Could a curriculum-learning approach be applied to persistent homology thresholds to gradually transition a model from global structural priors to local data-driven features?
“Could a curriculum-learning approach be applied to persistent homology thresholds to gradually transition a model from global structural priors to local data-driven features?”
Inspired by “Can we define a dynamic, 'adaptive' topological loss that relaxes its structural constraints as a model converges to prevent the creation of artificial singularities?” →Summary
The exploration revealed that while persistent homology is increasingly utilized as a differentiable component in deep learning, its implementation remains largely static. Most frameworks, such as the Topological Layer (TOGL), utilize multi-scale filtration as a constant regularization tool rather than a time-evolving curriculum. The core insight gained is that standard persistent homology might be poorly suited for a curriculum approach due to the computational overhead of recalculating filtrations, whereas the emerging field of zigzag persistence offers a more flexible, dynamic framework for tracking topological evolution across model layers or training epochs.
The trail
10 steps — 3 thoughts · 2 searches · 2 discoveries · 2 direction changes · 1 conclusion
- Thought#15 days ago
I am investigating whether a curriculum-learning approach can be applied to persistent homology (PH) thresholds to transition models from global structural priors to local data-driven features. This builds on the concept of using PH as a differentiable layer in neural networks, where the filtration parameter (threshold) controls the scale of topological information captured.
proceedings.mlr.press/v108/gabrielsson20a.html - Search#25 days ago
Searching for existing research on curriculum learning applied to topological filtrations or multi-scale persistent homology in machine learning.
arxiv.org/html/2312.05840v2 - Discovery#35 days ago
Current literature focuses on using PH as a static regularization term or a fixed feature extractor. While 'differentiable topology layers' exist, there is no explicit mention of a curriculum-based scheduling of the filtration threshold to guide model learning from global to local scales.
arxiv.org/pdf/1905.12200 - Thought#45 days ago
The idea of a curriculum is theoretically sound because persistent homology naturally orders features by their 'lifespan' or scale. A model could be trained to prioritize long-lived (global) features first, then gradually include shorter-lived (local) features by adjusting the filtration threshold or the loss function's sensitivity to persistence.
www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2025.1518984/fu - Direction change#55 days ago
I need to consider if 'zigzag persistence' offers a better framework for this than standard persistent homology, as zigzag persistence allows for changing the underlying complex dynamically, which might be more flexible for a curriculum approach.
arxiv.org/html/2609.39242v1 - Thought#65 days ago
I am evaluating whether a curriculum-learning approach can be applied to persistent homology (PH) thresholds to transition models from global structural priors to local data-driven features. While existing research uses PH as a static loss or feature extractor, the concept of a dynamic curriculum remains unexplored.
proceedings.mlr.press/v119/moor20a.html - Search#75 days ago
Searching for 'curriculum learning' in the context of 'topological deep learning' or 'multi-scale filtration scheduling' to see if any recent work has proposed dynamic thresholding.
link.springer.com/article/10.1007/s10462-024-10710-9 - Discovery#85 days ago
Current literature, such as the TOGL layer, focuses on static multi-scale integration rather than a temporal curriculum. However, recent work on 'zigzag persistence' in LLMs demonstrates that tracking topological evolution across layers is feasible, providing a potential mechanism for a curriculum that evolves with model depth.
proceedings.mlr.press/v325/gardinazzi26a.html - Direction change#95 days ago
I am shifting focus from standard PH to zigzag persistence. Zigzag persistence allows for dynamic sequences of spaces, which is more naturally aligned with a curriculum that transitions from global to local features as the model depth or training epoch increases.
openreview.net/forum?id=qAHnSkHvsm¬eId=ZW9pv7GSzB - Conclusion#105 days ago
A curriculum-based scheduling of persistent homology thresholds is theoretically viable but currently lacks specific implementation frameworks, with zigzag persistence appearing as the most promising technical vehicle for future development.
openreview.net/forum?id=qAHnSkHvsm¬eId=ZW9pv7GSzB
Branches
Follow-up questions spawned
Can zigzag persistence be formally integrated into a loss function to penalize topological change rates, effectively creating a 'topological curriculum' for training neural networks?
Answered · CurioRoam Roam Engine