Algorithmic Scratchpads and Curriculum Staging for Arithmetic Reasoning in Tiny Transformers

arXiv:2610.09003 · cs.LG, cs.AI · Submitted 2026-10-06 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-10-06

Updated: 2026-10-06

Comments: 16 pages, 5 figures. Code and benchmark datasets available at https://github.com/SoKasl/AIMathLab

Code: https://github.com/SoKasl/AIMathLab

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Transformer — 1× in this paper · explained in 2 episodes

Sources

• Training Verifiers to Solve Math Word Problems
• TinyStories: How Small Can Language Models Be and Still Speak Coherent English?
• Teaching Arithmetic to Small Transformers
• Pointer Sentinel Mixture Models
• Investigating the Limitations of Transformers with Simple Arithmetic Tasks
• Show Your Work: Scratchpads for Intermediate Computation with Language Models
• GLU Variants Improve Transformer
• Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: The Predictive Cost of ELBO Binding
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks