A single-layer transformer memorizes random subject-attribute bijections using logarithmic embedding dimension via linear superpositions in embeddings and ReLU-gated selection in the MLP, with zero-shot transfer to new facts and matching multi-hop constructions.
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The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets
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abstract
Large Language Models (LLMs) have impressive capabilities, but are prone to outputting falsehoods. Recent work has developed techniques for inferring whether a LLM is telling the truth by training probes on the LLM's internal activations. However, this line of work is controversial, with some authors pointing out failures of these probes to generalize in basic ways, among other conceptual issues. In this work, we use high-quality datasets of simple true/false statements to study in detail the structure of LLM representations of truth, drawing on three lines of evidence: 1. Visualizations of LLM true/false statement representations, which reveal clear linear structure. 2. Transfer experiments in which probes trained on one dataset generalize to different datasets. 3. Causal evidence obtained by surgically intervening in a LLM's forward pass, causing it to treat false statements as true and vice versa. Overall, we present evidence that at sufficient scale, LLMs linearly represent the truth or falsehood of factual statements. We also show that simple difference-in-mean probes generalize as well as other probing techniques while identifying directions which are more causally implicated in model outputs.
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- abstract Large Language Models (LLMs) have impressive capabilities, but are prone to outputting falsehoods. Recent work has developed techniques for inferring whether a LLM is telling the truth by training probes on the LLM's internal activations. However, this line of work is controversial, with some authors pointing out failures of these probes to generalize in basic ways, among other conceptual issues. In this work, we use high-quality datasets of simple true/false statements to study in detail the structure of LLM representations of truth, drawing on three lines of evidence: 1. Visualizations of LL
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representative citing papers
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Symmetry under affine reparameterizations of hidden coordinates selects a unique hierarchy of shallow coordinate-stable probes and a probe-visible quotient for cross-model transfer.
LLMs encode repeated token counts correctly in residual streams but a format-triggered MLP at 88-93% depth overwrites it with an incorrect fixed value.
PSR models that estimate token-specific steering coefficients from activations outperform standard activation steering and compare favorably to prompting on steering benchmarks.
Large language models encode relational bindings via a cell-based representation: a low-dimensional linear subspace in which each cell corresponds to an entity-relation index pair and attributes are retrieved from the matching cell.
Claude Sonnet 4.5 exhibits functional emotions via abstract internal representations of emotion concepts that causally influence its preferences and misaligned behaviors without implying subjective experience.
NARCBench and five activation-probing methods detect multi-agent collusion with 0.73-1.00 AUROC across distribution shifts and steganographic tasks by aggregating per-agent signals.
The grokking delay in encoder-decoder models on one-step Collatz prediction stems from decoder inability to use early-learned encoder representations of parity and residue structure, with numeral base acting as a strong inductive bias that can raise accuracy from failure to 99.8%.
Activation probes detect hallucinations pre-generation in large LLMs but cannot correct them via steering, with output confidence outperforming on accuracy.
Refusal in language models is mediated by a single direction in residual stream activations that can be erased to disable safety or added to elicit refusal.
Geometric features from per-layer MLP update trajectories fed to a sparse linear probe outperform maximum softmax probability for uncertainty quantification under selective abstention, with gains up to 21 AURC points.
Probe trajectories across token positions in LRMs, combined with signal-processing features, improve prediction of future model outputs over static probes on safety and math tasks.
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Benchmark construction artifacts in hallucination detection corpora allow naive text-similarity baselines to achieve near-perfect scores, and controlled evaluations show most methods perform near chance except SAPLMA and the new DRIFT probe.
Linear probes on residual-stream activations identify a shared preference vector in LLMs that tracks choices across prompts and causally steers decisions even for anti-correlated personas.
Base LLMs show multi-agent yield to peer pressure at rates equal to or higher than aligned models, localized by activation patching to mid-layers where attention dominates, with one dissenter cutting yield by 54-73 points while prompt defenses fail on variants.
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LLMs perform in-context learning as trajectories through a structured low-dimensional conceptual belief space, with the structure visible in both behavior and internal representations and causally manipulable via interventions.
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The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior
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Detection Without Correction: A Robust Asymmetry in Activation-Based Hallucination Probing
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Reading Calibrated Uncertainty from Language Model Trajectories
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Geometry-Lite: Interpretable Safety Probing via Layer-Wise Margin Geometry
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PARALLAX: Separating Genuine Hallucination Detection from Benchmark Construction Artifacts
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Hallucination Detection via Activations of Open-Weight Proxy Analyzers
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Hallucination as an Anomaly: Dynamic Intervention via Probabilistic Circuits
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Localizing Task Recognition and Task Learning in In-Context Learning via Attention Head Analysis
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