Peter Balogh

Peter Balogh

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.

Peter Balogh

The final MLP of GPT-2 Small exhibits a fully legible routing program -- 27 named neurons organized into a three-tier exception handler -- while the knowledge it routes remains entangled across ~3,040 residual neurons. We decompose all 3,072 neurons (to numerical precision) into: 5 fused Core neurons that reset vocabulary toward function words, 10 Differentiators that suppress wrong candidates, 5 Specialists that detect structural boundaries, and 7 Consensus neurons that each monitor a distinct linguistic dimension. The consensus-exception crossover -- where MLP intervention shifts from helpful to harmful -- is statistically sharp (bootstrap 95% CIs exclude zero at all consensus levels; crossover between 4/7 and 5/7). Three experiments show that "knowledge neurons" (Dai et al., 2022), at L11 of this model, function as routing infrastructure rather than fact storage: the MLP amplifies or suppresses signals already present in the residual stream from attention, scaling with contextual constraint. A garden-path experiment reveals a reversed garden-path effect -- GPT-2 uses verb subcategorization immediately, consistent with the exception handler operating at token-level predictability rather than syntactic structure. This architecture crystallizes only at the terminal layer -- in deeper models, we predict equivalent structure at the final layer, not at layer 11. Code and data: https://github.com/pbalogh/transparent-gpt2

Peter Balogh

We show that they do. Schank's conceptual dependency theory proposed that all events decompose into primitive operations -- ATRANS, PTRANS, MTRANS, and others -- hand-coded from linguistic intuition. Can the same primitives be discovered automatically through compression pressure alone? We adapt DreamCoder's wake-sleep library learning to event state transformations. Given events as before/after world state pairs, our system finds operator compositions explaining each event (wake), then extracts recurring patterns as new operators optimized under Minimum Description Length (sleep). Starting from four generic primitives, it discovers operators mapping directly to Schank's: MOVE_PROP_has = ATRANS, CHANGE_location = PTRANS, SET_knows = MTRANS, SET_consumed = INGEST, plus compound operators ("mail" = ATRANS + PTRANS) and novel emotional state operators absent from Schank's taxonomy. We validate on synthetic events and real-world commonsense data from the ATOMIC knowledge graph. On synthetic data, discovered operators achieve Bayesian MDL within 4% of Schank's hand-coded primitives while explaining 100% of events vs. Schank's 81%. On ATOMIC, results are more dramatic: Schank's primitives explain only 10% of naturalistic events, while the discovered library explains 100%. Dominant operators are not physical-action primitives but mental and emotional state changes -- CHANGE_wants (20%), CHANGE_feels (18%), CHANGE_is (18%) -- none in Schank's original taxonomy. These results provide the first empirical evidence that event primitives can be derived from compression pressure, that Schank's core primitives are information-theoretically justified, and that the complete inventory is substantially richer than proposed -- with mental/emotional operators dominating in naturalistic data.

Peter Balogh

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.

Peter Balogh

Some transformer attention heads appear to function as membership testers, dedicating themselves to answering the question "has this token appeared before in the context?" We identify these heads across four language models (GPT-2 small, medium, and large; Pythia-160M) and show that they form a spectrum of membership-testing strategies. Two heads (L0H1 and L0H5 in GPT-2 small) function as high-precision membership filters with false positive rates of 0-4\% even at 180 unique context tokens -- well above the $d_\text{head} = 64$ bit capacity of a classical Bloom filter. A third head (L1H11) shows the classic Bloom filter capacity curve: its false positive rate follows the theoretical formula $p \approx (1 - e^{-kn/m})^k$ with $R^2 = 1.0$ and fitted capacity $m \approx 5$ bits, saturating by $n \approx 20$ unique tokens. A fourth head initially identified as a Bloom filter (L3H0) was reclassified as a general prefix-attention head after confound controls revealed its apparent capacity curve was a sequence-length artifact. Together, the three genuine membership-testing heads form a multi-resolution system concentrated in early layers (0-1), taxonomically distinct from induction and previous-token heads, with false positive rates that decay monotonically with embedding distance -- consistent with distance-sensitive Bloom filters. These heads generalize broadly: they respond to any repeated token type, not just repeated names, with 43\% higher generalization than duplicate-token-only heads. Ablation reveals these heads contribute to both repeated and novel token processing, indicating that membership testing coexists with broader computational roles. The reclassification of L3H0 through confound controls strengthens rather than weakens the case: the surviving heads withstand the scrutiny that eliminated a false positive in our own analysis.