Granular Concept Circuit (GCC)

• Granular Concept Circuit (GCC) is a method defining circuits as sets of neurons across multiple layers that encode image-specific concepts.
• It uses a directed acyclic graph structure with dual criteria—functional dependency and semantic alignment—to select neuron connections.
• GCC’s iterative, thresholded search produces fine-grained, concept-specific visual circuits that enhance interpretability in deep vision models.

Granular Concept Circuit (GCC) is a circuit-discovery method for deep vision models in which each circuit is defined as a set of neurons across multiple layers that encodes a concept relevant to a given query. In the formulation introduced for image classification models, a GCC is represented as a directed acyclic graph (DAG) whose nodes are neurons and whose edges connect neurons in adjacent layers when two criteria are jointly satisfied: functional dependency and semantic alignment. The method is designed to discover multiple circuits for a single query, so that one image can be decomposed into several fine-grained concept-specific circuits rather than a single diffuse class-level explanation (Kwon et al., 3 Aug 2025).

1. Definition, scope, and representational unit

The operational definition of a Granular Concept Circuit is explicit: it is “a set of neurons across multiple layers within a model that encodes a concept relevant to a given query” (Kwon et al., 3 Aug 2025). In the main formulation, the query is a single input image $x_q$, although the method is also described as extending to multiple queries, including the discovery of common concepts across samples and unique concepts among them. A single query may yield multiple GCCs because the procedure begins from multiple root nodes, each of which is expanded independently into its own circuit.

The graph structure is constrained. Each node corresponds to a neuron, and each edge connects neurons in adjacent layers only. In convolutional networks, a neuron is treated as a channel; in Transformers, it is treated as a hidden dimension. Repeated adjacent-layer expansion yields a multi-layer DAG, which is intended to track hierarchical concept formation from lower-level patterns to more specialized representations. The paper presents this as a concept-wise rather than class-wise decomposition of model behavior (Kwon et al., 3 Aug 2025).

The paper’s notion of granularity is specific. It does not denote granularity at the level of architectural blocks or classes, but at the level of “specific visual concepts within a query.” The reported examples illustrate this point directly. For a “scoreboard” image, the discovered circuits correspond to “sky background,” “flags,” and “clock.” A “merged” visualization is also shown, in which 20 circuits for one query in ResNet50 are aggregated into a larger query-level graph, while individual circuits remain available as separate objects (Kwon et al., 3 Aug 2025).

Formally, the analyzed model is written as

$\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$

and the activation at layer $l$ for query $x_q$ is

$f^{l:0}(x_q) = a^l.$

The initial root set is denoted

$R = \{n_{r_1}, \dots, n_{r_k}\}.$

These notations anchor the method in a layerwise view of hierarchical representations (Kwon et al., 3 Aug 2025).

2. Circuit construction and search procedure

Given a trained model $\mathcal{F}$ and a query image $x_q$, GCC proceeds through root-node extraction, adjacent-layer connection search, iterative expansion across layers, and repetition for all roots. Root nodes are selected as neurons whose activations rank within the top $1\%$ across all samples. Appendix remarks indicate that this threshold can be loosened, for example to top $10\%$, which increases diversity but reduces query specificity (Kwon et al., 3 Aug 2025).

The core connectivity decision uses two signals. The first is the Neuron Sensitivity Score $\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$0, which measures functional dependency by zero-masking a source neuron and observing how target activations in the next layer change. The second is the Semantic Flow Score $\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$1, which measures semantic alignment by comparing the top-$\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$2 activating samples of the source and target neurons. A target is retained only when both criteria are met: $\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$3 and

$\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$4

This conjunction is the defining design choice of GCC: dependency alone is treated as insufficient, because strong nonlinear dependence can still connect semantically unrelated neurons (Kwon et al., 3 Aug 2025).

Candidate pruning is local and layerwise. For a given source node, GCC evaluates all neurons in the next layer, thresholds $\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$5 using $\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$6, computes $\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$7 only for surviving candidates, and then keeps only those targets whose semantic score exceeds $\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$8. The threshold $\mathcal{F} = f^L \dots \circ f^l \dots \circ f^0,$9 is chosen automatically by Peak-over-Threshold (POT) from extreme value theory, while $l$0 is set to the average $l$1 over the target layer. Surviving edges are added to the circuit, and their weights in the final graph are given by the corresponding $l$2 values; Sankey visualizations use these values as link thickness (Kwon et al., 3 Aug 2025).

The search itself is an iterative graph traversal with a frontier initialized at a single root node $l$3. The paper summarizes the next-layer candidate set as

$l$4

All accepted targets are added both as outgoing neighbors and as new frontier nodes. The procedure continues until no valid next-layer targets remain. The paper also notes an engineering optimization: previously computed source-node connections are reused and recursive techniques are used to reduce duplicate computation (Kwon et al., 3 Aug 2025).

3. Functional dependency, semantic alignment, and computational approximation

Functional dependency in GCC is intervention-based. A source neuron is zero-masked, the modified activation is forwarded to the next layer, and the decrease in each target neuron is measured. Negative effects are clipped to zero, because the method retains only positively correlated relationships. The paper characterizes this as a first-order approximation, noting that exhaustive analysis over all source-neuron combinations would be exponential,

$l$5

and is therefore intractable (Kwon et al., 3 Aug 2025).

Semantic alignment is defined through sample-set overlap. Each neuron’s “semantic content” is approximated by the dataset samples that activate it most strongly. GCC then measures whether the target neuron is activated by many of the same high-activating samples as the source. The score is asymmetric, since it is normalized by the size of the source set. The stated rationale is that semantic continuity across an edge is preserved when the target retains the source neuron’s activating sample profile (Kwon et al., 3 Aug 2025).

The two scores play different roles. $l$6 establishes whether information functionally flows from one neuron to the next; $l$7 establishes whether that flow is semantically coherent. Figure 1 in the paper distinguishes low-$l$8/low-$l$9, high-$x_q$0/low-$x_q$1, and high-$x_q$2/high-$x_q$3 cases, with the last treated as the intended interpretable regime. This makes GCC a thresholded forward search procedure rather than a learned end-to-end objective: the paper explicitly states that there is no global optimization objective or learned loss for GCC (Kwon et al., 3 Aug 2025).

This design also explains the method’s claim to specificity. Each circuit begins from a query-specific highly activated neuron, uses a dependency threshold to avoid weak connections, imposes an above-average semantic-overlap filter, and preserves root-wise independence instead of collapsing all relevant structure into a single graph. A plausible implication is that GCC favors localized concept traces even when the underlying representation is distributed, although the paper also acknowledges that one concept may still split across multiple circuit pathways under strict thresholds (Kwon et al., 3 Aug 2025).

4. Experimental regime and empirical findings

The reported evaluation spans VGG19, ResNet50, ResNet101, MobileNetV3, and ViT in the main paper, with ViT-B/32, Swin Transformer, and CLIP-ViT added in the appendix. The pretrained models are evaluated on ImageNet-1K, with additional fine-grained bird experiments on CUB-200-2011. The compared or discussed methods are CRP, VCC, ADVC, and GCC; Table 1 presents GCC as the only method in that comparison returning $x_q$4 circuits per query with concept specificity (Kwon et al., 3 Aug 2025).

The main quantitative evidence comes from pruning-based faithfulness tests. For CNNs, the paper reports average logit change after ablating random neurons, GCC neurons, and complement neurons. Original logits are 17.17 for ResNet50, 17.46 for ResNet101, 20.94 for VGG19, and 17.34 for MobileNetV3. Random ablation yields 15.66, 13.80, 19.03, and 15.01, corresponding to an average drop of $x_q$5. GCC ablation yields 6.41, 6.18, 12.93, and 12.95, corresponding to an average drop of $x_q$6; the text specifically highlights $x_q$7 in ResNets. Complement ablation yields 16.12, 14.58, 19.93, and 15.88, for an average drop of $x_q$8. The interpretation given is that GCCs are both faithful and relatively complete, because removing them harms output much more than random pruning, while removing their complement harms output much less (Kwon et al., 3 Aug 2025).

The transformer results are stronger in absolute magnitude because the paper uses accuracy drop rather than logit drop. Appendix results report ablation drops from 76.61 to 58.47 for ViT, from 81.92 to 36.92 for Swin-T, and from 62.19 to 23.78 for CLIP-ViT. The average random-ablation accuracy drop is $x_q$9, whereas GCC ablation produces an average drop of $f^{l:0}(x_q) = a^l.$0. This is presented as evidence that the method extends beyond CNNs (Kwon et al., 3 Aug 2025).

Edge-level evaluation uses deletion and insertion curves on the last block of ResNet-50. Ranking edges by $f^{l:0}(x_q) = a^l.$1 is shown to be meaningful: removing top-ranked edges degrades performance, and adding them improves performance. The paper notes that AVCD has slightly steeper curves, but emphasizes that GCC is aimed at fine-grained multi-concept circuits rather than a single class-linked circuit (Kwon et al., 3 Aug 2025).

A user study with 33 participants adds a human interpretability signal. Average scores out of 5 are 3.65 for query relativeness, 4.0 for diversity, and 4.45 for prototypicality or multiple-query representativeness. The paper further reports that more than $f^{l:0}(x_q) = a^l.$2 of users found node-to-node and query-node connections appropriate, and that $f^{l:0}(x_q) = a^l.$3 agreed GCC captures more meaningful and diverse concepts than VCC (Kwon et al., 3 Aug 2025).

5. Visualization, use cases, and interpretation

GCC is not only a discovery procedure but also a visualization framework. Circuits are shown with Sankey diagrams whose link thickness is proportional to $f^{l:0}(x_q) = a^l.$4. Individual nodes are visualized by four representative cropped images selected from the top 10 activating validation images, with threshold-based masking and cropping used to highlight salient regions. This visualization strategy is central to the paper’s claim of concept-level interpretability, because node semantics are inferred from representative activation patterns rather than from labels or predefined concept ontologies (Kwon et al., 3 Aug 2025).

The qualitative examples are intended to show hierarchical concept flow. In ResNet50, a peacock image yields a “decorative blue tone” circuit that evolves into blue scales and textured blue surfaces. In ViT-B/32, a cauliflower image yields a “circular shape” circuit that progresses through ball-, flower-, and hot-air-balloon-like patterns to turtle shell and cherry tomatoes. In CUB bird images, the paper reports a “red and orange color” concept that progresses from part-level to whole-bird encoding. These cases are used to support the view that GCC captures multi-layer concept evolution rather than isolated neuron saliency (Kwon et al., 3 Aug 2025).

The paper also presents applied interpretability use cases. In a misclassification example, a “Schipperke” image is classified as “soccer ball” by ResNet50. GCCs extracted from the last residual block are then inhibited or amplified. Some circuits correspond to soccer-ball-like concepts and strongly influence the erroneous prediction; others correspond more to Schipperke-related concepts and help recover the true class when stimulated. In a separate multi-query setting, GCC is used to identify common concepts across classes, including a shared “radiant” pattern across daisy and peacock, and a shared “wheel” concept across tanks, minibuses, and moving vans (Kwon et al., 3 Aug 2025).

6. Limitations, related methods, and terminological disambiguation

The explicit limitations are methodological rather than rhetorical. The paper states that model-centric connectivity may still be hard to interpret, that a single concept may split across multiple pathways, that full combinational causal analysis is intractable and is replaced by a first-order approximation, and that threshold choices affect relevance–diversity trade-offs. It also relies on two strong assumptions: that a neuron’s semantic content can be approximated by its top-activating samples, and that semantic continuity can be captured by sample-set overlap. These assumptions are integral to the method rather than hidden implementation details (Kwon et al., 3 Aug 2025).

Within the broader literature on interpretable circuit structure, adjacent work occupies different points in the design space. “Concept Graph Convolutions” operates on node-level concepts in graph neural networks and is presented as a convolution that performs message passing on a combination of raw and concept representations, including a pure variant operating only in concept space (Magister et al., 22 Apr 2026). “Multi-Granular Node Pruning for Circuit Discovery” addresses circuit discovery in transformer LLMs by learning masks across multiple granularities, from blocks to individual neurons, within a unified pruning objective (Haider et al., 11 Dec 2025). These works are related through their emphasis on concept-oriented or multi-granular internal structure, but they are not Granular Concept Circuits in the sense defined for vision models.

The acronym “GCC” also requires disambiguation. In “Implementing Continuation based language in GCC,” the term refers to a partial implementation of Continuation based C inside GCC 4.2.3, with GCC denoting the compiler infrastructure rather than a concept-circuit method (Kono et al., 2011). In “Compiling Combinatorial Genetic Circuits with Semantic Inference,” GCC denotes the Genetic Circuit Compiler, and the phrase “Granular Concept Circuit” does not appear (Waites et al., 2018). In current technical usage, “Granular Concept Circuit” therefore refers specifically to the fine-grained circuit-discovery framework for concept representations in deep vision models introduced in 2025 (Kwon et al., 3 Aug 2025).