Mixture of Chapters: Scaling Learnt Memory in Transformers

Transformers lack an explicit architectural mechanism for storing and organizing knowledge acquired during training. We introduce learnable sparse memory banks: a set of latent tokens, randomly initialized and trained end-to-end, that transformer layers query via cross-attention to retrieve stored knowledge. To scale memory capacity without prohibitive attention costs, we propose chapter-based routing inspired by Mixture-of-Experts architectures, partitioning the memory bank into chapters and training a router to select relevant subsets per input. This enables scaling to 262K memory tokens while maintaining tractable computation. We evaluate our approach against standard transformers (in iso-FLOP settings) on pre-training and instruction fine-tuning across relevant benchmarks. Our models surpass iso-FLOP baselines suggesting scope for a new axis of scaling, demonstrating that explicit associative memory provides complementary capacity to what is captured implicitly in model parameters. Additionally, we observe improved knowledge retention under continued training, with robustness to forgetting when transitioning between training phases (e.g., pretraining to instruction fine-tuning).

SBSC: Step-By-Step Coding for Improving Mathematical Olympiad Performance

We propose Step-by-Step Coding (SBSC): a multi-turn math reasoning framework that enables Large Language Models (LLMs) to generate sequence of programs for solving Olympiad level math problems. At each step/turn, by leveraging the code execution outputs and programs of previous steps, the model generates the next sub-task and the corresponding program to solve it. This way, SBSC, sequentially navigates to reach the final answer. SBSC allows more granular, flexible and precise approach to problem-solving compared to existing methods. Extensive experiments highlight the effectiveness of SBSC in tackling competition and Olympiad-level math problems. For Claude-3.5-Sonnet, we observe SBSC (greedy decoding) surpasses existing state-of-the-art (SOTA) program generation based reasoning strategies by absolute 10.7% on AMC12, 8% on AIME and 12.6% on MathOdyssey. Given SBSC is multi-turn in nature, we also benchmark SBSC's greedy decoding against self-consistency decoding results of existing SOTA math reasoning strategies and observe performance gain by absolute 6.2% on AMC, 6.7% on AIME and 7.4% on MathOdyssey.