# HyperLens: Quantifying Cognitive Effort in LLMs with Fine-grained Confidence Trajectory

arXiv: https://arxiv.org/abs/2605.05741 · HTML: https://mlsanity.com/paper/2605.05741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 47 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 30 of 41)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [Towards AI-Complete Question Answering: A Set of Prerequisite Toy Tasks](https://mlsanity.com/paper/1502.05698/) (2015)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [Information-Theoretic Probing with Minimum Description Length](https://mlsanity.com/paper/2003.12298/) (2020)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Learning to Mine Aligned Code and Natural Language Pairs from Stack Overflow](https://mlsanity.com/paper/1805.08949/) (2018)
- [All Bark and No Bite: Rogue Dimensions in Transformer Language Models Obscure Representational Quality](https://mlsanity.com/paper/2109.04404/) (2021)

## Abstract (arXiv)

While Large Language Models (LLMs) achieve strong performance across diverse tasks, their inference dynamics remain poorly understood because of the limited resolution of existing analysis tools. In this work, we identify an intrinsic magnification mechanism in transformer architectures: deeper layers inherently magnify the small changes of layer-wise confidence, providing a fine-grained confidence trajectory. Building on this insight, we introduce HyperLens, a high-resolution probe designed to trace confidence trajectories and quantify the cognitive effort during inference. Across LLMs and datasets, HyperLens reveals a consistent divergence in confidence trajectories that separates complex from simple tasks. We abstract this pattern into a quantitative cognitive effort metric. Our analysis reveals a fundamental principle: complex tasks consistently require higher cognitive effort. Finally, we provide a mechanistic diagnosis of a common side effect of standard Supervised Fine-Tuning (SFT): it can reduce cognitive effort and consequently degrade performance on in-domain tasks.