Enilnets 1.0.1

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Enilnets Library Documentation

A pure NumPy-based deep learning library with support for dense, convolutional, pooling, batch normalization, dropout, and sparse layers. Includes multiple optimizers, loss functions, activation functions, and weight initialization methods.

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Table of Contents

1. Quick Start
2. Core Architecture
3. Model Configuration
   • NeuralNet Constructor
   • Summary
4. Layer Types
   • Dense Layer
   • Sparse Layer
   • Conv2D Layer
   • Flatten Layer
   • MaxPool2D Layer
   • AvgPool2D Layer
   • BatchNorm Layer
   • Dropout Layer
5. Forward Pass
6. Backward Pass
7. Optimizers
8. Loss Functions
9. Training
10. Activation Functions
11. Weight Initialization
12. Reinforcement Learning
13. Model I/O
14. Utility Functions

---

Quick Start

from Enilnets import NeuralNet
import numpy as np

# Create a simple classifier
model = NeuralNet(learning_rate=0.001, optimizer="adam", l2_lambda=0.01)

# Build architecture
model.add_dense(784, 256, activation="relu")
model.add_dropout(0.3)
model.add_dense(256, 10, activation="softmax")

# Train
X_train = np.random.randn(1000, 784)
Y_train = np.eye(10)[np.random.randint(0, 10, 1000)]

history = model.Train(X_train, Y_train, epochs=10, batch_size=32)

# Predict
predictions = model.Forward(X_test)

---

Core Architecture

The library is built around the NeuralNet class in base.py, which maintains:

Attribute	Type	Description
layers	list	Layer definitions with weights, biases, and hyperparameters
learning_rate	float	Global learning rate
optimizer_type	str	Optimizer name: "sgd", "rmsprop", "adagrad", "adam"
l2_lambda	float	L2 regularization coefficient
momentum	float	Momentum coefficient for SGD
outputs	list	Cached layer outputs during forward pass
pre_activations	list	Cached pre-activation values (z)
batchnorm_cache	list	BatchNorm statistics cache
deltas	list	Gradient errors per layer
opt_state	list	Optimizer state (momentum, velocity)
t	int	Global timestep for bias correction (Adam)

---

Model Configuration

NeuralNet Constructor

NeuralNet(learning_rate=0.001, optimizer="adam", l2_lambda=0.01, momentum=0.9)

Parameters:

Parameter	Default	Description
learning_rate	0.001	Step size for parameter updates
optimizer	"adam"	Optimization algorithm. Options: "sgd", "rmsprop", "adagrad", "adam"
l2_lambda	0.01	L2 regularization strength applied to weights
momentum	0.9	Momentum factor for SGD optimizer

Example:

# Adam with low regularization
model = NeuralNet(learning_rate=0.001, optimizer="adam", l2_lambda=0.001)

# SGD with high momentum
model = NeuralNet(learning_rate=0.01, optimizer="sgd", momentum=0.95, l2_lambda=0.0)

Summary

model.summary()

Prints a model architecture overview including layer types, dimensions, and total parameter count. No parameters, returns None.

Output Example:

Model Summary
============================================================
Optimizer: ADAM | LR: 0.001 | L2: 0.01
============================================================
Layer 0: DENSE - Input: 784, Output: 256, Params: 200960
Layer 1: DROPOUT
Layer 2: DENSE - Input: 256, Output: 10, Params: 2570
Total Parameters: 203530
============================================================

---

Layer Types

All layer methods are bound to the NeuralNet class and return None (they mutate self.layers).

Dense Layer

model.add_dense(n_in, n_out, activation="relu", init_method="xavier_uniform")

Fully connected (linear) layer: output = activation(x @ W^T + b)

Parameters:

Parameter	Default	Description
n_in	required	Number of input features
n_out	required	Number of output features (neurons)
activation	"relu"	Activation function name (see Activation Functions)
init_method	"xavier_uniform"	Weight initialization method (see Weight Initialization)

Layer Dictionary Keys:

• type: "dense"
• weights: (n_out, n_in) ndarray
• bias: (n_out,) ndarray
• activation: activation string

Example:

model.add_dense(784, 256, activation="relu", init_method="he_normal")
model.add_dense(256, 10, activation="softmax")

---

Sparse Layer

model.add_sparse(n_in, n_out, connectivity=0.5, activation="relu", init_method="xavier_uniform")

Dense layer with random connectivity masking. Only a fraction of weights are non-zero.

Parameters:

Parameter	Default	Description
n_in	required	Number of input features
n_out	required	Number of output features
connectivity	0.5	Fraction of weights to keep (0.0 to 1.0)
activation	"relu"	Activation function name
init_method	"xavier_uniform"	Weight initialization method

Layer Dictionary Keys:

• type: "sparse"
• weights: (n_out, n_in) ndarray (masked)
• bias: (n_out,) ndarray
• mask: (n_out, n_in) boolean ndarray
• activation: activation string

Note: During backpropagation, gradients are masked by layer["mask"] to maintain sparsity.

Example:

# 30% connectivity sparse layer
model.add_sparse(784, 256, connectivity=0.3, activation="relu")

---

Conv2D Layer

model.add_conv2d(in_ch, out_ch, k, activation="relu", init_method="he_normal")

2D convolutional layer. Uses im2col for efficient convolution computation.

Parameters:

Parameter	Default	Description
in_ch	required	Number of input channels
out_ch	required	Number of output channels (filters)
k	required	Kernel size (square kernel: k x k)
activation	"relu"	Activation function name
init_method	"he_normal"	Weight initialization method

Layer Dictionary Keys:

• type: "conv2d"
• weights: (out_ch, in_ch, k, k) ndarray
• bias: (out_ch,) ndarray
• in_ch, out_ch, k: integers
• activation: activation string

Notes:

• Stride is fixed at 1, padding is fixed at 0.
• Output spatial dimensions: (H - k + 1, W - k + 1)
• Input must be 4D: (batch, channels, height, width)

Example:

# 3x3 conv, 1 input channel -> 32 output channels
model.add_conv2d(1, 32, k=3, activation="relu")
# 3x3 conv, 32 input channels -> 64 output channels
model.add_conv2d(32, 64, k=3, activation="relu")

---

Flatten Layer

model.add_flatten()

Flattens multi-dimensional input to 2D: (batch, ...) -> (batch, -1).

Parameters: None

Layer Dictionary Keys:

• type: "flatten"

Example:

model.add_conv2d(1, 32, k=3)
model.add_maxpool2d(2)
model.add_flatten()  # Flattens (B, 32, H, W) to (B, 32*H*W)
model.add_dense(32*14*14, 128)

---

MaxPool2D Layer

model.add_maxpool2d(pool_size=2)

Max pooling with square kernel. Reduces spatial dimensions by pool_size.

Parameters:

Parameter	Default	Description
pool_size	2	Size of pooling window (p x p)

Layer Dictionary Keys:

• type: "maxpool2d"
• p: pool size integer

Notes:

• Input is trimmed to multiples of pool_size before pooling.
• Backpropagation routes gradient only to the max-valued position(s) in each window.

Example:

model.add_conv2d(1, 32, k=3)
model.add_maxpool2d(pool_size=2)  # Halves spatial dimensions

---

AvgPool2D Layer

model.add_avgpool2d(pool_size=2)

Average pooling with square kernel.

Parameters:

Parameter	Default	Description
pool_size	2	Size of pooling window (p x p)

Layer Dictionary Keys:

• type: "avgpool2d"
• p: pool size integer

Notes:

• Backpropagation distributes gradient equally across all positions in each window.

Example:

model.add_conv2d(1, 32, k=3)
model.add_avgpool2d(pool_size=2)

---

BatchNorm Layer

model.add_batchnorm(num_features, epsilon=1e-5, momentum=0.1)

Batch normalization layer. Normalizes across the batch dimension.

Parameters:

Parameter	Default	Description
num_features	required	Number of features (must match flattened input dimension)
epsilon	1e-5	Small constant for numerical stability
momentum	0.1	Running statistics update momentum (0.1 means 90% old, 10% new)

Layer Dictionary Keys:

• type: "batchnorm"
• num_features: integer
• epsilon, momentum: floats
• running_mean, running_var: running statistics
• gamma: scale parameter, initialized to 1
• beta: shift parameter, initialized to 0

Notes:

• Input is flattened to 2D, normalized, then reshaped back.
• During training, uses batch statistics and updates running statistics.
• During inference (training=False), uses running statistics.

Example:

model.add_dense(256, 128)
model.add_batchnorm(128)  # Must match output of previous layer
model.add_dense(128, 10, activation="softmax")

---

Dropout Layer

model.add_dropout(rate=0.5)

Randomly zeroes elements during training with probability rate.

Parameters:

Parameter	Default	Description
rate	0.5	Dropout probability (0.0 = no dropout, 1.0 = drop everything)

Layer Dictionary Keys:

• type: "dropout"
• rate: float
• mask: cached mask during training (set during forward pass)

Notes:

• Active only when training=True in Forward() or TrainBatch().
• Scales surviving activations by 1/(1-rate) (inverted dropout).

Example:

model.add_dense(256, 128, activation="relu")
model.add_dropout(0.3)  # 30% dropout
model.add_dense(128, 10, activation="softmax")

---

Forward Pass

Forward / Predict

output = model.Forward(inputs, training=False, dropout_rate=0.0)
output = model.predict(inputs)  # Alias for Forward

Runs the forward pass through all layers.

Parameters:

Parameter	Default	Description
inputs	required	Input array. Can be 1D (features,), 2D (batch, features), 3D (channels, height, width), or 4D (batch, channels, height, width)
training	False	Whether to enable training-specific behavior (dropout, batch norm updates)
dropout_rate	0.0	Fallback dropout rate if layer doesn't specify one

Returns:

• output: ndarray of shape matching the last layer's output

Side Effects:

• Populates self.outputs (layer-by-layer activations)
• Populates self.pre_activations (pre-activation values for dense/conv layers)
• Populates self.batchnorm_cache (batch norm statistics)
• Sets layer["mask"] for dropout layers during training

Example:

# Inference
pred = model.Forward(X_test, training=False)

# Training (enables dropout and batch norm updates)
pred = model.Forward(X_batch, training=True)

---

Backward Pass

Backward

model.Backward(targets)

Computes gradients via backpropagation and stores them in self.deltas.

Parameters:

Parameter	Type	Description
targets	ndarray	Target values. Shape: (batch, output_dim) or (output_dim,) for single sample

Side Effects:

• Populates self.deltas with gradients for each layer
• For batch norm layers, stores d_gamma and d_beta in the layer dict

Gradient Computation:

• Output layer: If softmax activation, uses delta = (output - targets) / batch_size
• Otherwise: delta = (output - targets) * activation_derivative(pre_activation) / batch_size
• Hidden layers: Propagates error backward through weights, then multiplies by activation derivative

Example:

model.Forward(X_batch, training=True)
model.Backward(Y_batch)
model.update()  # Apply gradients

---

Optimizers

Update

model.update()

Applies computed gradients to update all layer parameters. No parameters, no return value.

Supported Optimizers:

Optimizer	Description	Hyperparameters Used
"sgd"	Stochastic Gradient Descent with momentum	learning_rate, momentum
"rmsprop"	RMSProp adaptive learning	learning_rate
"adagrad"	AdaGrad adaptive learning	learning_rate
"adam"	Adam (default)	learning_rate, t (timestep)

Adam Configuration (fixed):

• beta1 = 0.9 (first moment decay)
• beta2 = 0.999 (second moment decay)
• epsilon = 1e-8 (numerical stability)
• Bias correction applied: m / (1 - beta1^t), v / (1 - beta2^t)

L2 Regularization:

• Applied to all dense, sparse, and conv2d weights: grad_w += l2_lambda * weights
• Not applied to biases or batch norm parameters

Sparse Layer Handling:

• Gradients are masked by layer["mask"] before update

Example:

model = NeuralNet(optimizer="adam", learning_rate=0.001)
# ... forward and backward ...
model.update()

---

Loss Functions

ComputeLoss

loss = model.ComputeLoss(output, target, function="mse", reduction="mean", **kwargs)

Computes the loss between predictions and targets.

Parameters:

Parameter	Default	Description
output	required	Model predictions
target	required	Ground truth values
function	"mse"	Loss function name (see below)
reduction	"mean"	"mean", "sum", or "none" (returns per-element loss)
**kwargs		Additional arguments for specific loss functions

Available Loss Functions:

Function	Description	Extra Args	Formula
"mse"	Mean Squared Error	none	(o - t)^2
"mae"	Mean Absolute Error	none	`
"huber"	Huber Loss	delta=1.0	0.5*diff^2 if diff < delta, else delta*(diff - 0.5*delta)
"smooth_l1"	Smooth L1 Loss	none	0.5*diff^2 if diff < 1, else diff - 0.5
"binary_cross_entropy"	Binary Cross-Entropy	none	-t*log(o) - (1-t)*log(1-o)
"cross_entropy" / "categorical_cross_entropy"	Categorical Cross-Entropy	none	-t*log(o)
"focal"	Focal Loss	alpha=0.25, gamma=2.0	Down-weights easy examples
"hinge"	Hinge Loss (SVM)	none	max(0, 1 - t*o)

Notes:

• For cross-entropy losses, outputs are clipped to [1e-12, 1.0] to prevent log(0).
• For binary cross-entropy, outputs are clipped to [1e-12, 1 - 1e-12].

Example:

# MSE loss
loss = model.ComputeLoss(pred, target, "mse", "mean")

# Focal loss for imbalanced classification
loss = model.ComputeLoss(pred, target, "focal", alpha=0.25, gamma=2.0)

# Per-sample losses (no reduction)
losses = model.ComputeLoss(pred, target, "cross_entropy", "none")

---

Training

TrainBatch

loss = model.TrainBatch(xs, ys, loss_function=None, **loss_kwargs)

Trains on a single batch (forward + backward + update).

Parameters:

Parameter	Default	Description
xs	required	Input batch
ys	required	Target batch
loss_function	None	Loss function name. Auto-detected: "cross_entropy" if last layer uses "softmax", else "mse"
**loss_kwargs		Extra arguments passed to ComputeLoss

Returns:

• loss: float, the computed loss value

Example:

loss = model.TrainBatch(X_batch, Y_batch, loss_function="cross_entropy")

---

Train

history = model.Train(X_train, Y_train, epochs=10, batch_size=32, 
                      X_val=None, Y_val=None, loss_function=None, 
                      verbose=True, **loss_kwargs)

Full training loop with batching, optional validation, and history tracking.

Parameters:

Parameter	Default	Description
X_train	required	Training inputs
Y_train	required	Training targets
epochs	10	Number of training epochs
batch_size	32	Batch size
X_val	None	Validation inputs (optional)
Y_val	None	Validation targets (optional)
loss_function	None	Loss function name (auto-detected if None)
verbose	True	Print progress per epoch
**loss_kwargs		Extra arguments for ComputeLoss

Returns:

• history: dict with keys "loss", "accuracy", "val_loss", "val_accuracy" (lists of floats)

Behavior:

• Shuffles data each epoch
• Computes average loss and accuracy per epoch
• If validation data provided, computes validation metrics after each epoch
• Accuracy: multi-class uses argmax, binary uses > 0.5 threshold

Example:

history = model.Train(
    X_train, Y_train,
    epochs=20, batch_size=64,
    X_val=X_val, Y_val=Y_val,
    loss_function="cross_entropy",
    verbose=True
)

# Plot training history
import matplotlib.pyplot as plt
plt.plot(history["loss"], label="train")
plt.plot(history["val_loss"], label="val")
plt.legend()
plt.show()

---

ComputeAccuracy

acc = model.compute_accuracy(predictions, targets)

Standalone accuracy computation.

Parameters:

Parameter	Description
predictions	Model output array
targets	Ground truth array

Returns:

• acc: float, proportion of correct predictions (0.0 to 1.0)

Logic:

• If last dimension > 1: multi-class, uses argmax
• If last dimension == 1: binary, uses > 0.5 threshold

Example:

acc = model.compute_accuracy(model.Forward(X_test), Y_test)
print(f"Accuracy: {acc:.4f}")

---

Activation Functions

Activation functions are defined in Enilnets.activations. Both activate() and derivative() are available as standalone functions, but are typically used internally by the library.

Standalone Functions

from Enilnets.activations import activate, derivative

out = activate("relu", x)
grad = derivative("relu", x)

Available Activations:

Name	Function activate(x)	Derivative derivative(x)	Notes
"relu"	max(0, x)	1 if x > 0, else 0	Default for hidden layers
"leakyrelu"	x if x > 0, else 0.01*x	1 if x > 0, else 0.01	Negative slope 0.01
"elu"	x if x > 0, else exp(x) - 1	1 if x > 0, else exp(x)
"selu"	scale * (x if x>0 else alpha*(exp(x)-1))	scale * (1 if x>0 else alpha*exp(x))	alpha=1.673, scale=1.051
"gelu"	0.5*x*(1+tanh(sqrt(2/pi)*(x+0.044715*x^3)))	cdf + x*pdf	Gaussian Error Linear Unit
"swish"	x * sigmoid(x)	s + x*s*(1-s)	Self-gated
"sigmoid"	1/(1+exp(-x))	sigmoid(x)*(1-sigmoid(x))	Clipped to [-500, 500]
"tanh"	tanh(x)	1 - tanh(x)^2
"softmax"	exp(x - max(x)) / sum(exp(x - max(x)))	N/A (handled specially in backprop)	Output layer only
"linear"	x	1	Default if no activation specified

Usage in Layers:

model.add_dense(256, 128, activation="gelu")
model.add_dense(128, 10, activation="softmax")

---

Weight Initialization

Weight initialization functions are defined in Enilnets.weight_init. Used internally by layer constructors.

Standalone Functions

from Enilnets.weight_init import init_weights, init_conv_weights

w, b = init_weights(n_in, n_out, method="xavier_uniform")
w, b = init_conv_weights(in_ch, out_ch, k, method="he_normal")

Available Methods:

Method	Dense Formula	Conv Formula	Best For
"xavier_uniform"	U(-sqrt(6/(n_in+n_out)), sqrt(6/(n_in+n_out)))	U(-sqrt(6/(in_ch*k*k+out_ch)), ...)	Sigmoid/tanh
"xavier_normal"	N(0, sqrt(2/(n_in+n_out)))	N(0, sqrt(2/(in_ch*k*k+out_ch)))	Sigmoid/tanh
"he_uniform"	U(-sqrt(6/n_in), sqrt(6/n_in))	U(-sqrt(6/(in_ch*k*k)), ...)	ReLU variants
"he_normal"	N(0, sqrt(2/n_in))	N(0, sqrt(2/(in_ch*k*k)))	ReLU variants (default for conv)
"normal"	N(0, 0.1)	N(0, 0.1)	General purpose
"orthogonal"	SVD-based orthogonal init	SVD-based, reshaped	RNNs, deep nets

Biases:

• All methods initialize biases to zeros.

---

Reinforcement Learning

Reinforce

best_score = model.Reinforce(inputs, score_fn, noise=0.05, tries=10, sigma=1.0)

Evolutionary strategy that perturbs weights and keeps the best performing variant.

Parameters:

Parameter	Default	Description
inputs	required	Input to evaluate on
score_fn	required	Callable that takes model output and returns a scalar score (higher = better)
noise	0.05	Standard deviation multiplier for weight perturbations
tries	10	Number of candidate networks to try
sigma	1.0	Base standard deviation for perturbations

Returns:

• best_score: float, the highest score achieved

Side Effects:

• Mutates self.layers to the best performing configuration
• Original weights are lost unless saved beforehand

Algorithm:

1. Evaluate baseline score with current weights
2. For each try: add Gaussian noise to all weights/biases, evaluate score
3. Keep the candidate with highest score
4. Restore best weights to model

Example:

def score_fn(output):
    # Higher score = better policy
    return np.mean(output[:, 0])  # Example: maximize first output dimension

model.Reinforce(state_input, score_fn, noise=0.1, tries=20)

---

Model I/O

Save

model.Save(file)

Saves model architecture, weights, and training state to disk.

Parameters:

Parameter	Description
file	File path. Extension determines format: .pkl for pickle, anything else for JSON

Saved Data:

• Layer configurations and weights
• Optimizer type and hyperparameters
• Training timestep t

Example:

model.Save("model.pkl")      # Binary pickle format
model.Save("model.json")     # Human-readable JSON format

---

Load

model.Load(file)

Restores model from saved file.

Parameters:

Parameter	Description
file	File path (.pkl or .json)

Restored Data:

• All layer weights and configurations
• Optimizer settings
• Resets opt_state (optimizer momentum buffers are cleared)

Example:

model = NeuralNet()
model.Load("model.pkl")
predictions = model.Forward(X_test)

---

Utility Functions

im2col

from Enilnets.forward import im2col

col = im2col(input_data, filter_h, filter_w, stride=1, pad=0)

Converts image batches to column format for efficient convolution.

Parameters:

Parameter	Default	Description
input_data	required	4D array (N, C, H, W)
filter_h	required	Filter height
filter_w	required	Filter width
stride	1	Stride
pad	0	Zero padding

Returns:

• col: 2D array (N * out_h * out_w, C * filter_h * filter_w)

Example:

col = im2col(images, 3, 3, stride=1, pad=1)
# Now matrix multiplication can replace convolution

---

Complete Example: MNIST Classifier

from Enilnets import NeuralNet
import numpy as np

# Load data (pseudo-code)
# X_train: (60000, 1, 28, 28), Y_train: (60000, 10) one-hot
# X_test: (10000, 1, 28, 28), Y_test: (10000, 10)

# Build model
model = NeuralNet(learning_rate=0.001, optimizer="adam", l2_lambda=0.0001)

# Conv block 1
model.add_conv2d(1, 32, k=3, activation="relu", init_method="he_normal")
model.add_maxpool2d(2)

# Conv block 2
model.add_conv2d(32, 64, k=3, activation="relu", init_method="he_normal")
model.add_maxpool2d(2)

# Classifier
model.add_flatten()
model.add_dense(64 * 7 * 7, 256, activation="relu")
model.add_dropout(0.5)
model.add_dense(256, 10, activation="softmax")

# Print summary
model.summary()

# Train
history = model.Train(
    X_train, Y_train,
    epochs=10, batch_size=128,
    X_val=X_test, Y_val=Y_test,
    loss_function="cross_entropy",
    verbose=True
)

# Save
model.Save("mnist_model.pkl")

# Load and predict later
model2 = NeuralNet()
model2.Load("mnist_model.pkl")
predictions = model2.Forward(X_test)

---

Architecture Notes

Data Format

The library uses channels-first format for convolutions:

• 4D input: (batch, channels, height, width)
• This matches PyTorch convention, not TensorFlow's channels-last.

Backward Pass Details

The backward pass handles layer transitions automatically:

From Layer	To Layer	Error Propagation
Dense/Sparse	Dense/Sparse	np.dot(delta, W.T)
Conv2D	Conv2D	conv2d_backward_input (full convolution with flipped weights)
Flatten	Dense	reshape to match output shape
MaxPool2D	Any	Routes to max positions only
AvgPool2D	Any	Distributes equally
Dropout	Any	Scales by mask / (1 - rate)
BatchNorm	Any	Backprop through normalization + gamma/beta gradients

Numerical Stability

• Sigmoid clips inputs to [-500, 500] to prevent overflow
• Cross-entropy clips probabilities to [1e-12, 1.0]
• BatchNorm uses epsilon=1e-5 for division stability
• All computations use float64 dtype

---

API Reference Summary

NeuralNet Methods

Method	Description
__init__(lr, opt, l2, mom)	Constructor
summary()	Print architecture
add_dense(n_in, n_out, ...)	Add dense layer
add_sparse(n_in, n_out, ...)	Add sparse layer
add_conv2d(in_ch, out_ch, k, ...)	Add conv layer
add_flatten()	Add flatten layer
add_maxpool2d(p)	Add max pool
add_avgpool2d(p)	Add avg pool
add_batchnorm(n_features, ...)	Add batch norm
add_dropout(rate)	Add dropout
Forward(x, training, dropout_rate)	Forward pass
predict(x)	Alias for Forward
Backward(targets)	Backpropagation
update()	Apply gradients
TrainBatch(xs, ys, ...)	Train one batch
Train(X, Y, epochs, ...)	Full training loop
ComputeLoss(out, tgt, ...)	Compute loss
compute_accuracy(pred, tgt)	Compute accuracy
Reinforce(inputs, score_fn, ...)	Evolutionary optimization
Save(file)	Save model
Load(file)	Load model

Standalone Functions

Function	Module	Description
activate(name, x)	Enilnets.activations	Apply activation
derivative(name, x)	Enilnets.activations	Activation derivative
init_weights(n_in, n_out, method)	Enilnets.weight_init	Init dense weights
init_conv_weights(in_ch, out_ch, k, method)	Enilnets.weight_init	Init conv weights
im2col(data, fh, fw, stride, pad)	Enilnets.forward	Image to columns
batchnorm_forward(x, layer, training)	Enilnets.forward	Batch norm forward
maxpool2d_backward(d, x, p)	Enilnets.backward	Max pool backprop
avgpool2d_backward(d, x, p)	Enilnets.backward	Avg pool backprop
batchnorm_backward(dout, cache)	Enilnets.backward	Batch norm backprop
conv2d_backward_input(d, w, shape)	Enilnets.backward	Conv input gradient