Valeria Ruscio

Valeria Ruscio, Umberto Nanni, Fabrizio Silvestri

RoPE-trained transformers distinguish absolute position in their attention patterns, even though RoPE encodes only relative offsets in the inner product. We trace this leakage to two architectural components, The causal mask is responsible for the first: its per-query softmax denominator depends on the absolute query position by construction. The residual stream supplies the second. Under causal attention the activation at position $0$ attends only to itself and runs as a closed dynamical system from the embedding of the token at that position; downstream attention reads this trajectory through sink-reading heads. Both components appear in all three architectures we study, in architecturally specific balance: NTK scaling suppresses the residual-stream component, sliding-window attention allows it to accumulate with depth, and standard RoPE sits between. Replacing the \texttt{BOS} embedding before the forward pass removes $40\%$ of the residual-stream component at early queries. Attention sinks are token-anchored stabilizers that pass forward a deterministic fingerprint of the token at position $0$, constant across inputs when that token is the auto-prepended \texttt{BOS} and varying with it otherwise.

Valeria Ruscio, Valentino Maiorca, Fabrizio Silvestri

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.

Valeria Ruscio, Keiran Thompson

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.

Valeria Ruscio, Eli-Shaoul Khedouri, Keiran Thompson

Cross-entropy pretraining and preference alignment update the same transformer weights, but leave geometrically distinct traces. We characterise this asymmetry with a relative-subspace-fraction probe that tracks how weight deltas align with residual-stream activation subspaces and with the prediction subspace defined by the unembedding. Alignment deltas concentrate in the read pathway ($W_Q$, $W_K$), along principal directions of attention-input activations, while remaining near-isotropic in the write pathway ($W_O$, $W_2$) relative to the prediction subspace. We explain this pattern through anisotropic gradient accumulation: updates to a matrix $W$ are sums of outer products $δ_t a_t^\top$, and inherit directional structure from whichever side has concentrated covariance. For read-pathway matrices, this side is the input activation $a_t$, whose covariance is spiked in trained transformers and therefore produces objective-agnostic concentration. For write-pathway matrices, the relevant side is the upstream gradient $δ_t$, whose anisotropy depends on the loss. Cross-entropy supplies the canonical sharp per-sample signal, inducing write-pathway prediction geometry during pretraining; alignment objectives typically add little further write-side concentration. We support this explanation with a within-checkpoint trajectory, a graded contrastive-objective control, and a closed-form rank-1 intervention with matched direction controls, providing causal evidence for the proposed weight-space geometry.

Valeria Ruscio, Umberto Nanni, Fabrizio Silvestri

This paper studies how Transformer models with Rotary Position Embeddings (RoPE) develop emergent, wavelet-like properties that compensate for the positional encoding's theoretical limitations. Through an analysis spanning model scales, architectures, and training checkpoints, we show that attention heads evolve to implement multi-resolution processing analogous to wavelet transforms. We demonstrate that this scale-invariant behavior is unique to RoPE, emerges through distinct evolutionary phases during training, and statistically adheres to the fundamental uncertainty principle. Our findings suggest that the effectiveness of modern Transformers stems from their remarkable ability to spontaneously develop optimal, multi-resolution decompositions to address inherent architectural constraints.

Valeria Ruscio, Umberto Nanni, Fabrizio Silvestri

Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.