# Hyperdimensional Probe: Decoding LLM Representations via Vector Symbolic Architectures

arXiv: https://arxiv.org/abs/2509.25045 · HTML: https://mlsanity.com/paper/2509.25045/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge and representations inside LLMs, one of 13 directions in Mechanistic interpretability.
- Builds on 35 of its 58 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

- Mechanistic interpretability / [Knowledge and representations inside LLMs](https://mlsanity.com/mechinterp/knowledge-and-representations-inside-llms/)

## Builds on (most cited first, 30 of 35)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [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)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Transcoders Find Interpretable LLM Feature Circuits](https://mlsanity.com/paper/2406.11944/) (2024)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [Residual Connections Encourage Iterative Inference](https://mlsanity.com/paper/1710.04773/) (2017)
- [A comparison of Vector Symbolic Architectures](https://mlsanity.com/paper/2001.11797/) (2020)
- [A Neuro-vector-symbolic Architecture for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2203.04571/) (2022)
- [Interpreting Attention Layer Outputs with Sparse Autoencoders](https://mlsanity.com/paper/2406.17759/) (2024)
- [A polar coordinate system represents syntax in large language models](https://mlsanity.com/paper/2412.05571/) (2024)
- [Attention Lens: A Tool for Mechanistically Interpreting the Attention Head Information Retrieval Mechanism](https://mlsanity.com/paper/2310.16270/) (2023)
- [Torchhd: An Open Source Python Library to Support Research on Hyperdimensional Computing and Vector Symbolic Architectures](https://mlsanity.com/paper/2205.09208/) (2022)

## Built on by (most cited first, 3 of 3)

- [Is One Layer Enough? Understanding Inference Dynamics in Tabular Foundation Models](https://mlsanity.com/paper/2605.06510/) (2026)
- [The Emergent Symbolic Structure of Artificial Neural Networks](https://mlsanity.com/paper/2608.29530/) (2026)
- [Where Polanyi Meets Galois: Tacit Knowing as an Algebro-Deterministic Operation, Toward Re-rooting AI-Generated Science](https://mlsanity.com/paper/2610.16102/) (2026)

## Abstract (arXiv)

Despite their capabilities, Large Language Models (LLMs) remain opaque with limited understanding of their internal representations. Current interpretability methods either focus on input-oriented feature extraction, such as supervised probes and Sparse Autoencoders (SAEs), or on output distribution inspection, such as logit-oriented approaches. A full understanding of LLM vector spaces, however, requires integrating both perspectives, something existing approaches struggle with due to constraints on latent feature definitions. We introduce the Hyperdimensional Probe, a hybrid supervised probe that combines symbolic representations with neural probing. Leveraging Vector Symbolic Architectures (VSAs) and hypervector algebra, it unifies prior methods: the top-down interpretability of supervised probes, SAE's sparsity-driven proxy space, and output-oriented logit investigation. By combining the supervised learning paradigm of traditional probes with the dictionary-based representation principle of SAEs, our approach enables deeper input-focused feature extraction while supporting output-oriented analysis. Our experiments demonstrate that our approach consistently extracts meaningful semantic information across different LLMs, embedding sizes, and configurations, uncovering concept-oriented insights into LLM inference across two distinct scenarios: input-completion tasks and QA-focused text generation. VSA-based probing overcomes the limitations of logit-based analyses, which are constrained by the model's token vocabulary, while also mitigating the noisier interpretability outcomes often produced by SAEs in settings with a bounded conceptual feature space. By supporting a joint investigation of input-output features, this work advances the semantic understanding of neural representations while unifying the complementary perspectives of prior methods.