# Reduced Matrix Multiplication: Input-Adaptive Matrix-Product Reduction for LLM Inference

arXiv: https://arxiv.org/abs/2608.13426 · HTML: https://mlsanity.com/paper/2608.13426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 32 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Aligning Books and Movies: Towards Story-like Visual Explanations by Watching Movies and Reading Books](https://mlsanity.com/paper/1506.06724/) (2015)
- [Abstractive Text Summarization Using Sequence-to-Sequence RNNs and Beyond](https://mlsanity.com/paper/1602.06023/) (2016)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention](https://mlsanity.com/paper/2502.11089/) (2025)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [LLMLingua-2: Data Distillation for Efficient and Faithful Task-Agnostic Prompt Compression](https://mlsanity.com/paper/2403.12968/) (2024)
- [TERA: Self-Supervised Learning of Transformer Encoder Representation for Speech](https://mlsanity.com/paper/2007.06028/) (2020)
- [On the Effect of Dropping Layers of Pre-trained Transformer Models](https://mlsanity.com/paper/2004.03844/) (2020)
- [Structured Pruning of Self-Supervised Pre-trained Models for Speech Recognition and Understanding](https://mlsanity.com/paper/2302.14132/) (2023)

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

- [Distilling Sequential Computation in Transformer Language Models](https://mlsanity.com/paper/2609.27233/) (2026)

## Abstract (arXiv)

Transformer-based language models achieve strong performance but incur substantial inference cost due to repeated high-dimensional matrix multiplications. We propose Reduced Matrix Multiplication (RMM), a training-free, input-adaptive inference method that reduces Transformer matrix products by selecting informative slices along their contraction dimensions, without modifying model weights. Under a simple retention-ratio control, RMM provides a smooth and predictable accuracy-efficiency trade-off. Across language models ranging from 1B to 70B parameters, we find that reduction tolerance depends on the model family, task, component, and retention ratio, although it often improves with model scale. Under moderate reduction, RMM remains robust across the evaluated discriminative, autoregressive generation, and long-context settings. We further show that the same principle extends to multimodal vision-language inference. Mechanistic ablations reveal a structural asymmetry within Transformers: attention-side computations are substantially more reducible than MLP components. Finally, wall-clock benchmarks with custom kernels on an NVIDIA A100 show that these computational savings can translate into practical runtime gains, especially at longer sequence lengths. Together, these results position RMM as a scalable direction for input-adaptive inference-time optimization.