Darkness Visible: Reading the Exception Handler of a Language Model

We show that MLP layers in transformer language models perform binary routing of continuous signals: the decision of whether a token needs nonlinear processing is well-captured by binary neuron activations, even though the signals being routed are continuous. In GPT-2 Small (124M parameters), we find that specific neurons implement a consensus architecture -- seven "default-ON" neurons and one exception handler (N2123 in Layer 11) that are 93-98% mutually exclusive -- creating a binary routing switch. A cross-layer analysis reveals a developmental arc: early layers (L1-3) use single gateway neurons to route exceptions without consensus quorums; middle layers (L4-6) show diffuse processing with neither gateway nor consensus; and late layers (L7-11) crystallize full consensus/exception architectures with increasing quorum size (1 to 3 to 7 consensus neurons). Causal validation confirms the routing is functional: removing the MLP at consensus breakdown costs 43.3% perplexity, while at full consensus removing it costs only 10.1% -- exceeding a 4x difference. Comparing binary vs. continuous features for the routing decision confirms that binarization loses essentially no information (79.2% vs. 78.8% accuracy), while continuous activations carry additional magnitude information (R^2 = 0.36 vs. 0.22). This binary routing structure explains why smooth polynomial approximation fails: cross-validated polynomial fits (degrees 2-7) never exceed R^2 = 0.06 for highly nonlinear layers. We propose that the well-established piecewise-affine characterization of deep networks can be complemented by a routing characterization: along the natural data manifold, the piecewise boundaries implement binary decisions about which tokens need nonlinear processing, routing continuous signals through qualitatively different computational paths.

We investigate when transformer MLP nonlinearity is actually necessary. A gate with $d+1$ parameters decides when to replace the full MLP with a linear surrogate. Through systematic investigation across six models (162M-2.8B parameters), two architectures, and three corpora, we establish that nonlinearity need cannot be predicted from token identity: cross-corpus correlation is zero ($r < 0.05$). The routing decision is fully contextual. Despite weak per-instance predictability, the gate exploits a heavily skewed distribution where most MLP computations are near-linear, achieving 25-56% linear routing at <1% perplexity cost in GPT-2. In GPT-2 Large, 11 of 36 layers beat baseline with gating and no layer exceeds 3.7% all-linear cost. This success is architecture-dependent: Pythia models show higher costs, though Pythia-2.8B's full 32-layer sweep reveals one layer that narrowly beats baseline. As a proof of concept, we progressively replace middle-layer MLPs with frozen linear matrices: 5 of 24 layers linearize at zero cost. With a full training budget, 4 linearized layers yield a 10.2% perplexity improvement -- and a two-phase gated approach pushes this to 17.3%, beating a vanilla fine-tuning control and confirming that the nonlinear MLPs at these layers were actively harmful.

Transformers commonly exhibit an attention sink: disproportionately high attention to the first position. We study this behavior in GPT-2-style models with learned query biases and absolute positional embeddings. Combining structural analysis with causal interventions, validated across natural-language, mathematical, and code inputs, we find that the sink arises from the interaction among (i) a learned query bias, (ii) the first-layer MLP transformation of the positional encoding, and (iii) structure in the key projection. Crucially, each component we identify is individually dispensable: architectures omitting each of them robustly exhibit sinks. This indicates that attention sinks may arise through distinct circuits across architectures. These findings inform mitigation of sinks, and motivate broader investigation into why sinks emerge.