# Path: scratch/neural_networks.py
# def sigmoid(t: float) -> float:
#     return 1 / (1 + math.exp(-t))
# 
# Path: scratch/probability.py
# def inverse_normal_cdf(p: float,
#                        mu: float = 0,
#                        sigma: float = 1,
#                        tolerance: float = 0.00001) -> float:
#     """Find approximate inverse using binary search"""
# 
#     # if not standard, compute standard and rescale
#     if mu != 0 or sigma != 1:
#         return mu + sigma * inverse_normal_cdf(p, tolerance=tolerance)
# 
#     low_z = -10.0                      # normal_cdf(-10) is (very close to) 0
#     hi_z  =  10.0                      # normal_cdf(10)  is (very close to) 1
#     while hi_z - low_z > tolerance:
#         mid_z = (low_z + hi_z) / 2     # Consider the midpoint
#         mid_p = normal_cdf(mid_z)      # and the cdf's value there
#         if mid_p < p:
#             low_z = mid_z              # Midpoint too low, search above it
#         else:
#             hi_z = mid_z               # Midpoint too high, search below it
# 
#     return mid_z
# 
# Path: scratch/linear_algebra.py
# def dot(v: Vector, w: Vector) -> float:
#     """Computes v_1 * w_1 + ... + v_n * w_n"""
#     assert len(v) == len(w), "vectors must be same length"
# 
#     return sum(v_i * w_i for v_i, w_i in zip(v, w))
# 
# Path: scratch/linear_algebra.py
# def squared_distance(v: Vector, w: Vector) -> float:
#     """Computes (v_1 - w_1) ** 2 + ... + (v_n - w_n) ** 2"""
#     return sum_of_squares(subtract(v, w))


from typing import List
from typing import Callable
from typing import Iterable, Tuple
from scratch.neural_networks import sigmoid
from scratch.probability import inverse_normal_cdf
from scratch.linear_algebra import dot
from typing import List
from scratch.linear_algebra import squared_distance
    from scratch.neural_networks import binary_encode, fizz_buzz_encode, argmax
import operator
import random
import math
import json
    import tqdm
    import mnist
    import matplotlib.pyplot as plt
    import tqdm
        return random_normal(*dims)
    elif init == 'uniform':
        return random_uniform(*dims)
    elif init == 'xavier':
        variance = len(dims) / sum(dims)
        return random_normal(*dims, variance=variance)
    else:
        raise ValueError(f"unknown init: {init}")


class Linear(Layer):
    def __init__(self, input_dim: int, output_dim: int, init: str = 'xavier') -> None:
        """
        A layer of output_dim neurons, each with input_dim weights
        (and a bias).
        """
        self.input_dim = input_dim
        self.output_dim = output_dim

        # self.w[o] is the weights for the o-th neuron
        self.w = random_tensor(output_dim, input_dim, init=init)

        # self.b[o] is the bias term for the o-th neuron
        self.b = random_tensor(output_dim, init=init)

    def forward(self, input: Tensor) -> Tensor:
        # Save the input to use in the backward pass.
        self.input = input

        # Return the vector of neuron outputs.

# Path: scratch/neural_networks.py
# def sigmoid(t: float) -> float:
#     return 1 / (1 + math.exp(-t))
# 
# Path: scratch/probability.py
# def inverse_normal_cdf(p: float,
#                        mu: float = 0,
#                        sigma: float = 1,
#                        tolerance: float = 0.00001) -> float:
#     """Find approximate inverse using binary search"""
# 
#     # if not standard, compute standard and rescale
#     if mu != 0 or sigma != 1:
#         return mu + sigma * inverse_normal_cdf(p, tolerance=tolerance)
# 
#     low_z = -10.0                      # normal_cdf(-10) is (very close to) 0
#     hi_z  =  10.0                      # normal_cdf(10)  is (very close to) 1
#     while hi_z - low_z > tolerance:
#         mid_z = (low_z + hi_z) / 2     # Consider the midpoint
#         mid_p = normal_cdf(mid_z)      # and the cdf's value there
#         if mid_p < p:
#             low_z = mid_z              # Midpoint too low, search above it
#         else:
#             hi_z = mid_z               # Midpoint too high, search below it
# 
#     return mid_z
# 
# Path: scratch/linear_algebra.py
# def dot(v: Vector, w: Vector) -> float:
#     """Computes v_1 * w_1 + ... + v_n * w_n"""
#     assert len(v) == len(w), "vectors must be same length"
# 
#     return sum(v_i * w_i for v_i, w_i in zip(v, w))
# 
# Path: scratch/linear_algebra.py
# def squared_distance(v: Vector, w: Vector) -> float:
#     """Computes (v_1 - w_1) ** 2 + ... + (v_n - w_n) ** 2"""
#     return sum_of_squares(subtract(v, w))


# Path: scratch/deep_learning.py
from typing import List
from typing import Callable
from typing import Iterable, Tuple
from scratch.neural_networks import sigmoid
from scratch.probability import inverse_normal_cdf
from scratch.linear_algebra import dot
from typing import List
from scratch.linear_algebra import squared_distance
    from scratch.neural_networks import binary_encode, fizz_buzz_encode, argmax
import operator
import random
import math
import json
    import tqdm
    import mnist
    import matplotlib.pyplot as plt
    import tqdm

        return random_normal(*dims)
    elif init == 'uniform':
        return random_uniform(*dims)
    elif init == 'xavier':
        variance = len(dims) / sum(dims)
        return random_normal(*dims, variance=variance)
    else:
        raise ValueError(f"unknown init: {init}")


class Linear(Layer):
    def __init__(self, input_dim: int, output_dim: int, init: str = 'xavier') -> None:
        """
        A layer of output_dim neurons, each with input_dim weights
        (and a bias).
        """
        self.input_dim = input_dim
        self.output_dim = output_dim

        # self.w[o] is the weights for the o-th neuron
        self.w = random_tensor(output_dim, input_dim, init=init)

        # self.b[o] is the bias term for the o-th neuron
        self.b = random_tensor(output_dim, init=init)

    def forward(self, input: Tensor) -> Tensor:
        # Save the input to use in the backward pass.
        self.input = input

        # Return the vector of neuron outputs.

        return [dot(input, self.w[o]) + self.b[o]