Layer Types¶

All 48 layer types supported by NNV. Every layer implements evaluate(x) for forward pass and reach(inputSet, method, ...) for reachability.

Common Interface¶

All layers follow this interface:

% Forward pass
y = layer.evaluate(x)

% Reachability (called internally by NN.reach)
outputSet = layer.reach(inputSet, method, option, relaxFactor, dis_opt, lp_solver)

% Static: parse from MATLAB layer (used by matlab2nnv)
L = LayerClass.parse(matlab_layer)

Input Layers¶

Layer	Constructor	Notes
`FeatureInputLayer`	`FeatureInputLayer(inputSize)`	Feature vector input
`ImageInputLayer`	`ImageInputLayer(inputSize)`	2D image input (H x W x C)
`Image3DInputLayer`	`Image3DInputLayer(inputSize)`	3D volume input (H x W x D x C)
`SequenceInputLayer`	`SequenceInputLayer(inputSize)`	Sequential/time-series input

Linear Layers¶

Layer	Constructor	Notes
`FullyConnectedLayer`	`FullyConnectedLayer(W, b)`	Dense: y = Wx + b
`ElementwiseAffineLayer`	`ElementwiseAffineLayer(scale, offset)`	Per-element: y = scale * x + offset

Convolutional Layers¶

Layer	Constructor	Notes
`Conv1DLayer`	`Conv1DLayer(W, b, ...)`	1D convolution with stride, padding, dilation
`Conv2DLayer`	`Conv2DLayer(W, b, ...)`	2D convolution (workhorse for CNN verification)
`Conv3DLayer`	`Conv3DLayer(W, b, ...)`	3D convolution for volumetric data
`TransposedConv1DLayer`	`TransposedConv1DLayer(W, b, ...)`	1D deconvolution
`TransposedConv2DLayer`	`TransposedConv2DLayer(W, b, ...)`	2D deconvolution (segmentation decoders)

Pooling Layers¶

Layer	Constructor	Notes
`MaxPooling2DLayer`	`MaxPooling2DLayer(poolSize, stride, padding)`	2D max pooling
`AveragePooling2DLayer`	`AveragePooling2DLayer(poolSize, stride, padding)`	2D average pooling
`AveragePooling3DLayer`	`AveragePooling3DLayer(...)`	3D average pooling
`GlobalAveragePooling1DLayer`	`GlobalAveragePooling1DLayer()`	Global average over 1D spatial dim
`GlobalAveragePooling2DLayer`	`GlobalAveragePooling2DLayer()`	Global average over 2D spatial dims
`GlobalAveragePooling3DLayer`	`GlobalAveragePooling3DLayer()`	Global average over 3D spatial dims
`MaxUnpooling2DLayer`	`MaxUnpooling2DLayer(...)`	Unpooling for segmentation

Activation Layers¶

Layer	Constructor	Notes
`ReluLayer`	`ReluLayer()`	ReLU: exact-star and approx-star reachability
`LeakyReluLayer`	`LeakyReluLayer(alpha)`	Leaky ReLU: y = max(alpha*x, x)
`SigmoidLayer`	`SigmoidLayer()`	Sigmoid activation
`TanhLayer`	`TanhLayer()`	Hyperbolic tangent
`HardSigmoidLayer`	`HardSigmoidLayer()`	Piecewise-linear sigmoid approximation
`SaturatingLinearLayer`	`SaturatingLinearLayer()`	Clip to [0, 1]
`SaturatingLinearSymmLayer`	`SaturatingLinearSymmLayer()`	Clip to [-1, 1]
`SignLayer`	`SignLayer()`	Sign/step function
`SoftmaxLayer`	`SoftmaxLayer()`	Softmax for classification output

Normalization Layers¶

Layer	Constructor	Notes
`BatchNormalizationLayer`	`BatchNormalizationLayer(...)`	Fused with preceding linear layer during verification
`LayerNormalizationLayer`	`LayerNormalizationLayer(...)`	Layer normalization

Graph Layers¶

Layer	Constructor	Notes
`GCNLayer`	`GCNLayer(W, b)`	Graph Convolutional Network layer
`GINELayer`	`GINELayer(W_e, b_e, W1, b1, W2, b2)`	Graph Isomorphism Network with Edge features

Recurrent Layers¶

Layer	Constructor	Notes
`LstmLayer`	`LstmLayer(Wi, Wh, b, ...)`	LSTM cell
`RecurrentLayer`	`RecurrentLayer(rnn_params)`	Simple RNN with Wi, Wh, bh, Wo kernels

Reshaping & Combination Layers¶

FlattenLayer, ReshapeLayer, Resize2DLayer, UpsampleLayer, AdditionLayer, ConcatenationLayer, DepthConcatenationLayer

Special Layers¶

ODEblockLayer (Neural ODE integration), PixelClassificationLayer (segmentation output), LayerS (custom layer support)