The Phenomenology of Hallucinations

We show that language models hallucinate not because they fail to detect uncertainty, but because of a failure to integrate it into output generation. Across architectures, uncertain inputs are reliably identified, occupying high-dimensional regions with 2-3$\times$ the intrinsic dimensionality of factual inputs. However, this internal signal is weakly coupled to the output layer: uncertainty migrates into low-sensitivity subspaces, becoming geometrically amplified yet functionally silent. Topological analysis shows that uncertainty representations fragment rather than converging to a unified abstention state, while gradient and Fisher probes reveal collapsing sensitivity along the uncertainty direction. Because cross-entropy training provides no attractor for abstention and uniformly rewards confident prediction, associative mechanisms amplify these fractured activations until residual coupling forces a committed output despite internal detection. Causal interventions confirm this account by restoring refusal when uncertainty is directly connected to logits.

Beyond position: how rotary embeddings shape representations and memory in autoregressive transfomers

Rotary Positional Embeddings (RoPE) enhance positional encoding in Transformer models, yet their full impact on model dynamics remains underexplored. This paper studies how RoPE introduces position-dependent rotations, causing phase shifts in token embeddings that influence higher-frequency components within the model's internal representations. Through spectral analysis, we demonstrate that RoPE's rotation matrices induce oscillatory behaviors in embeddings, affecting information retention across layers and shaping temporal modeling capabilities. We show that activation functions in feed-forward networks interact with RoPE-modulated embeddings to generate harmonics, leading to constructive or destructive interference based on phase alignment. Our findings reveal that phase alignment amplifies activations and sharpens attention, while misalignment weakens activations and disrupts focus on positional patterns. This study underscores the importance of frequency components as intrinsic elements of model behavior, offering new insights beyond traditional analyses.

Attention-likelihood relationship in transformers

We analyze how large language models (LLMs) represent out-of-context words, investigating their reliance on the given context to capture their semantics. Our likelihood-guided text perturbations reveal a correlation between token likelihood and attention values in transformer-based language models. Extensive experiments reveal that unexpected tokens cause the model to attend less to the information coming from themselves to compute their representations, particularly at higher layers. These findings have valuable implications for assessing the robustness of LLMs in real-world scenarios. Fully reproducible codebase at https://github.com/Flegyas/AttentionLikelihood.