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.
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.
MAML outperforms NAL in diverse task landscapes.
problem Understanding when and how MAML outperforms NAL in various task landscapes.
method Analytical and numerical studies in a linear regression setting with a mixture of easy and hard tasks.
result MAML gains over NAL when there is task hardness discrepancy and optimal solutions of hard tasks are closely packed.
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.
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.
EpiMer merges models by solving Fréchet mean on a Riemannian manifold.
problem Integrating knowledge from multiple models without retraining.
method EpiMer casts model merging as solving the Fréchet mean on a Riemannian manifold, restricting computation to a low-rank subspace.
result EpiMer outperforms flat-geometry methods on image classification tasks.
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.
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.
Choosing the best-performing optimizer(s) out of a portfolio of optimization algorithms is usually a difficult and complex task. It gets even worse, if the underlying functions are unknown, i.e., so-called Black-Box problems, and function evaluations are considered to be expensive. In the case of continuous single-obje…
Adaptor 'E' extends gradient-based optimizers to explore loss landscapes, improving generalization.
problem Finding lower and better-generalizing minima in deep learning.
method Proposes an adaptor 'E' to extend gradient-based optimizers, encouraging exploration along landscape valleys.
result Adapted optimizers increase test accuracy by an average of 2.5% in large-batch training tasks.
MD tree diagnoses model failures using loss landscape metrics.
problem Diagnose model failures without knowing training configuration.
method MD tree based on loss landscape metrics.
result MD tree achieves 87.7% accuracy in dataset transfer tasks, outperforming validation-based approaches.
Convolutional neural networks have had a great success in numerous tasks, including image classification, object detection, sequence modelling, and many more. It is generally assumed that such neural networks are translation invariant, meaning that they can detect a given feature independent of its location in the inpu…
Paper analyzes Transformer learning dynamics, proving benign landscape for in-context learning.
problem Understanding how Transformers learn in context with nonlinear features.
method Mean-field and two-timescale analysis of Transformer dynamics, proving nonconvex but benign landscape.
result Proves mean-field dynamics avoid saddle points, leading to improved optimization.
Regionalization is the task of dividing up a landscape into homogeneous patches with similar properties. Although this task has a wide range of applications, it has two notable challenges. First, it is assumed that the resulting regions are both homogeneous and spatially contiguous. Second, it is well-recognized that l…
We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show differentiability with respect to layer inputs, for a general persistent homology with …
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…
The local geometry of high dimensional neural network loss landscapes can both challenge our cherished theoretical intuitions as well as dramatically impact the practical success of neural network training. Indeed recent works have observed 4 striking local properties of neural loss landscapes on classification tasks: …
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.
Neural collapse occurs in normalized features over a Riemannian manifold.
problem Understanding neural collapse in normalized feature models.
method Simplified multi-class classification task to a nonconvex optimization problem over the Riemannian manifold, analyzing the landscape of critical points.
result The only global minimizers are neural collapse solutions, with all other critical points being strict saddles.
New framework to understand and exploit curvature in deep learning loss landscapes.
problem Understanding and optimizing the loss landscape in deep learning models.
method New conceptual framework and techniques to estimate and exploit curvature of expected loss changes.
result Alice algorithm optimizes training by incorporating curvature terms and step bounds.
Due to the success of deep learning to solving a variety of challenging machine learning tasks, there is a rising interest in understanding loss functions for training neural networks from a theoretical aspect. Particularly, the properties of critical points and the landscape around them are of importance to determine …
New method uses LLMs to generate detailed scientific hypotheses.
problem Generating detailed, actionable scientific hypotheses from coarse initial directions.
method Hierarchical search method that incrementally adds details to hypotheses.
result Hierarchical search method consistently outperforms strong baselines on expert-annotated hypotheses.
We compute the transition probability between two learning tasks, and show that it decomposes into two factors. The first depends on the geometry of the loss landscape of a model trained on each task, independent of any particular model used. This is related to an information theoretic distance function, but is insuffi…
Flexible Kernels for Protein Property Prediction
problem Predicting protein properties from sparse experimental data
method Sequence kernels using evolutionary substitution matrices and local linearity
result Data-efficient models of protein property landscapes
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.
Sampling strategies significantly affect feature approximations in ELA, impacting classifier accuracy.
problem The impact of sampling strategies on feature approximations in ELA.
method Analysis of feature approximations from different sampling strategies and sample sizes.
result Feature approximations from different sampling strategies do not converge, affecting classifier accuracy.
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.
In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be estimated. A standard solution to flatten the corresponding rough landscape consists in summing the losses associated to different data poin…
Less-than-one-shot learning tackles few-shot learning with minimal data.
problem Training models on very small datasets while maintaining accuracy.
method Soft-label k-Nearest Neighbors classifier and theoretical lower bounds analysis.
result Achieving learning of multiple classes with fewer than the required samples.
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.
Transformers struggle to learn Markovian dynamics, showing NP-hard optimization challenges.
problem Understanding transformers' limitations in learning Markovian dynamical functions.
method Investigated through a structured ICL setup, analyzing loss landscapes and parameter optimization.
result Recovering optimal transformer parameters for Markovian functions is NP-hard.
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.
The optimization of multilayer neural networks typically leads to a solution with zero training error, yet the landscape can exhibit spurious local minima and the minima can be disconnected. In this paper, we shed light on this phenomenon: we show that the combination of stochastic gradient descent (SGD) and over-param…
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.
Many image processing tasks involve image-to-image mapping, which can be addressed well by fully convolutional networks (FCN) without any heavy preprocessing. Although empirically designing and training FCNs can achieve satisfactory results, reasons for the improvement in performance are slightly ambiguous. Our study i…
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.
Analyzes why neural networks generalize beyond training data.
problem Understanding why neural networks generalize beyond training data.
method Examined loss landscapes of neural networks to identify the mismatch between training and test losses.
result Identified the 'LU mechanism' explaining grokking in various tasks.
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.
One of the main difficulties in analyzing neural networks is the non-convexity of the loss function which may have many bad local minima. In this paper, we study the landscape of neural networks for binary classification tasks. Under mild assumptions, we prove that after adding one special neuron with a skip connection…
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.
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.
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.
DPlis improves privacy in deep learning models by smoothing loss functions.
problem Privacy leakage in deep learning models trained on private data and low model performance.
method DPlis constructs a smooth loss function to favor noise-resilient models.
result DPlis effectively boosts model quality and training stability under privacy constraints.