# The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction

arXiv: https://arxiv.org/abs/2312.13558 · HTML: https://mlsanity.com/paper/2312.13558/

## Key facts

- Cited by 123 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 21 Dec 2023.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 27 of 27)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [Measuring and Improving Consistency in Pretrained Language Models](https://mlsanity.com/paper/2102.01017/) (2021)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Fine-grained Analysis of Sentence Embeddings Using Auxiliary Prediction Tasks](https://mlsanity.com/paper/1608.04207/) (2016)
- [Surgical Fine-Tuning Improves Adaptation to Distribution Shifts](https://mlsanity.com/paper/2210.11466/) (2022)
- [Learning Low-rank Deep Neural Networks via Singular Vector Orthogonality Regularization and Singular Value Sparsification](https://mlsanity.com/paper/2004.09031/) (2020)
- [Characterizing Intrinsic Compositionality in Transformers with Tree Projections](https://mlsanity.com/paper/2211.01288/) (2022)
- [Pruning's Effect on Generalization Through the Lens of Training and Regularization](https://mlsanity.com/paper/2210.13738/) (2022)
- [Of Non-Linearity and Commutativity in BERT](https://mlsanity.com/paper/2101.04547/) (2021)

## Built on by (most cited first, 30 of 123)

- [Assessing the Brittleness of Safety Alignment via Pruning and Low-Rank Modifications](https://mlsanity.com/paper/2402.05162/) (2024)
- [The Unreasonable Ineffectiveness of the Deeper Layers](https://mlsanity.com/paper/2403.17887/) (2024)
- [LLM Inference Unveiled: Survey and Roofline Model Insights](https://mlsanity.com/paper/2402.16363/) (2024)
- [How do Large Language Models Handle Multilingualism?](https://mlsanity.com/paper/2402.18815/) (2024)
- [The Remarkable Robustness of LLMs: Stages of Inference?](https://mlsanity.com/paper/2406.19384/) (2024)
- [Rethinking Interpretability in the Era of Large Language Models](https://mlsanity.com/paper/2402.01761/) (2024)
- [LoRA vs Full Fine-tuning: An Illusion of Equivalence](https://mlsanity.com/paper/2410.21228/) (2024)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap](https://mlsanity.com/paper/2402.19450/) (2024)
- [Palu: Compressing KV-Cache with Low-Rank Projection](https://mlsanity.com/paper/2407.21118/) (2024)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [LoFiT: Localized Fine-tuning on LLM Representations](https://mlsanity.com/paper/2406.01563/) (2024)
- [Spectral Filters, Dark Signals, and Attention Sinks](https://mlsanity.com/paper/2402.09221/) (2024)
- [LoRC: Low-Rank Compression for LLMs KV Cache with a Progressive Compression Strategy](https://mlsanity.com/paper/2410.03111/) (2024)
- [Pruner-Zero: Evolving Symbolic Pruning Metric from scratch for Large Language Models](https://mlsanity.com/paper/2406.02924/) (2024)
- [Weight decay induces low-rank attention layers](https://mlsanity.com/paper/2410.23819/) (2024)
- [Pruning for Protection: Increasing Jailbreak Resistance in Aligned LLMs Without Fine-Tuning](https://mlsanity.com/paper/2401.10862/) (2024)
- [Holmes: A Benchmark to Assess the Linguistic Competence of Language Models](https://mlsanity.com/paper/2404.18923/) (2024)
- [Compress then Serve: Serving Thousands of LoRA Adapters with Little Overhead](https://mlsanity.com/paper/2407.00066/) (2024)
- [The Universal Weight Subspace Hypothesis](https://mlsanity.com/paper/2512.05117/) (2025)
- [Efficient Learning With Sine-Activated Low-rank Matrices](https://mlsanity.com/paper/2403.19243/) (2024)
- [Faster and Lighter LLMs: A Survey on Current Challenges and Way Forward](https://mlsanity.com/paper/2402.01799/) (2024)
- [Small Singular Values Matter: A Random Matrix Analysis of Transformer Models](https://mlsanity.com/paper/2410.17770/) (2024)
- [On Efficient Variants of Segment Anything Model: A Survey](https://mlsanity.com/paper/2410.04960/) (2024)
- [Towards a theory of model distillation](https://mlsanity.com/paper/2403.09053/) (2024)
- [Understanding the Language Model to Solve the Symbolic Multi-Step Reasoning Problem from the Perspective of Buffer Mechanism](https://mlsanity.com/paper/2405.15302/) (2024)
- [UNComp: Can Matrix Entropy Uncover Sparsity? -- A Compressor Design from an Uncertainty-Aware Perspective](https://mlsanity.com/paper/2410.03090/) (2024)
- [Sculpting Subspaces: Constrained Full Fine-Tuning in LLMs for Continual Learning](https://mlsanity.com/paper/2504.07097/) (2025)
- [SLIP: Securing LLMs IP Using Weights Decomposition](https://mlsanity.com/paper/2407.10886/) (2024)
- [Guiding Reasoning in Small Language Models with LLM Assistance](https://mlsanity.com/paper/2504.09923/) (2025)

## Abstract (arXiv)

Transformer-based Large Language Models (LLMs) have become a fixture in modern machine learning. Correspondingly, significant resources are allocated towards research that aims to further advance this technology, typically resulting in models of increasing size that are trained on increasing amounts of data. This work, however, demonstrates the surprising result that it is often possible to significantly improve the performance of LLMs by selectively removing higher-order components of their weight matrices. This simple intervention, which we call LAyer-SElective Rank reduction (LASER), can be done on a model after training has completed, and requires no additional parameters or data. We show extensive experiments demonstrating the generality of this finding across language models and datasets, and provide in-depth analyses offering insights into both when LASER is effective and the mechanism by which it operates.