CSP-Atlas: Concept-Specific Neural Circuits in a Sparse Python Transformer

Do independently trained language models come to represent the same thing in the same way? We answer for code, extending a recently introduced concept-circuit extraction method to a 2x2 design -- Python and Rust crossed with Qwen2.5-Coder-7B and DeepSeek-Coder-V1-6.7B -- and measuring a complete inventory of grammatical concepts (58 Python, 57 Rust) identically in all four cells: the smallest design that separates what depends on the task, the language, and the model. The answer splits into three parts. What earns dedicated circuitry is set by the task: the models agree on which concepts receive circuits (Spearman $ρ$ = 0.638 for Python, 0.673 for Rust, both p < $10^{-7}$). Where those circuits sit is set by the model: Qwen processes concepts in a late band (~L17-19), DeepSeek at L6-7, for both languages. How circuits grow across layers is also set by the model: Qwen gives its atomic concepts an early spike that DeepSeek does not. "Are circuits universal?" thus has no single answer: yes for What, no for Where and How -- universality is a property of representational content, not of computational organisation. None of this structure was fixed in advance. The agreement could have landed anywhere between independence and identity; it lands at $ρ\approx 0.65$. Rust constructs receive 2-3x more concept-specific circuitry than their Python equivalents, in both models. Both models share neurons between the languages (6/7 and 7/7 paired constructs), DeepSeek 1.94x more than Qwen -- a direction no prior result predicts. And Qwen binds nine keywords of Rust's type-and-trait machinery into one tight neuron cluster (Jaccard 0.535 vs null 0.112, p < 0.001), a semantic dimension invisible in surface syntax. Ablation and linear probes confirm the circuits are functional. All claims are scoped to this 2x2; whether the per-model profile predicts a third model is the designed next test.

Mechanistic interpretability defines features as the fundamental units of a neural network and circuits as the weighted subgraphs that carry out its computation. Because individual neurons are polysemantic, Cross-Layer Transcoders (CLTs) were introduced as a way to approximate a model's circuits by generating an attribution graph. The nodes of that graph, however, are unlabeled features: reading a graph means pruning it and then working out by hand what each surviving node means. To make CLTs easier to use for circuit discovery, we introduce Circuit-Diff, which intervenes on the model itself with a low-rank factual edit and takes the features whose role in the attribution graph changes under that edit as related to the edited knowledge. On the edits we examine, the flagged nodes are not only detectors of the object token: read off the CLT's released feature dashboards, they include features for the history, geography and associations surrounding the old and new objects. We formalize the method, measure how reliable a frozen CLT remains after a factual edit, test the selected nodes causally by patching them on up to 24 CounterFact edits, give a case study, and release an open-source implementation built on the circuit-tracer package, together with two further tools (multi-prompt aggregation and rule-based supernode labeling).

We present a PyTorch package that compiles neural networks and their weights from Turing machine descriptions, producing models that exactly simulate the specified machine without any training. Given a transition function and a set of terminal states, the package constructs a model whose forward pass corresponds to one step of the Turing machine. Two architectures are implemented, each realizing a different theoretical result: (1) a transformer with self-attention, cross-attention, and feedforward layers based on Wei, Chen, and Ma (2021), and (2) a recurrent network based on Siegelmann and Sontag (1995) that encodes the stack in a Cantor set. We develop the constructions from first principles, showing how ReLU networks implement Boolean circuits (AND, OR, NOT, XOR gates and their composition into DNF formulas and binary adders) and how hard attention implements positional lookup on the tape. The package serves as a concrete, runnable reference for the symbolic-neural bridge, and as a foundation for future work on the stability of constructed solutions under gradient-based optimization. Code is available at https://github.com/jonrbates/turing.