Repeated-Token Counting Reveals a Dissociation Between Representations and Outputs

Large language models fail at counting repeated tokens despite strong performance on broader reasoning benchmarks. These failures are commonly attributed to limitations in internal count tracking. We show this attribution is wrong. Linear probes on the residual stream decode the correct count with near-perfect accuracy at every post-embedding layer, across all model depths. This holds even at the exact layers where the wrong answer crystallizes while the model simultaneously outputs an incorrect count. Attention patterns show no evidence of collapse over repeated tokens and tokenization artifacts account for none of the failure. Instead, a format-triggered multi-layer perceptron (MLP) block overwrites the correctly-encoded count with a fixed wrong answer at roughly 88--93,% network depth. This prior fires for repeated word-tokens in space-separated list format and is absent for repeated digit-tokens. It is suppressed by comma-separated delimiters in larger models but persists in smaller ones. The finding holds across Llama-3.2 (1B and 3B) and Qwen2.5 (1.5B, 3B and 7B) at consistent relative depth. Counting failure is a failure of routing not of representation and the two require different interventions.

Negative Before Positive: Asymmetric Valence Processing in Large Language Models

Mechanistic interpretability has revealed how concepts are encoded in large language models (LLMs), but emotional content remains poorly understood at the mechanistic level. We study whether LLMs process emotional valence through dedicated internal structure or through surface token matching. Using activation patching and steering on open-source LLMs, we find that negative and positive valence are processed at different network depths. Negative outcomes localize to early layers while positive outcomes peak at mid-to-late layers. Holding topic fixed while flipping valence produces sign-opposite responses, ruling out topic detection. Steering with the good-news direction at the identified layers shifts neutral prompts toward positive valence, showing these layers encode valence as a manipulable direction. Emotional valence in LLMs is localized, causal and steerable, making it a concrete target for interpretability-based oversight.

Large Language Models are Algorithmically Blind

Large language models (LLMs) demonstrate remarkable breadth of knowledge, yet their ability to reason about computational processes remains poorly understood. Closing this gap matters for practitioners who rely on LLMs to guide algorithm selection and deployment. We address this limitation using causal discovery as a testbed and evaluate eight frontier LLMs against ground truth derived from large-scale algorithm executions and find systematic, near-total failure. Models produce ranges far wider than true confidence intervals yet still fail to contain the true algorithmic mean in the majority of instances; most perform worse than random guessing and the marginal above-random performance of the best model is most consistent with benchmark memorization rather than principled reasoning. We term this failure algorithmic blindness and argue it reflects a fundamental gap between declarative knowledge about algorithms and calibrated procedural prediction.

On the Non-Identifiability of Steering Vectors in Large Language Models

Activation steering methods are widely used to control large language model (LLM) behavior and are often interpreted as revealing meaningful internal representations. This interpretation assumes steering directions are identifiable and uniquely recoverable from input-output behavior. We show that, under white-box single-layer access, steering vectors are fundamentally non-identifiable due to large equivalence classes of behaviorally indistinguishable interventions. Empirically, we show that orthogonal perturbations achieve near-equivalent efficacy with negligible effect sizes across multiple models and traits. Critically, we show that the non-identifiability is a robust geometric property that persists across diverse prompt distributions. These findings reveal fundamental interpretability limits and highlight the need for structural constraints beyond behavioral testing to enable reliable alignment interventions.

On the Identifiability of Steering Vectors in Large Language Models

Activation steering methods, such as persona vectors, are widely used to control large language model behavior and increasingly interpreted as revealing meaningful internal representations. This interpretation implicitly assumes steering directions are identifiable and uniquely recoverable from input-output behavior. We formalize steering as an intervention on internal representations and prove that, under realistic modeling and data conditions, steering vectors are fundamentally non-identifiable due to large equivalence classes of behaviorally indistinguishable interventions. Empirically, we validate this across multiple models and semantic traits, showing orthogonal perturbations achieve near-equivalent efficacy with negligible effect sizes. However, identifiability is recoverable under structural assumptions including statistical independence, sparsity constraints, multi-environment validation or cross-layer consistency. These findings reveal fundamental interpretability limits and clarify structural assumptions required for reliable safety-critical control.