FTB Graph: Determining and Validating First-token Broadcasters and Language-Identity Head Circuits in Multilingual Language Models

Why do multilingual language models sometimes generate in the wrong language, and why is this so hard to fix? We introduce Language Identity Head Ablation (LIHA), a causal intervention that zeros each attention head individually and measures the resulting language switch rate across a parallel dataset of 2,700 prompt-language pairs spanning seven languages. Applied to GPT-2, LIHA identifies a small set of first-token broadcaster heads - led by L6H1 (switch rate 0.32, 3.23 $σ$ above the population mean) - that attend persistently to the first prompt token, propagating its language signal throughout generation. Compensatory redistribution when heads are ablated is statistically significant (p < $10^{-5}$) and follows a directional, hierarchical pattern: compensation always recruits heads in layers above the ablated head, suggesting a feedforward cascade rather than global diffusion. To probe how training regime shapes these circuits, we apply LIHA to a controlled pair - Qwen2.5-1.5B-Base and Qwen2.5-1.5B-Instruct - identical in architecture and size, differing only in training. The base model is nearly flat (max SR=0.016, 200/336 heads at SR=0.0); the instruct model concentrates causal influence sharply at layer 0, led by L0H5 (SR=0.224, 8.93 $σ$ above mean), with all other layers near zero. This controlled comparison provides direct causal evidence that instruction tuning reorganizes language identity circuits toward early-layer localization. Extended experiments with Chinese and Russian confirm that first-token broadcasting is script-specific in GPT-2, with non-Latin languages handled at layer 0 - the same locus as the instruction-tuned model. Code and data will be released upon publication.

Finding circuits in language models usually means running many careful interventions. We try something simpler: treat attention as a routing map from one forward pass, keep a small set of routes that point toward the answer, and ask whether those routes actually matter. They often do. On induction and IOI (tasks where the "right" circuit is already known), ablating our extracted edges hurts the model much more than ablating a random set of the same size. We evaluate n=100 prompts per cell on GPT-2 Small, GPT-2 Medium, and Pythia-410M, with paired gap tests and bootstrap confidence intervals. The extract step costs one forward; a head-by-head patch sweep costs about two orders of magnitude more. We are not claiming a complete circuit atlas. We are claiming a cheap sketch that carries real causal signal on known tasks, with clear failure modes when it does not. Code and evaluation artifacts are at https://github.com/Aquinf03/live-circuit-routing.

Multilingual LLMs answer the same multi-hop reasoning question across languages, but we lack a mechanistic account of whether they share an internal circuit. We identify Bridge Routing Heads (BRH) in two large multilingual LLMs through a three-stage pipeline. The resulting language-specific head sets exhibit near-complete mutual exclusivity across the five languages, with a mean Jaccard similarity of only 0.017 for Llama 3.1 70B and 0.057 for Qwen 2.5 72B, revealing language-idiosyncratic circuits. Ablating general BRH increases two-hop Negative Log-Likelihood (NLL) by 39-89x the random-head baseline, providing direct causal evidence of their role. Amplifying these heads in a failing target-language pass rescues up to 51.7% of cross-lingual failures, with no training. The two models share this dual-circuit pattern but allocate heads differently: Llama concentrates chaining in a large general pool, while Qwen leans on larger language-specific pools. Together these results show that activation-level intervention alone can recover correct answers from cross-lingual reasoning failures.