# Landscaper: Understanding Loss Landscapes Through Multi-Dimensional Topological Analysis

arXiv: https://arxiv.org/abs/2602.07135 · HTML: https://mlsanity.com/paper/2602.07135/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Builds on (most cited first, 30 of 30)

- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [Qualitatively characterizing neural network optimization problems](https://mlsanity.com/paper/1412.6544/) (2014)
- [Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data](https://mlsanity.com/paper/2002.06716/) (2020)
- [Traditional and Heavy-Tailed Self Regularization in Neural Network Models](https://mlsanity.com/paper/1901.08276/) (2019)
- [On Robustness and Transferability of Convolutional Neural Networks](https://mlsanity.com/paper/2007.08558/) (2020)
- [Traces of Class/Cross-Class Structure Pervade Deep Learning Spectra](https://mlsanity.com/paper/2008.11865/) (2020)
- [The MultiBERTs: BERT Reproductions for Robustness Analysis](https://mlsanity.com/paper/2106.16163/) (2021)
- [A Modern Look at the Relationship between Sharpness and Generalization](https://mlsanity.com/paper/2302.07011/) (2023)
- [Heavy-Tailed Universality Predicts Trends in Test Accuracies for Very Large Pre-Trained Deep Neural Networks](https://mlsanity.com/paper/1901.08278/) (2019)
- [Taxonomizing local versus global structure in neural network loss landscapes](https://mlsanity.com/paper/2107.11228/) (2021)
- [The Goldilocks zone: Towards better understanding of neural network loss landscapes](https://mlsanity.com/paper/1807.02581/) (2018)
- [Wide-minima Density Hypothesis and the Explore-Exploit Learning Rate Schedule](https://mlsanity.com/paper/2003.03977/) (2020)
- [An empirical analysis of the optimization of deep network loss surfaces](https://mlsanity.com/paper/1612.04010/) (2016)
- [Evaluating natural language processing models with generalization metrics that do not need access to any training or testing data](https://mlsanity.com/paper/2202.02842/) (2022)
- [A Three-regime Model of Network Pruning](https://mlsanity.com/paper/2305.18383/) (2023)
- [Mitigating Memorization In Language Models](https://mlsanity.com/paper/2410.02159/) (2024)
- [Evaluating Loss Landscapes from a Topology Perspective](https://mlsanity.com/paper/2411.09807/) (2024)
- [Visualizing Loss Functions as Topological Landscape Profiles](https://mlsanity.com/paper/2411.12136/) (2024)
- [LossLens: Diagnostics for Machine Learning through Loss Landscape Visual Analytics](https://mlsanity.com/paper/2412.13321/) (2024)

## Built on by (most cited first, 1 of 1)

- [A Geometric Perspective on Stabilizing Value Conflict Resolution](https://mlsanity.com/paper/2607.17946/) (2026)

## Abstract (arXiv)

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 arbitrary-dimensional loss landscape analysis. Landscaper combines Hessian-based subspace construction with topological data analysis to reveal geometric structures such as basin hierarchy and connectivity. A key component is the Saddle-Minimum Average Distance (SMAD) for quantifying landscape smoothness. We demonstrate Landscaper's effectiveness across various architectures and tasks, including those involving pre-trained language models, showing that SMAD captures training transitions, such as landscape simplification, that conventional metrics miss. We also illustrate Landscaper's performance in challenging chemical property prediction tasks, where SMAD can serve as a metric for out-of-distribution generalization, offering valuable insights for model diagnostics and architecture design in data-scarce scientific machine learning scenarios.