima, and less severe tradeoffs between depth and width of minima.
Model explains surprising properties of neural network training landscapes.
problem Understanding the geometry of neural network loss landscapes.
method Developed a simple theoretical model of gradients and Hessians.
result Unified model accounts for 4 surprising properties of neural loss landscapes.
China and EU race to develop hydrogen for energy transition.
problem Developing hydrogen for sustainable energy systems.
method Comparative analysis framework using key factors.
result Customized solutions for local hydrogen industries.
Riemannian geometry improves protein dynamics analysis.
problem Efficient analysis of protein dynamics data in non-linear spaces.
method Developed a local approximation technique for geodesics and a smooth manifold of protein conformations.
result Geodesics approximate molecular dynamics trajectories and provide realistic summary statistics.
EWFM trains continuous flows with only energy evaluations, improving sample quality with fewer computations.
problem Efficiently sampling from complex, high-dimensional Boltzmann distributions using only energy evaluations.
method Energy-Weighted Flow Matching (EWFM) using importance sampling and iterative/annealed training.
result Improved sample quality with up to 3 orders of magnitude fewer energy evaluations compared to existing methods.
Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the can…
Black holes offer insights into machine learning's loss landscapes.
problem Understanding the loss landscape in machine learning.
method Comparing machine learning loss landscapes to black hole entropy.
result Black holes provide an infinite family of potential landscapes with known minima.
Smoothed fitness landscape improves protein optimization.
problem Infeasibility of combinatorially large protein sequence space.
method Formulate protein fitness as a graph signal, smooth using Tikunov regularization, and optimize with Gibbs sampling.
result 2.5 fold fitness improvement over training set.
Quantum annealing outperforms classical in solving non-convex optimization problems crucial for machine learning.
problem Solving non-convex optimization problems efficiently.
method Designing a classical energy function and adding a quantum transverse field to facilitate tunneling.
result Quantum annealing converges efficiently to optimal solutions in a wide class of non-convex problems, unlike classical thermal annealing.
DMs emerge from DenseAMs, transitioning from memorization to generalization.
problem Hindered memory retrieval in DenseAMs due to spurious states.
method Examined diffusion models through the lens of DenseAMs, focusing on their generative process.
result Identified a critical phase in DMs transitioning from memorization to generalization.
Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach for these challenging problems. Deriving an algebraic representation allows us to…
Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixedpoints of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases o…
FEAT estimates free energy using adaptive transports.
problem Estimating free energy across scientific domains.
method Uses learned transports and stochastic interpolants.
result Provides consistent, minimum-variance estimators.
Exploring loss landscapes of XOR networks reveals complex structures.
problem Understanding the optimization landscape of XOR networks.
method Using molecular science optimization tools, analyzing the number and types of stationary points.
result The landscape of XOR networks becomes more convex with increased regularisation, embedding smaller networks in larger ones.
mAIS improves free energy evaluation efficiency.
problem Computational infeasibility of exact free energy evaluation.
method mAIS, a marginalized version of AIS.
result mAIS is more efficient under certain conditions.
Study of neural network training using mean-field Langevin dynamics and energy landscapes.
problem Understanding convergence of stochastic gradient algorithms for non-convex learning tasks.
method Leverage infinite-dimensional convexification, Mean-Field Langevin Dynamics, and energy functional.
result Gradient flow converges to a unique minimizer in 2-Wasserstein metric, with exponential convergence under regularisation.
Gradient-free optimizers are ineffective on barren plateaus in quantum computing.
problem Effect of barren plateaus on gradient-free optimization in quantum computing.
method Numerical simulations and theoretical analysis of gradient-free optimization algorithms.
result Gradient-free optimizers are not effective in barren plateau landscapes due to exponentially suppressed cost function differences.
GDML learns effective CG models from all-atom data.
problem Learning effective coarse-grained force fields efficiently.
method Ensemble learning with stratified sampling and GDML.
result GDML yields smaller free energy error than neural networks.