# SpectR: Dynamically Composing LM Experts with Spectral Routing

arXiv: https://arxiv.org/abs/2504.03454 · HTML: https://mlsanity.com/paper/2504.03454/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 54 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 30 of 42)

- [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)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [I-BERT: Integer-only BERT Quantization](https://mlsanity.com/paper/2101.01321/) (2021)
- [The case for 4-bit precision: k-bit Inference Scaling Laws](https://mlsanity.com/paper/2212.09720/) (2022)
- [Simple, Scalable Adaptation for Neural Machine Translation](https://mlsanity.com/paper/1909.08478/) (2019)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [DepGraph: Towards Any Structural Pruning](https://mlsanity.com/paper/2301.12900/) (2023)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)
- [Large Language Model Routing with Benchmark Datasets](https://mlsanity.com/paper/2309.15789/) (2023)
- [Pushing Mixture of Experts to the Limit: Extremely Parameter Efficient MoE for Instruction Tuning](https://mlsanity.com/paper/2309.05444/) (2023)
- [AdaMix: Mixture-of-Adaptations for Parameter-efficient Model Tuning](https://mlsanity.com/paper/2210.17451/) (2022)

## Built on by (most cited first, 6 of 6)

- [Understanding LoRA as Knowledge Memory: An Empirical Analysis](https://mlsanity.com/paper/2603.01097/) (2026)
- [Effective LoRA Adapter Routing using Task Representations](https://mlsanity.com/paper/2601.21795/) (2026)
- [Unveiling Language Routing Isolation in Multilingual MoE Models for Interpretable Subnetwork Adaptation](https://mlsanity.com/paper/2604.03592/) (2026)
- [Parametric Memory Decoding for Zero-Shot Routing in LoRA-Based External Parametric Memory](https://mlsanity.com/paper/2607.04118/) (2026)
- [SEQR: Secure and Efficient QR-based LoRA Routing](https://mlsanity.com/paper/2509.18093/) (2025)
- [GPart: End-to-End Isometric Fine-Tuning via Global Parameter Partitioning](https://mlsanity.com/paper/2605.14841/) (2026)

## Abstract (arXiv)

Training large, general-purpose language models poses significant challenges. The growing availability of specialized expert models, fine-tuned from pretrained models for specific tasks or domains, offers a promising alternative. Leveraging the potential of these existing expert models in real-world applications requires effective methods to select or merge the models best suited for a given task. This paper introduces SPECTR, an approach for dynamically composing expert models at each time step during inference. Notably, our method requires no additional training and enables flexible, token- and layer-wise model combinations. Our experimental results demonstrate that SPECTR improves routing accuracy over alternative training-free methods, increasing task performance across expert domains.