# Structuring Relations Among Learning Paradigms via Protocol--Objective--Resource Reductions

arXiv: https://arxiv.org/abs/2609.32766 · HTML: https://mlsanity.com/paper/2609.32766/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 62 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
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- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
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- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Minimax Lower Bounds for Transfer Learning with Linear and One-hidden Layer Neural Networks](https://mlsanity.com/paper/2006.10581/) (2020)
- [Towards Robust Graph Incremental Learning on Evolving Graphs](https://mlsanity.com/paper/2402.12987/) (2024)
- [MSPipe: Efficient Temporal GNN Training via Staleness-Aware Pipeline](https://mlsanity.com/paper/2402.15113/) (2024)
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- [On the Limitation and Experience Replay for GNNs in Continual Learning](https://mlsanity.com/paper/2302.03534/) (2023)
- [Temporal-Aware Evaluation and Learning for Temporal Graph Neural Networks](https://mlsanity.com/paper/2412.07273/) (2024)
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- [Improving Implicit Regularization of SGD with Preconditioning for Least Square Problems](https://mlsanity.com/paper/2403.08585/) (2024)
- [A Non-Asymptotic Convergent Analysis for Scored-Based Graph Generative Model via a System of Stochastic Differential Equations](https://mlsanity.com/paper/2508.14351/) (2025)
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- [On the Interplay between Graph Structure and Learning Algorithms in Graph Neural Networks](https://mlsanity.com/paper/2508.14338/) (2025)
- [Full-Graph vs. Mini-Batch Training: Comprehensive Analysis from a Batch Size and Fan-Out Size Perspective](https://mlsanity.com/paper/2601.22678/) (2026)
- [When Do Multi-Agent Systems Outperform? Analysing the Learning Efficiency of Agentic Systems](https://mlsanity.com/paper/2602.08272/) (2026)
- [Structuring Semantic Embeddings for Principle Evaluation: A Prototype-Guided Contrastive Learning Approach](https://mlsanity.com/paper/2608.15224/) (2026)

## Abstract (arXiv)

Modern machine learning spans supervised, transfer, continual, meta-learning, and related regimes that often reuse the same hypothesis classes, architectures, and optimizers but differ in information access, objectives, memory, adaptation, and sample accounting. This makes it difficult to determine whether one paradigm is genuinely distinct, a special case of another, or part of a broader structural hierarchy. We introduce a protocol-objective-resource (POR) framework that separates representational capacity from these design choices. A paradigm is specified by an environment class, observation protocol, admissible learners, performance functional, and resource accounting rule. POR reductions combine environment embeddings, learner compilers, threshold maps, and calibrated resource overheads. Our main theorem shows that such reductions imply worst-case complexity domination on embedded comparison classes, transferring upper bounds forward and lower bounds backward; under labeled-example accounting, this yields sample complexity domination. We also show that calibrated nontrivial accuracy regimes are necessary to avoid vacuous comparisons, and that strengthening the objective can strictly increase minimax sample complexity even with unchanged protocols and learner classes. Instantiating the framework for supervised, transfer, continual, and meta-learning yields canonical special-case relations: continual contains transfer, transfer contains supervised, and meta-learning contains supervised under aligned raw-example accounting. We further derive a non-exact episode-to-example reduction for episodic meta-learning and capture within-paradigm refinements such as replay memory and task identifiers. The framework thus provides a unified language for structuring learning paradigms and transferring complexity guarantees across them.