Revealing Pathway Interactions in Network Computations with Complete Path Contribution

Understanding how neural networks compute is central to the study of artificial and biological intelligence. Networks pass signals through many layers of interconnected units, so explaining what they compute means tracing how information travels from input to output and how pathways interact. Most existing approaches analyze only pairwise interactions between components such as units, layers or attention heads. Although some uses of these methods combine these measurements ad hoc to form a circuit from input to output, these approaches inherently do not capture the higher-order interactions along full causal chains (paths) from input to output, and therefore cannot address how the exponential number of causal paths interact to construct network computation. This leaves a large set of mechanistic questions unanswerable, for example whether inhibitory pathways veto excitatory ones, and how the two combine to yield network decisions. To address this gap, we introduce Complete Path Contribution, a method to decompose the network output into mathematically complete contributions of individual causal chains to study path-level interactions directly and at scale. This decomposition induces definitions of contributions for any circuit at any granularity level via partial summation, with completeness guaranteed at every level, enabling observations that are not feasible with methods that analyze neurons or synapses in isolation. We further present an efficient algorithm that identifies the $k$ strongest causal paths without examining all of them, which would be exponential in the number of layers. Instead, the runtime is empirically linear in the number of chosen paths. By applying Path Contribution to benchmark image classification networks, we quantify excitatory-inhibitory interactions and show how they collectively construct network decisions at a level of detail previously unmeasurable. Furthermore, applying Path Contribution to an interpretable model of the mouse retina reveals how dynamic receptive fields emerge from excitatory-inhibitory interaction motifs among pathways between different cell types in response to time-varying natural stimuli. Overall, Path Contribution reveals how a network’s causal pathways interact at scale to transform input to output.