# Progressive distillation induces an implicit curriculum

arXiv: https://arxiv.org/abs/2410.05464 · HTML: https://mlsanity.com/paper/2410.05464/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 84 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 30 of 40)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [A Survey on Retrieval-Augmented Text Generation](https://mlsanity.com/paper/2202.01110/) (2022)
- [Linearized two-layers neural networks in high dimension](https://mlsanity.com/paper/1904.12191/) (2019)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [SGD learning on neural networks: leap complexity and saddle-to-saddle dynamics](https://mlsanity.com/paper/2302.11055/) (2023)
- [The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networks](https://mlsanity.com/paper/2202.08658/) (2022)
- [Sudden Drops in the Loss: Syntax Acquisition, Phase Transitions, and Simplicity Bias in MLMs](https://mlsanity.com/paper/2309.07311/) (2023)
- [Infinite attention: NNGP and NTK for deep attention networks](https://mlsanity.com/paper/2006.10540/) (2020)
- [Best Practices and Lessons Learned on Synthetic Data](https://mlsanity.com/paper/2404.07503/) (2024)
- [In-Context Language Learning: Architectures and Algorithms](https://mlsanity.com/paper/2401.12973/) (2024)
- [Physics of Language Models: Part 1, Learning Hierarchical Language Structures](https://mlsanity.com/paper/2305.13673/) (2023)
- [Unified Visual Transformer Compression](https://mlsanity.com/paper/2203.08243/) (2022)
- [Simplicity Bias in Transformers and their Ability to Learn Sparse Boolean Functions](https://mlsanity.com/paper/2211.12316/) (2022)

## Built on by (most cited first, 15 of 15)

- [Replaying pre-training data improves fine-tuning](https://mlsanity.com/paper/2603.04964/) (2026)
- [What Happens During the Loss Plateau? Understanding Abrupt Learning in Transformers](https://mlsanity.com/paper/2506.13688/) (2025)
- [In Good GRACEs: Principled Teacher Selection for Knowledge Distillation](https://mlsanity.com/paper/2511.02833/) (2025)
- [LLM4Cov: Execution-Aware Agentic Learning for High-coverage Testbench Generation](https://mlsanity.com/paper/2602.16953/) (2026)
- [Provable Benefit of Curriculum in Transformer Tree-Reasoning Post-Training](https://mlsanity.com/paper/2511.07372/) (2025)
- [Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic](https://mlsanity.com/paper/2601.22510/) (2026)
- [Pedagogically-Inspired Data Synthesis for Language Model Knowledge Distillation](https://mlsanity.com/paper/2602.12172/) (2026)
- [Efficient Knowledge Distillation via Curriculum Extraction](https://mlsanity.com/paper/2503.17494/) (2025)
- [The Benefits of Temporal Correlations: SGD Learns k-Juntas from Random Walks Efficiently](https://mlsanity.com/paper/2605.10237/) (2026)
- [Curriculum Learning-Guided Progressive Distillation in Large Language Models](https://mlsanity.com/paper/2605.11260/) (2026)
- [Enhancing Reasoning Capabilities in SLMs with Reward Guided Dataset Distillation](https://mlsanity.com/paper/2507.00054/) (2025)
- [Following the Teacher's Footsteps: Scheduled Checkpoint Distillation for Domain-Specific LLMs](https://mlsanity.com/paper/2601.10114/) (2026)
- [Level Up: Defining and Exploiting Transitional Problems for Curriculum Learning](https://mlsanity.com/paper/2603.13761/) (2026)
- [Knowledge Distillation During Mid-Training Favors Reasoning over Factual Recall](https://mlsanity.com/paper/2609.01532/) (2026)
- [Rank-Reliable Teacher-Guided Fitness Approximation for Expensive Evolutionary Optimization: A TinyML Architecture Search Study](https://mlsanity.com/paper/2609.30553/) (2026)

## Abstract (arXiv)

Knowledge distillation leverages a teacher model to improve the training of a student model. A persistent challenge is that a better teacher does not always yield a better student, to which a common mitigation is to use additional supervision from several ``intermediate'' teachers. One empirically validated variant of this principle is progressive distillation, where the student learns from successive intermediate checkpoints of the teacher. Using sparse parity as a sandbox, we identify an implicit curriculum as one mechanism through which progressive distillation accelerates the student's learning. This curriculum is available only through the intermediate checkpoints but not the final converged one, and imparts both empirical acceleration and a provable sample complexity benefit to the student. We then extend our investigation to Transformers trained on probabilistic context-free grammars (PCFGs) and real-world pre-training datasets (Wikipedia and Books). Through probing the teacher model, we identify an analogous implicit curriculum where the model progressively learns features that capture longer context. Our theoretical and empirical findings on sparse parity, complemented by empirical observations on more complex tasks, highlight the benefit of progressive distillation via implicit curriculum across setups.