Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.22695

A Survey on the Linear Representation Hypothesis

Sewoong Lee·Marc E. Canby·Ikhyun Cho·Julia Hockenmaier
View original source ↗Read source document ↗Export metadata ↓

Abstract

The term "linear representation hypothesis" (LRH) has appeared across diverse subfields of artificial intelligence, neuroscience, and cognitive science. But previous works have not consistently treated the LRH as a falsifiable scientific hypothesis; we analyze these inconsistencies and examine their implications for how prior theoretical and methodological results should be interpreted. Based on this analysis, we argue that claims regarding linear representations become well-defined only through careful examination of the model, representation location, feature definition, and evaluation dataset. We therefore propose a more rigorous formalization of the LRH that makes these dependencies explicit and allows the hypothesis to be evaluated as a falsifiable scientific claim. Finally, we identify some non-trivial open problems that warrant further attention from the research community.

Explore related subjects

cs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sewoong Lee, Marc E. Canby, Ikhyun Cho, Julia Hockenmaier. 2026-09-19. A Survey on the Linear Representation Hypothesis. https://arxiv.org/abs/2609.22695

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Memory-Free Continual Learning with Null Space Adaptation for Zero-Shot Vision-Language Models

Pre-trained vision-language models (VLMs), such as CLIP, have demonstrated remarkable zero-shot generalization, enabling deployment in a wide range of real-world tasks without additional task-specific training. However, in real deployment scenarios with evolving environments or emerging classes, these models inevitably face distributional shifts and novel tasks. In such contexts, static zero-shot capabilities are insufficient, and there is a growing need for continual learning methods that allow models to adapt over time while avoiding catastrophic forgetting. We introduce NuSA-CL (Null Space Adaptation for Continual Learning), a lightweight memory-free continual learning framework designed to address this challenge. NuSA-CL employs low-rank adaptation and constrains task-specific weight updates to lie within an approximate null space of the model's current parameters. This strategy minimizes interference with previously acquired knowledge, effectively preserving the zero-shot capabilities of the original model. Unlike methods relying on replay buffers or costly distillation, NuSA-CL imposes minimal computational and memory overhead, making it practical for deployment in resource-constrained, real-world continual learning environments. Experiments show that our framework not only effectively preserves zero-shot transfer capabilities but also achieves highly competitive performance on continual learning benchmarks. These results position NuSA-CL as a practical and scalable solution for continually evolving zero-shot VLMs in real-world applications.

cs.AI↗
arXiv2026

VeRA: Renewing Reasoning Benchmarks with Executable Specifications

Reasoning benchmarks need renewal along two axes: freshness and headroom. VeRA makes both executable and auditable by turning each item into a task family: a natural-language template, an input generator, and a deterministic answer program. VeRA-E draws fresh instances within a family; VeRA-H modifies the family toward harder tasks; and VeRA-H Pro selects one judge-ranked candidate from up to five validated proposals per seed. Execution checks, seed anchoring, answer discrimination, and independent human solving validate specifications and items. Accepted programs generate further labeled instances through local computation. Across 16 models, AIME-2024 accuracy decreases from 84.46% on seeds to 70.25% on VeRA-E variants, exposing a gap between fixed-item success and fresh-instance robustness. On AIME-2024-II, the human-audited VeRA-H Pro release lowers accuracy from 84.91% to 58.57%. Across the three hardening sources, H Pro has lower mean accuracy than H. On AMO-Bench, both releases average higher accuracy than the seeds under the evaluated budget. Initial auditing accepts 75.4% of hardened candidates; targeted repair raises usable yield to 95.1%. Executable families thus support repeatable benchmark renewal, with validation improving task quality and selection shaping the delivered challenge.

cs.AI↗
arXiv2026

When can we trust untrusted monitoring? A safety case sketch across collusion strategies

AIs are increasingly being deployed with greater autonomy and capabilities, which increases the risk that a misaligned AI may be able to cause catastrophic harm. Untrusted monitoring -- using one untrusted model to oversee another -- is one approach to reducing risk. Justifying the safety of an untrusted monitoring deployment is challenging because developers cannot safely deploy a misaligned model to test their protocol directly. In this paper, we develop upon existing methods for rigorously demonstrating safety based on pre-deployment testing. We relax assumptions that previous AI control research made about the collusion strategies a misaligned AI might use to subvert untrusted monitoring. We develop a taxonomy covering passive self-recognition, causal collusion (hiding pre-shared signals), acausal collusion (hiding signals via Schelling points), and combined strategies. We create a safety case sketch to clearly present our argument, explicitly state our assumptions, and highlight unsolved challenges. We identify conditions under which passive self-recognition could be a more effective collusion strategy than those studied previously. Our work builds towards more robust evaluations of untrusted monitoring.

cs.AI↗