Monotonic Neural Networks (MonoNet)
Some domains contain directional knowledge. Holding everything else constant, a validated risk marker should not make predicted risk go down as the marker rises. A standard neural network can learn a curve that wiggles in either direction.
A monotonic neural network builds the direction into the architecture. MonoNet constrains a block between learned high-level features and outputs so each output moves consistently up or down as a chosen feature increases.
Enforce the Direction You Can Defend
Suppose a validated biomarker should never lower predicted risk when every other input stays fixed. Toggle the structural constraint and inspect the learned response.
Predicted risk
40.1%
One structural route is to use monotonic activation functions and constrain connecting weights to be nonnegative. If every step in a path preserves order, increasing the selected feature cannot reduce the downstream output. Component-wise sign choices can represent either an increasing or decreasing relationship.
This lets a practitioner make a stable statement: as this learned feature increases, this output moves in a known direction, independent of the other constrained high-level features.
MonoNet Architecture
MonoNet splits the network into two blocks. Hover each block to see its role.
Unconstrained block
Learns arbitrary representations from raw inputs. No restrictions on the learned function — this is a standard network sub-graph.
Not directly interpretable. Requires post-hoc explanation methods.
Monotonic block
Enforces a monotonic relationship between a chosen interpretable hidden layer and the output. Transparent by construction.
Relationships are directly readable — sign and magnitude per neuron-output pair.
The constraint is only as good as the domain claim
Many relationships are monotonic only within a range or after conditioning on other variables. If the true effect is U-shaped, forcing one direction will distort the model.
MonoNet constrains the relationship from an interpretable hidden layer to the output. Earlier layers can still learn complex transformations from raw inputs. That makes the network more transparent, not fully interpretable with respect to every original feature.
What does MonoNet's monotonic block guarantee?
Name a feature-outcome pair you might constrain monotonically. What evidence would you require before enforcing it?