Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine lea…
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48 results for “landscape”
Reviews recent findings on neural network landscapes.
problem Non-convexity of loss functions causing bad landscapes.
method Rigorous geometric analysis and empirical exploration.
result Wide neural nets may have sub-optimal local minima.
The study examines when MAML's objective has a benign landscape.
problem Understanding when MAML's objective landscape is benign.
method Analyzing the landscape of MAML objective on LQR tasks.
result The benign landscape of the MAML objective depends on task similarities.
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.
Adversarial training makes logistic regression weight loss landscapes sharper.
problem Understanding why adversarial training sharpens the weight loss landscape in logistic regression.
method Theoretical analysis of linear logistic regression model with L2 norm constraints, and experiments on ResNet18.
result Adversarial training sharpens the weight loss landscape in linear logistic regression models.
AWP improves robustness by flattening weight loss landscape.
problem Improving robustness of deep neural networks against adversarial examples.
method Explicitly regularizes the flatness of weight loss landscape through adversarial weight perturbation.
result AWP forms a double-perturbation mechanism in adversarial training, leading to flatter weight loss landscape.
Efficiently infers graph edges from genetic similarity data in landscape genetics.
problem Inferring unknown graph edges from genetic similarity data in a heterogeneous landscape.
method Developed an efficient first-order optimization method to solve the inverse landscape genetics problem.
result Our method provides fast and reliable convergence, significantly outperforming existing heuristics.
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.
Researchers improve visualization of neural network loss landscapes.
problem Understanding neural network generalization performance.
method Novel 'jump and retrain' procedure, non-linear dimensionality reduction (PHATE), computational homology.
result Improved visualization and quantification of neural network generalization performance.
Deeper models have a more favorable optimization landscape, making them more robust to noise.
problem Characterizing the effect of depth on the optimization landscape of linear regression models.
method Robust and over-parameterized setting, simple sub-gradient method.
result A simple sub-gradient method converges to a balanced solution that is close to the ground truth and enjoys a flat local landscape.
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…
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 analyze the optimization landscape of α-loss in logistic models.
problem Optimization landscape of α-loss in logistic models.
method Tools from strictly-locally-quasi-convex functions and geometric techniques.
result Evolution of optimization landscape with respect to α.
Study reveals sharp characterisation of local minima in neural network loss landscapes.
problem Characterizing local minima in high-dimensional two-layer ReLU neural networks.
method Exact low-dimensional representation of local minima using summary statistics and link with one-pass SGD dynamics.
result Local minima in overparameterized neural networks form discrete families with varying stability and reachability.
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.
SGD vs quasi-Newton optimization in neural networks: different landscapes, different generalizability.
problem Understanding neural network optimization and generalizability.
method Comparison of stochastic gradient descent (SGD) and quasi-Newton optimization methods using computational tools.
result SGD solutions are separated by lower barriers than quasi-Newton solutions, but quasi-Newton solutions are deeper and more isolated.
Visualizing the Loss Landscape of Actor Critic Methods with Applications in Inventory Optimizationcs.LG
Study visualizes actor-critic loss landscapes for inventory optimization.
problem Difficulties in solving multi-store dynamic inventory control problems.
method Low-dimensional visualizations of actor loss function.
result Loss landscapes favor optimal policies in reinforcement learning.
Complex energy landscapes in spiked-tensor and simple glassy models: ruggedness, arrangements of local minima and phase transitionscond-mat.dis-nn
We study rough high-dimensional landscapes in which an increasingly stronger preference for a given configuration emerges. Such energy landscapes arise in glass physics and inference. In particular we focus on random Gaussian functions, and on the spiked-tensor model and generalizations. We thoroughly analyze the stati…
Considering the creation of persistence landscape on a parametrized curve and structure of sampling, there exists a random process for which a finite mixture model of persistence landscape (FMMPL) can provide a better description for a given dataset. In this paper, a nonparametric approach for computing integrated mean…
Analyzes adversarial training's impact on loss landscape, proposing PAS to improve model performance.
problem Challenges in optimizing models under adversarial training due to loss landscape properties.
method Analytical studies of adversarial loss functions, numerical analyses, PAS strategy.
result Adversarial training impairs optimization, but PAS strategy improves model performance.
LSAM optimizes deep learning training with improved efficiency.
problem Inefficiency in distributed large-batch training with Sharpness-Aware Minimization (SAM).
method Integrates SAM's adversarial steps with an asynchronous distributed sampling strategy.
result Higher final accuracy compared to data-parallel SAM.
Paper characterizes optimization landscape of Tucker decomposition.
problem Finding exact Tucker decomposition is a nonconvex optimization problem.
method Characterized the optimization landscape and provided a local search algorithm.
result All local minima are globally optimal if tensor has an exact Tucker decomposition.
Researchers improve NCE by addressing its flat loss landscape issues.
problem NCE's poor performance due to an ill-behaved loss landscape.
method Introduced eNCE with an exponential loss and normalized gradient descent.
result Proven that landscape issues arise from inappropriate noise distribution.
Embedding principle explains loss landscape of deep neural networks.
problem Understanding the structure of loss landscapes in deep neural networks.
method Proposed an embedding principle that critical points of narrower DNNs can be embedded to critical points of wider DNNs.
result Wide DNNs are often attracted by highly-degenerate critical points embedded from narrower DNNs.
There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High dimensionality plays a key role in our model. Our core idea is to model the loss la…
The landscape of empirical risk has been widely studied in a series of machine learning problems, including low-rank matrix factorization, matrix sensing, matrix completion, and phase retrieval. In this work, we focus on the situation where the corresponding population risk is a degenerate non-convex loss function, nam…
The study tests inferences about neural network optimization from linear interpolation of loss landscapes.
problem Understanding the difficulty of neural network optimization problems.
method Linear interpolation of neural network loss landscapes, systematic evaluation of various factors.
result Linear interpolation does not correlate with model performance, challenging prior intuition.
The paper analyzes phase retrieval under limited samples, ensuring a benign local landscape for convergence.
problem Ensuring a benign local landscape for phase retrieval under limited samples.
method Fine-grained analysis of local landscape properties under the regime of limited samples.
result Gradient descent can converge to an -loss solution exponentially fast under certain conditions.
Deep ReLU networks with extra parameters have mostly good loss landscapes.
problem Finding good local minima in the loss landscape of deep neural networks.
method Analyzing shallow and deep ReLU networks with extra parameters on a generic dataset.
result Most activation patterns correspond to regions with no bad local minima.
We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q. Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repet…
This work shows how to efficiently simulate parts of quantum landscapes using classical computers.
problem Identifying where quantum computers are advantageous and offloading computations.
method Developed a quantum-enhanced classical algorithm to simulate sub-regions of quantum landscapes.
result It is possible to generate a classical surrogate of a sub-region of a quantum landscape.
This work justifies neural collapse under MSE loss and analyzes the optimization landscape.
problem Understanding neural collapse in deep neural networks under MSE loss.
method Global landscape analysis of vanilla nonconvex MSE loss.
result The only global minimizers are neural collapse solutions.
Geodesics connect model modes in neural network loss landscapes.
problem Connecting modes in neural network loss landscapes.
method Reframed mode connectivity in Information Geometry, hypothesized geodesics as mode-connecting paths, proposed algorithm to approximate geodesics.
result Geodesics achieve mode connectivity in neural networks.
New method simplifies optimization landscapes by transforming saddle points.
problem Saddle points hinder non-convex optimization in machine learning.
method Variable elimination algorithms, like VarPro, are compared to reveal geometric insights.
result Variable elimination reshapes critical point structure, creating local maxima from saddle points.
Realistic evolutionary fitness landscapes are notoriously difficult to construct. A recent cutting-edge model of virus assembly consists of a dodecahedral capsid with corresponding packaging signals in three affinity bands. This whole genome/phenotype space consisting of genomes has been explored via comp…
Deep learning dynamics exhibit anomalous superdiffusion initially, aiding escape from local minima.
problem Understanding the dynamics of learning in deep neural networks.
method Novel analysis of SGD dynamics and loss landscape structure.
result SGD exhibits anomalous superdiffusion initially, transitioning to subdiffusion as learning progresses.
Study identifies new stable climate states in climate model.
problem Understanding multistability and transitions in climate models.
method Combination of quasipotential theory and manifold learning.
result Discovery of a third stable climate state not previously known.
SmoothDARTS stabilizes DARTS-based architecture search by smoothing loss landscapes.
problem DARTS-based NAS methods suffer from instability, leading to deteriorating architectures.
method SmoothDARTS (SDARTS) uses perturbation-based regularization to smooth the loss landscape.
result SmoothDARTS improves the generalizability and performance of DARTS-based methods.
Consensus-based adaptive sampling and approximation for high-dimensional energy landscapesphysics.comp-ph
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.
Looped transformers outperform standard transformers in complex reasoning tasks due to a specific loss landscape geometry.
problem Understanding why looped transformers outperform standard transformers in complex reasoning tasks.
method Explained through loss landscape geometry, distinguishing between U-shaped and V-shaped valleys, and proposing SHIFT training strategy.
result Looped transformers' recursive architecture induces a River-V-Valley landscape, leading to better loss convergence and complex pattern learning.
Training an artificial neural network involves an optimization process over the landscape defined by the cost (loss) as a function of the network parameters. We explore these landscapes using optimisation tools developed for potential energy landscapes in molecular science. The number of local minima and transition sta…
Neural network training relies on our ability to find "good" minimizers of highly non-convex loss functions. It is well-known that certain network architecture designs (e.g., skip connections) produce loss functions that train easier, and well-chosen training parameters (batch size, learning rate, optimizer) produce mi…
Wide deep neural networks are easy to optimize without constraints.
problem Optimizing wide deep neural networks.
method Analysis of optimization landscapes and empirical-risk minimization.
result Wide neural networks have no confined points, making optimization easier.
Training neural networks involves finding minima of a high-dimensional non-convex loss function. Knowledge of the structure of this energy landscape is sparse. Relaxing from linear interpolations, we construct continuous paths between minima of recent neural network architectures on CIFAR10 and CIFAR100. Surprisingly, …
New function class characterizes loss landscape of deep neural networks without over-parametrization.
problem Complex loss landscape of deep neural networks without over-parametrization.
method Proposed a novel class of functions to characterize loss landscape without over-parametrization.
result Gradient-based optimizers possess theoretical guarantees of convergence under the new function class assumption.
New findings on optimization landscape of Toeplitz covariance estimation.
problem Understanding the geometry of the Gaussian maximum-likelihood objective for Toeplitz covariance estimation.
method Overparameterized Carathéodory representation of positive definite Toeplitz covariance matrices, focusing on both amplitudes and frequencies.
result Joint optimization of amplitudes and frequencies leads to a benign population landscape, allowing for global recovery of the true Toeplitz covariance.
Overparametrization bends the landscape: BBP transitions at initialization in simple Neural Networkscond-mat.dis-nn
Study shows overparametrization can shift and bend loss landscapes, affecting signal recovery.
problem Understanding how overparametrization affects loss landscapes in neural networks.
method Field theory analysis of Hessian spectrum at initialization.
result Overparametrization can shift the BBP transition point, potentially reaching weak-recovery threshold.
Tilting loss functions improves machine learning performance.
problem Improving machine learning models, especially in under- and over-parameterized networks.
method Using evolving loss functions that emphasize different classes cyclically.
result Dynamical loss functions lead to better generalization and stability in training.