# Language Model Cascades: Token-level uncertainty and beyond

arXiv: https://arxiv.org/abs/2404.10136 · HTML: https://mlsanity.com/paper/2404.10136/

## Key facts

- Cited by 121 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 85 references that are in the map.
- First posted on arXiv 15 Apr 2024.

## Builds on (most cited first, 30 of 61)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [SentencePiece: A simple and language independent subword tokenizer and detokenizer for Neural Text Processing](https://mlsanity.com/paper/1808.06226/) (2018)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [BLEURT: Learning Robust Metrics for Text Generation](https://mlsanity.com/paper/2004.04696/) (2020)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Adversarial NLI: A New Benchmark for Natural Language Understanding](https://mlsanity.com/paper/1910.14599/) (2019)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [FlexGen: High-Throughput Generative Inference of Large Language Models with a Single GPU](https://mlsanity.com/paper/2303.06865/) (2023)
- [TyDi QA: A Benchmark for Information-Seeking Question Answering in Typologically Diverse Languages](https://mlsanity.com/paper/2003.05002/) (2020)
- [Towards a Human-like Open-Domain Chatbot](https://mlsanity.com/paper/2001.09977/) (2020)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [How Good Are GPT Models at Machine Translation? A Comprehensive Evaluation](https://mlsanity.com/paper/2302.09210/) (2023)

## Built on by (most cited first, 30 of 121)

- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [Trust or Escalate: LLM Judges with Provable Guarantees for Human Agreement](https://mlsanity.com/paper/2407.18370/) (2024)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [RouterDC: Query-Based Router by Dual Contrastive Learning for Assembling Large Language Models](https://mlsanity.com/paper/2409.19886/) (2024)
- [Universal Model Routing for Efficient LLM Inference](https://mlsanity.com/paper/2502.08773/) (2025)
- [Harnessing Multiple Large Language Models: A Survey on LLM Ensemble](https://mlsanity.com/paper/2502.18036/) (2025)
- [A Unified Approach to Routing and Cascading for LLMs](https://mlsanity.com/paper/2410.10347/) (2024)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)
- [Reasoning Models Better Express Their Confidence](https://mlsanity.com/paper/2505.14489/) (2025)
- [BLoB: Bayesian Low-Rank Adaptation by Backpropagation for Large Language Models](https://mlsanity.com/paper/2406.11675/) (2024)
- [Cost-Effective Online Multi-LLM Selection with Versatile Reward Models](https://mlsanity.com/paper/2405.16587/) (2024)
- [Faster Cascades via Speculative Decoding](https://mlsanity.com/paper/2405.19261/) (2024)
- [A Stitch in Time Saves Nine: Small VLM is a Precise Guidance for Accelerating Large VLMs](https://mlsanity.com/paper/2412.03324/) (2024)
- [CITER: Collaborative Inference for Efficient Large Language Model Decoding with Token-Level Routing](https://mlsanity.com/paper/2502.01976/) (2025)
- [Diversity-Incentivized Exploration for Versatile Reasoning](https://mlsanity.com/paper/2509.26209/) (2025)
- [Estimating LLM Uncertainty with Evidence](https://mlsanity.com/paper/2502.00290/) (2025)
- [LLM Probability Concentration: How Alignment Shrinks the Generative Horizon](https://mlsanity.com/paper/2506.17871/) (2025)
- [Division-of-Thoughts: Harnessing Hybrid Language Model Synergy for Efficient On-Device Agents](https://mlsanity.com/paper/2502.04392/) (2025)
- [A Survey on the Honesty of Large Language Models](https://mlsanity.com/paper/2409.18786/) (2024)
- [CoT-UQ: Improving Response-wise Uncertainty Quantification in LLMs with Chain-of-Thought](https://mlsanity.com/paper/2502.17214/) (2025)
- [LongSpec: Long-Context Lossless Speculative Decoding with Efficient Drafting and Verification](https://mlsanity.com/paper/2502.17421/) (2025)
- [An Empirical Analysis of Uncertainty in Large Language Model Evaluations](https://mlsanity.com/paper/2502.10709/) (2025)
- [Prune 'n Predict: Optimizing LLM Decision-making with Conformal Prediction](https://mlsanity.com/paper/2501.00555/) (2024)
- [Direct Reasoning Optimization: Token-Level Reasoning Reflectivity Meets Rubric Gates for Unverifiable Tasks](https://mlsanity.com/paper/2506.13351/) (2025)
- [On Subjective Uncertainty Quantification and Calibration in Natural Language Generation](https://mlsanity.com/paper/2406.05213/) (2024)
- [Agreement-Based Cascading for Efficient Inference](https://mlsanity.com/paper/2407.02348/) (2024)
- [UncertaintyRAG: Span-Level Uncertainty Enhanced Long-Context Modeling for Retrieval-Augmented Generation](https://mlsanity.com/paper/2410.02719/) (2024)
- [Cost-Aware Contrastive Routing for LLMs](https://mlsanity.com/paper/2508.12491/) (2025)
- [Cascade-Aware Training of Language Models](https://mlsanity.com/paper/2406.00060/) (2024)
- [A Little Help Goes a Long Way: Efficient LLM Training by Leveraging Small LMs](https://mlsanity.com/paper/2410.18779/) (2024)

## Abstract (arXiv)

Recent advances in language models (LMs) have led to significant improvements in quality on complex NLP tasks, but at the expense of increased inference costs. Cascading offers a simple strategy to achieve more favorable cost-quality tradeoffs: here, a small model is invoked for most "easy" instances, while a few "hard" instances are deferred to the large model. While the principles underpinning cascading are well-studied for classification tasks - with deferral based on predicted class uncertainty favored theoretically and practically - a similar understanding is lacking for generative LM tasks. In this work, we initiate a systematic study of deferral rules for LM cascades. We begin by examining the natural extension of predicted class uncertainty to generative LM tasks, namely, the predicted sequence uncertainty. We show that this measure suffers from the length bias problem, either over- or under-emphasizing outputs based on their lengths. This is because LMs produce a sequence of uncertainty values, one for each output token; and moreover, the number of output tokens is variable across examples. To mitigate this issue, we propose to exploit the richer token-level uncertainty information implicit in generative LMs. We argue that naive predicted sequence uncertainty corresponds to a simple aggregation of these uncertainties. By contrast, we show that incorporating token-level uncertainty through learned post-hoc deferral rules can significantly outperform such simple aggregation strategies, via experiments on a range of natural language benchmarks with FLAN-T5 models. We further show that incorporating embeddings from the smaller model and intermediate layers of the larger model can give an additional boost in the overall cost-quality tradeoff.