# Small Models, Smarter Learning: The Power of Joint Task Training

arXiv: https://arxiv.org/abs/2505.18369 · HTML: https://mlsanity.com/paper/2505.18369/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 23 May 2025.

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

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [Physics of Language Models: Part 3.3, Knowledge Capacity Scaling Laws](https://mlsanity.com/paper/2404.05405/) (2024)
- [ListOps: A Diagnostic Dataset for Latent Tree Learning](https://mlsanity.com/paper/1804.06028/) (2018)
- [Teaching Arithmetic to Small Transformers](https://mlsanity.com/paper/2307.03381/) (2023)
- [Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task](https://mlsanity.com/paper/2310.09336/) (2023)
- [Strategic Data Ordering: Enhancing Large Language Model Performance through Curriculum Learning](https://mlsanity.com/paper/2405.07490/) (2024)
- [A Percolation Model of Emergence: Analyzing Transformers Trained on a Formal Language](https://mlsanity.com/paper/2408.12578/) (2024)
- [MuMath-Code: Combining Tool-Use Large Language Models with Multi-perspective Data Augmentation for Mathematical Reasoning](https://mlsanity.com/paper/2405.07551/) (2024)
- [Intelligence at the Edge of Chaos](https://mlsanity.com/paper/2410.02536/) (2024)
- [Task Generalization With AutoRegressive Compositional Structure: Can Learning From D Tasks Generalize to DT Tasks?](https://mlsanity.com/paper/2502.08991/) (2025)
- [Benchmarking GPT-4 on Algorithmic Problems: A Systematic Evaluation of Prompting Strategies](https://mlsanity.com/paper/2402.17396/) (2024)
- [Investigating Symbolic Capabilities of Large Language Models](https://mlsanity.com/paper/2405.13209/) (2024)

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

- [Learning Large-Scale Modular Addition with an Auxiliary Modulus](https://mlsanity.com/paper/2605.07648/) (2026)

## Abstract (arXiv)

Multi-task learning improves generalization, but when does it reduce the model capacity required to learn? We provide a systematic study of how joint training affects the learning transition, the minimum model size at which a task can be learned, using nested arithmetic (ListOps) and permutation groups as controlled testbeds. Certain task pairings dramatically reduce model size requirements: combining easy operations (MAX, MIN, PROD) with hard ones (modular addition, permutation products) enables learning with 2-7 times fewer parameters. Crucially, we also identify when synergies fail: pairing structurally similar hard tasks (e.g., ADD with alternating-sign NADD) provides no benefit, nor does pairing tasks lacking shared computational primitives. PCA of learned embeddings reveals that successful joint training induces structured number representations (ordering, parity, modular structure) absent in single-task models. Transfer experiments confirm these representations are causal: models pretrained on easy tasks learn addition at 7 times smaller sizes. Our results establish that task compatibility, not mere diversity, determines whether joint training reduces capacity requirements, providing quantitative guidance for curriculum design.