# WMF-AM: Probing LLM Working Memory via Depth-Parameterized Cumulative State Tracking

arXiv: https://arxiv.org/abs/2603.27343 · HTML: https://mlsanity.com/paper/2603.27343/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 63 references that are in the map.
- First posted on arXiv 28 Mar 2026.

## Builds on (most cited first, 30 of 46)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Measurement and Fairness](https://mlsanity.com/paper/1912.05511/) (2019)

## Built on by (most cited first, 4 of 4)

- [World-Model Collapse as a Phase Transition](https://mlsanity.com/paper/2606.31399/) (2026)
- [PathCal: State-Aware Reflection-Marker Calibration for Efficient Reasoning](https://mlsanity.com/paper/2605.23074/) (2026)
- [The Complexity Ceiling Benchmark: A Multi-Domain Evaluation of Sequential Reasoning Under Depth Scaling](https://mlsanity.com/paper/2606.29278/) (2026)
- [CogArena: A Multimethod Evaluation of Cognitive Ability Structure in Large Language Models](https://mlsanity.com/paper/2607.24999/) (2026)

## Abstract (arXiv)

Existing large language models (LLMs) evaluations use fixed-difficulty benchmarks that cannot adapt as models improve, and rarely isolate specific cognitive processes. We introduce Working Memory Fidelity-Active Manipulation (WMF-AM), a probe of cumulative state tracking, the ability to maintain and update intermediate results across K sequential operations within a single query, without a scratchpad. Unlike multi-step agent benchmarks that stress task orchestration, WMF-AM isolates within-pass cumulative load by parameterizing depth K. The core probe uses arithmetic accumulation on 28 models from 12 families (0.5B to frontier); a matched non-arithmetic extension (permissions, schedules, inventories) confirms the design generalizes beyond arithmetic. Three construct-isolation ablations confirm that cumulative load, not arithmetic skill or entity tracking, drives difficulty. We release WMF-AM as a lightweight, recalibratable diagnostic for characterizing where models degrade under cumulative load. Code and data can be accessed at https://github.com/dengzhe-hou/WMF-AM