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Neural networks are powerful models that solve a variety of complex real-world problems. However, the stochastic nature of training and large number of parameters in a typical neural model makes them difficult to evaluate via inspection.…

The remarkable performance of modern deep neural networks (DNNs) is largely driven by their massive scale, often comprising tens to hundreds of millions-or even billions-of parameters. However, such a scale incurs substantial storage and…

We explore some mathematical features of the loss landscape of overparameterized neural networks. A priori one might imagine that the loss function looks like a typical function from $\mathbb{R}^n$ to $\mathbb{R}$ - in particular,…

We extend the concept of loss landscape mode connectivity to the input space of deep neural networks. Mode connectivity was originally studied within parameter space, where it describes the existence of low-loss paths between different…

It has been argued in the past that high-dimensional neural networks do not exhibit local minima capable of trapping an optimisation algorithm. However, the relationship between loss surface modality and the neural architecture parameters,…

Machine Learning with Deep Neural Networks (DNNs) has become a successful tool in solving tasks across various fields of application. However, the complexity of DNNs makes it difficult to understand how they solve their learned task. To…

Loss landscapes are a powerful tool for understanding neural network optimization and generalization, yet traditional low-dimensional analyses often miss complex topological features. We present Landscaper, an open-source Python package for…

The geometric structure of an optimization landscape is argued to be fundamentally important to support the success of deep neural network learning. A direct computation of the landscape beyond two layers is hard. Therefore, to capture the…

The loss landscape of neural networks is a critical aspect of their training, and understanding its properties is essential for improving their performance. In this paper, we investigate how the loss surface changes when the sample size…

Quantification of the stationary points and the associated basins of attraction of neural network loss surfaces is an important step towards a better understanding of neural network loss surfaces at large. This work proposes a novel method…

When training deep neural networks for classification tasks, an intriguing empirical phenomenon has been widely observed in the last-layer classifiers and features, where (i) the class means and the last-layer classifiers all collapse to…

Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve…

Loss landscape analysis is extremely useful for a deeper understanding of the generalization ability of deep neural network models. In this work, we propose a layerwise loss landscape analysis where the loss surface at every layer is…

A central challenge in sensory neuroscience is describing how the activity of populations of neurons can represent useful features of the external environment. However, while neurophysiologists have long been able to record the responses of…

The loss landscapes of deep neural networks are not well understood due to their high nonconvexity. Empirically, the local minima of these loss functions can be connected by a learned curve in model space, along which the loss remains…

Exploring the loss landscape offers insights into the inherent principles of deep neural networks (DNNs). Recent work suggests an additional asymmetry of the valley beyond the flat and sharp ones, yet without thoroughly examining its causes…

Studying neural network loss landscapes provides insights into the nature of the underlying optimization problems. Unfortunately, loss landscapes are notoriously difficult to visualize in a human-comprehensible fashion. One common way to…

We provide the first global optimization landscape analysis of $Neural\;Collapse$ -- an intriguing empirical phenomenon that arises in the last-layer classifiers and features of neural networks during the terminal phase of training. As…

A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…

The work "Loss Landscape Sightseeing with Multi-Point Optimization" (Skorokhodov and Burtsev, 2019) demonstrated that one can empirically find arbitrary 2D binary patterns inside loss surfaces of popular neural networks. In this paper we…