# IO-SVD: Input-Output Whitened SVD for Adaptive-Rank LLM Compression

arXiv: https://arxiv.org/abs/2605.15626 · HTML: https://mlsanity.com/paper/2605.15626/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 46 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 30 of 38)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [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)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [Atom: Low-bit Quantization for Efficient and Accurate LLM Serving](https://mlsanity.com/paper/2310.19102/) (2023)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [QServe: W4A8KV4 Quantization and System Co-design for Efficient LLM Serving](https://mlsanity.com/paper/2405.04532/) (2024)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [LUT-GEMM: Quantized Matrix Multiplication based on LUTs for Efficient Inference in Large-Scale Generative Language Models](https://mlsanity.com/paper/2206.09557/) (2022)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [MARLIN: Mixed-Precision Auto-Regressive Parallel Inference on Large Language Models](https://mlsanity.com/paper/2408.11743/) (2024)
- [Dobi-SVD: Differentiable SVD for LLM Compression and Some New Perspectives](https://mlsanity.com/paper/2502.02723/) (2025)

## Abstract (arXiv)

Large language models deliver strong performance across language and reasoning tasks, but their storage and compute costs remain major barriers to deployment in resource-constrained and latency-sensitive settings. SVD-based post-training compression offers a hardware-agnostic way to reduce model size and improve inference efficiency through low-rank factorization. However, existing methods often rely on input-only whitening spaces, homogeneous rank allocation, or loss-agnostic allocation heuristics, limiting their ability to preserve model quality under aggressive compression. We propose Input-Output Whitened SVD (IO-SVD), a post-training compression method that forms a KL-aware double-sided whitening space for model weights. Using a second-order expansion of the KL loss over the top-K token probabilities, IO-SVD constructs an output-side metric that captures predictive sensitivity, while input whitening captures activation statistics. We further introduce an efficient heterogeneous rank-allocation strategy that scores whitened singular components using first-order calibration loss estimates and prunes the least sensitive components under a global budget. Inspired by prior work that combines SVD truncation with quantization, we improve hybrid SVD-quantization compression through loss-aware remapping, which selects low-rank factor rows for 8-bit quantization based on the predicted loss change incurred by quantizing them. Extensive experiments across diverse LLM and VLM families, and inference-time analysis shows that IO-SVD compresses LLMs with minimal performance degradation while delivering practical inference speedups. Code is available at https://github.com/mint-vu/IO-SVD.git