EML-CD unveils interpretable causal equations from black-box neural nets
10 of 11 math functions recovered with 96% accuracy, no black box needed.
Neural-network-based causal discovery has long suffered from a fundamental flaw: the causal mechanisms learned remain black boxes, making it impossible to know exactly how variables influence each other. Sota Asanuma's new paper, EML-CD, tackles this head-on by replacing opaque neural weights with gated symbolic trees inspired by the EML (Elementary Mathematical Language) operator. Each causal edge in the discovered DAG is represented as a binary tree that composes elementary functions, yielding a closed-form equation that can be inspected, differentiated, and understood theoretically.
Validation across multiple benchmarks shows the approach is both accurate and transparent. On the Sachs protein-signaling dataset (11 variables), EML-CD achieves a structural Hamming distance of 11.2 ± 0.4—competitive with PC/GES—while outputting human-readable equations per edge. Controlled tests recover 10 of 11 elementary function families flawlessly (shape correlation ≥0.96). On a symbolic synthetic benchmark, mechanism-level mean squared error drops to 3.67 vs. 7,644 for fixed SINDy dictionaries, and on Causal Chambers light-tunnel data, a depth-2 model raises F1 from 0.273 to 0.444. The trade-off? Structure recovery (SHD) matches but does not beat specialized optimizers, and high-frequency sine remains partially learned.
- EML-CD converts each causal edge into a gated binary tree of elementary functions, generating fully interpretable, closed-form equations.
- On Sachs protein data (d=11), it achieves SHD=11.2±0.4 and edge precision 0.756/recall 0.365, matching PC/GES while adding transparency.
- Held-out mechanism MSE on symbolic benchmarks is 3.67 vs. 7,644 for fixed SINDy dictionaries—a >2,000x improvement—though structure recovery remains on par with baseline optimizers.
Why It Matters
Interpretable causal discovery lets researchers trust and reuse AI models in science, medicine, and engineering.