730 lines
21 KiB
Python
730 lines
21 KiB
Python
import numpy as np
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_f = np.float32
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# just for speed, not strictly essential:
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from scipy.special import expit as sigmoid
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# used for numbering layers like Keras:
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from collections import defaultdict
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_layer_counters = defaultdict(lambda: 0)
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def _check(a):
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assert isinstance(a, np.ndarray) or type(a) == _f, type(a)
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assert a.dtype == _f, a.dtype
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return a
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_0 = _f(0)
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_1 = _f(1)
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_2 = _f(2)
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_inv2 = _f(1/2)
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_sqrt2 = _f(np.sqrt(2))
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_invsqrt2 = _f(1/np.sqrt(2))
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_pi = _f(np.pi)
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# Initializations {{{1
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# note: these are currently only implemented for 2D shapes.
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def init_he_normal(size, ins, outs):
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s = np.sqrt(2 / ins)
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return np.random.normal(0, s, size=size)
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def init_he_uniform(size, ins, outs):
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s = np.sqrt(6 / ins)
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return np.random.uniform(-s, s, size=size)
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# Loss functions {{{1
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class Loss:
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per_batch = False
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def mean(self, r):
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return np.average(self.f(r))
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def dmean(self, r):
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d = self.df(r)
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return d / len(d)
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class Squared(Loss):
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def f(self, r):
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return np.square(r)
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def df(self, r):
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return 2 * r
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class Absolute(Loss):
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def f(self, r):
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return np.abs(r)
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def df(self, r):
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return np.sign(r)
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# Optimizers {{{1
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class Optimizer:
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def __init__(self, alpha=0.1):
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self.alpha = _f(alpha)
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self.reset()
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def reset(self):
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pass
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def compute(self, dW, W):
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return -self.alpha * dW
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def update(self, dW, W):
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W += self.compute(dW, W)
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# the following optimizers are blatantly lifted from tiny-dnn:
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# https://github.com/tiny-dnn/tiny-dnn/blob/master/tiny_dnn/optimizers/optimizer.h
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class Momentum(Optimizer):
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def __init__(self, alpha=0.01, lamb=0, mu=0.9, nesterov=False):
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self.alpha = _f(alpha) # learning rate
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self.lamb = _f(lamb) # weight decay
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self.mu = _f(mu) # momentum
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self.nesterov = bool(nesterov)
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self.reset()
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def reset(self):
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self.dWprev = None
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def compute(self, dW, W):
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if self.dWprev is None:
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#self.dWprev = np.zeros_like(dW)
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self.dWprev = np.copy(dW)
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V = self.mu * self.dWprev - self.alpha * (dW + W * self.lamb)
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self.dWprev[:] = V
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if self.nesterov: # TODO: is this correct? looks weird
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return self.mu * V - self.alpha * (dW + W * self.lamb)
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else:
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return V
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class RMSprop(Optimizer):
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# RMSprop generalizes* Adagrad, etc.
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# * RMSprop == Adagrad when
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# RMSprop.mu == 1
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def __init__(self, alpha=0.0001, mu=0.99, eps=1e-8):
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self.alpha = _f(alpha) # learning rate
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self.mu = _f(mu) # decay term
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self.eps = _f(eps)
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# one might consider the following equation when specifying mu:
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# mu = e**(-1/t)
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# default: t = -1/ln(0.99) = ~99.5
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# therefore the default of mu=0.99 means
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# an input decays to 1/e its original amplitude over 99.5 epochs.
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# (this is from DSP, so how relevant it is in SGD is debatable)
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self.reset()
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def reset(self):
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self.g = None
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def compute(self, dW, W):
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if self.g is None:
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self.g = np.zeros_like(dW)
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# basically apply a first-order low-pass filter to delta squared
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self.g[:] = self.mu * self.g + (1 - self.mu) * dW * dW
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# equivalent (though numerically different?):
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#self.g += (dW * dW - self.g) * (1 - self.mu)
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# finally sqrt it to complete the running root-mean-square approximation
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return -self.alpha * dW / np.sqrt(self.g + self.eps)
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class Adam(Optimizer):
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# Adam generalizes* RMSprop, and
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# adds a decay term to the regular (non-squared) delta, and
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# does some decay-gain voodoo. (i guess it's compensating
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# for the filtered deltas starting from zero)
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# * Adam == RMSprop when
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# Adam.b1 == 0
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# Adam.b2 == RMSprop.mu
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# Adam.b1_t == 0
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# Adam.b2_t == 0
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def __init__(self, alpha=0.001, b1=0.9, b2=0.999, b1_t=0.9, b2_t=0.999, eps=1e-8):
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self.alpha = _f(alpha) # learning rate
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self.b1 = _f(b1) # decay term
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self.b2 = _f(b2) # decay term
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self.b1_t_default = _f(b1_t) # decay term power t
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self.b2_t_default = _f(b2_t) # decay term power t
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self.eps = _f(eps)
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self.reset()
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def reset(self):
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self.mt = None
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self.vt = None
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self.b1_t = self.b1_t_default
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self.b2_t = self.b2_t_default
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def compute(self, dW, W):
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if self.mt is None:
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self.mt = np.zeros_like(dW)
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if self.vt is None:
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self.vt = np.zeros_like(dW)
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# decay gain
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self.b1_t *= self.b1
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self.b2_t *= self.b2
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# filter
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self.mt[:] = self.b1 * self.mt + (1 - self.b1) * dW
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self.vt[:] = self.b2 * self.vt + (1 - self.b2) * dW * dW
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return -self.alpha * (self.mt / (1 - self.b1_t)) \
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/ np.sqrt((self.vt / (1 - self.b2_t)) + self.eps)
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# Abstract Layers {{{1
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class Layer:
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def __init__(self):
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self.parents = []
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self.children = []
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self.input_shape = None
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self.output_shape = None
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kind = self.__class__.__name__
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global _layer_counters
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_layer_counters[kind] += 1
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self.name = "{}_{}".format(kind, _layer_counters[kind])
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self.size = None # total weight count (if any)
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self.unsafe = False # disables assertions for better performance
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def __str__(self):
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return self.name
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# methods we might want to override:
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def F(self, X):
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raise NotImplementedError("unimplemented", self)
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def dF(self, dY):
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raise NotImplementedError("unimplemented", self)
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def do_feed(self, child):
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self.children.append(child)
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def be_fed(self, parent):
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self.parents.append(parent)
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def make_shape(self, shape):
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if not self.unsafe:
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assert shape is not None
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if self.output_shape is None:
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self.output_shape = shape
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return shape
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# TODO: rename this multi and B crap to something actually relevant.
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def multi(self, B):
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if not self.unsafe:
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assert len(B) == 1, self
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return self.F(B[0])
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def dmulti(self, dB):
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if len(dB) == 1:
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return self.dF(dB[0])
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else:
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dX = None
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for dY in dB:
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if dX is None:
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dX = self.dF(dY)
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else:
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dX += self.dF(dY)
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return dX
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# general utility methods:
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def compatible(self, parent):
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if self.input_shape is None:
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# inherit shape from output
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shape = self.make_shape(parent.output_shape)
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if shape is None:
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return False
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self.input_shape = shape
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if np.all(self.input_shape == parent.output_shape):
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return True
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else:
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return False
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def feed(self, child):
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if not child.compatible(self):
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fmt = "{} is incompatible with {}: shape mismatch: {} vs. {}"
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raise Exception(fmt.format(self, child, self.output_shape, child.input_shape))
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self.do_feed(child)
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child.be_fed(self)
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return child
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def validate_input(self, X):
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assert X.shape[1:] == self.input_shape, (str(self), X.shape[1:], self.input_shape)
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def validate_output(self, Y):
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assert Y.shape[1:] == self.output_shape, (str(self), Y.shape[1:], self.output_shape)
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def forward(self, lut):
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if not self.unsafe:
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assert len(self.parents) > 0, self
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B = []
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for parent in self.parents:
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# TODO: skip over irrelevant nodes (if any)
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X = lut[parent]
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if not self.unsafe:
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self.validate_input(X)
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B.append(X)
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Y = self.multi(B)
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if not self.unsafe:
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self.validate_output(Y)
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return Y
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def backward(self, lut):
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if not self.unsafe:
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assert len(self.children) > 0, self
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dB = []
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for child in self.children:
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# TODO: skip over irrelevant nodes (if any)
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dY = lut[child]
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if not self.unsafe:
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self.validate_output(dY)
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dB.append(dY)
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dX = self.dmulti(dB)
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if not self.unsafe:
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self.validate_input(dX)
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return dX
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# Nonparametric Layers {{{1
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class Sum(Layer):
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def multi(self, B):
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return np.sum(B, axis=0)
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def dmulti(self, dB):
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#assert len(dB) == 1, "unimplemented"
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return dB[0] # TODO: does this always work?
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class Input(Layer):
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def __init__(self, shape):
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assert shape is not None
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super().__init__()
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self.shape = tuple(shape)
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self.input_shape = self.shape
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self.output_shape = self.shape
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def F(self, X):
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return X
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def dF(self, dY):
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#self.dY = dY
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return np.zeros_like(dY)
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class Affine(Layer):
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def __init__(self, a=1, b=0):
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super().__init__()
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self.a = _f(a)
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self.b = _f(b)
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def F(self, X):
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return self.a * X + self.b
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def dF(self, dY):
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return dY * self.a
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class Sigmoid(Layer): # aka Logistic
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def F(self, X):
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self.sig = sigmoid(X)
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return X * self.sig
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def dF(self, dY):
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return dY * self.sig * (1 - self.sig)
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class Tanh(Layer):
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def F(self, X):
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self.sig = np.tanh(X)
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return X * self.sig
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def dF(self, dY):
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return dY * (1 - self.sig * self.sig)
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class Relu(Layer):
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def F(self, X):
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self.cond = X >= 0
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return np.where(self.cond, X, 0)
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def dF(self, dY):
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return np.where(self.cond, dY, 0)
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class Elu(Layer):
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# paper: https://arxiv.org/abs/1511.07289
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def __init__(self, alpha=1):
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super().__init__()
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self.alpha = _f(alpha)
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def F(self, X):
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self.cond = X >= 0
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self.neg = np.exp(X) - 1
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return np.where(self.cond, X, self.neg)
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def dF(self, dY):
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return dY * np.where(self.cond, 1, self.neg + 1)
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class GeluApprox(Layer):
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# paper: https://arxiv.org/abs/1606.08415
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# plot: https://www.desmos.com/calculator/ydzgtccsld
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def F(self, X):
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self.a = 1.704 * X
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self.sig = sigmoid(self.a)
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return X * self.sig
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def dF(self, dY):
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return dY * self.sig * (1 + self.a * (1 - self.sig))
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# Parametric Layers {{{1
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class Dense(Layer):
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def __init__(self, dim, init=init_he_uniform):
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super().__init__()
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self.dim = int(dim)
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self.output_shape = (dim,)
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self.weight_init = init
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self.size = None
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def make_shape(self, shape):
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super().make_shape(shape)
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if len(shape) != 1:
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return False
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self.nW = self.dim * shape[0]
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self.nb = self.dim
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self.size = self.nW + self.nb
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return shape
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def init(self, W, dW):
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ins, outs = self.input_shape[0], self.output_shape[0]
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self.W = W
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self.dW = dW
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self.coeffs = self.W[:self.nW].reshape(ins, outs)
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self.biases = self.W[self.nW:].reshape(1, outs)
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self.dcoeffs = self.dW[:self.nW].reshape(ins, outs)
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self.dbiases = self.dW[self.nW:].reshape(1, outs)
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self.coeffs.flat = self.weight_init(self.nW, ins, outs)
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self.biases.flat = 0
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self.std = np.std(self.W)
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def F(self, X):
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self.X = X
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Y = X.dot(self.coeffs) + self.biases
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return Y
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def dF(self, dY):
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dX = dY.dot(self.coeffs.T)
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self.dcoeffs[:] = self.X.T.dot(dY)
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self.dbiases[:] = dY.sum(0, keepdims=True)
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return dX
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class DenseOneLess(Dense):
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def init(self, W, dW):
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super().init(W, dW)
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ins, outs = self.input_shape[0], self.output_shape[0]
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assert ins == outs, (ins, outs)
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def F(self, X):
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np.fill_diagonal(self.coeffs, 0)
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self.X = X
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Y = X.dot(self.coeffs) + self.biases
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return Y
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def dF(self, dY):
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dX = dY.dot(self.coeffs.T)
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self.dcoeffs[:] = self.X.T.dot(dY)
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self.dbiases[:] = dY.sum(0, keepdims=True)
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np.fill_diagonal(self.dcoeffs, 0)
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return dX
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# Models {{{1
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class Model:
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def __init__(self, x, y, unsafe=False):
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assert isinstance(x, Layer), x
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assert isinstance(y, Layer), y
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self.x = x
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self.y = y
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self.ordered_nodes = self.traverse([], self.y)
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self.make_weights()
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for node in self.ordered_nodes:
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node.unsafe = unsafe
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def make_weights(self):
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self.param_count = 0
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for node in self.ordered_nodes:
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if node.size is not None:
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self.param_count += node.size
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self.W = np.zeros(self.param_count, dtype=_f)
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self.dW = np.zeros(self.param_count, dtype=_f)
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offset = 0
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for node in self.ordered_nodes:
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if node.size is not None:
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end = offset + node.size
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node.init(self.W[offset:end], self.dW[offset:end])
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offset += node.size
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def traverse(self, nodes, node):
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if node == self.x:
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return [node]
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for parent in node.parents:
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if parent not in nodes:
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new_nodes = self.traverse(nodes, parent)
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for new_node in new_nodes:
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if new_node not in nodes:
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nodes.append(new_node)
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if nodes:
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nodes.append(node)
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return nodes
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def forward(self, X):
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lut = dict()
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input_node = self.ordered_nodes[0]
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output_node = self.ordered_nodes[-1]
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lut[input_node] = input_node.multi(np.expand_dims(X, 0))
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for node in self.ordered_nodes[1:]:
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lut[node] = node.forward(lut)
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return lut[output_node]
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def backward(self, error):
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lut = dict()
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input_node = self.ordered_nodes[0]
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output_node = self.ordered_nodes[-1]
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lut[output_node] = output_node.dmulti(np.expand_dims(error, 0))
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for node in reversed(self.ordered_nodes[:-1]):
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lut[node] = node.backward(lut)
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#return lut[input_node] # meaningless value
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return self.dW
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def load_weights(self, fn):
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# seemingly compatible with keras' Dense layers.
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# ignores any non-Dense layer types.
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# TODO: assert file actually exists
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import h5py
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f = h5py.File(fn)
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weights = {}
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def visitor(name, obj):
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if isinstance(obj, h5py.Dataset):
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weights[name.split('/')[-1]] = np.array(obj[:], dtype=_f)
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f.visititems(visitor)
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f.close()
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denses = [node for node in self.ordered_nodes if isinstance(node, Dense)]
|
|
for i in range(len(denses)):
|
|
a, b = i, i + 1
|
|
b_name = "dense_{}".format(b)
|
|
# TODO: write a Dense method instead of assigning directly
|
|
denses[a].coeffs[:] = weights[b_name+'_W']
|
|
denses[a].biases[:] = np.expand_dims(weights[b_name+'_b'], 0)
|
|
|
|
def save_weights(self, fn, overwrite=False):
|
|
import h5py
|
|
f = h5py.File(fn, 'w')
|
|
|
|
denses = [node for node in self.ordered_nodes if isinstance(node, Dense)]
|
|
for i in range(len(denses)):
|
|
a, b = i, i + 1
|
|
b_name = "dense_{}".format(b)
|
|
# TODO: write a Dense method instead of assigning directly
|
|
grp = f.create_group(b_name)
|
|
data = grp.create_dataset(b_name+'_W', denses[a].coeffs.shape, dtype=_f)
|
|
data[:] = denses[a].coeffs
|
|
data = grp.create_dataset(b_name+'_b', denses[a].biases.shape, dtype=_f)
|
|
data[:] = denses[a].biases
|
|
|
|
f.close()
|
|
|
|
# Rituals {{{1
|
|
|
|
class Ritual: # i'm just making up names at this point
|
|
def __init__(self, learner=None, loss=None, mloss=None):
|
|
self.learner = learner if learner is not None else Learner(Optimizer())
|
|
self.loss = loss if loss is not None else Squared()
|
|
self.mloss = mloss if mloss is not None else loss
|
|
|
|
def reset(self):
|
|
self.learner.reset(optim=True)
|
|
|
|
def measure(self, residual):
|
|
return self.mloss.mean(residual)
|
|
|
|
def derive(self, residual):
|
|
return self.loss.dmean(residual)
|
|
|
|
def learn(self, inputs, outputs):
|
|
predicted = self.model.forward(inputs)
|
|
residual = predicted - outputs
|
|
self.model.backward(self.derive(residual))
|
|
return residual
|
|
|
|
def update(self):
|
|
self.learner.optim.update(self.model.dW, self.model.W)
|
|
|
|
def prepare(self, model):
|
|
self.en = 0
|
|
self.bn = 0
|
|
self.model = model
|
|
|
|
def train_batched(self, inputs, outputs, batch_size, return_losses=False):
|
|
self.en += 1
|
|
cumsum_loss = _0
|
|
batch_count = inputs.shape[0] // batch_size
|
|
losses = []
|
|
for b in range(batch_count):
|
|
self.bn += 1
|
|
bi = b * batch_size
|
|
batch_inputs = inputs[ bi:bi+batch_size]
|
|
batch_outputs = outputs[bi:bi+batch_size]
|
|
|
|
if self.learner.per_batch:
|
|
self.learner.batch(b / batch_count)
|
|
|
|
residual = self.learn(batch_inputs, batch_outputs)
|
|
self.update()
|
|
|
|
batch_loss = self.measure(residual)
|
|
if np.isnan(batch_loss):
|
|
raise Exception("nan")
|
|
cumsum_loss += batch_loss
|
|
if return_losses:
|
|
losses.append(batch_loss)
|
|
avg_loss = cumsum_loss / _f(batch_count)
|
|
if return_losses:
|
|
return avg_loss, losses
|
|
else:
|
|
return avg_loss
|
|
|
|
# Learners {{{1
|
|
|
|
class Learner:
|
|
per_batch = False
|
|
|
|
def __init__(self, optim, epochs=100, rate=None):
|
|
assert isinstance(optim, Optimizer)
|
|
self.optim = optim
|
|
self.start_rate = optim.alpha if rate is None else _f(rate)
|
|
self.epochs = int(epochs)
|
|
self.reset()
|
|
|
|
def reset(self, optim=False):
|
|
self.started = False
|
|
self.epoch = 0
|
|
if optim:
|
|
self.optim.reset()
|
|
|
|
@property
|
|
def epoch(self):
|
|
return self._epoch
|
|
|
|
@epoch.setter
|
|
def epoch(self, new_epoch):
|
|
self._epoch = int(new_epoch)
|
|
self.rate = self.rate_at(self._epoch)
|
|
|
|
@property
|
|
def rate(self):
|
|
return self.optim.alpha
|
|
|
|
@rate.setter
|
|
def rate(self, new_rate):
|
|
self.optim.alpha = new_rate
|
|
|
|
def rate_at(self, epoch):
|
|
return self.start_rate
|
|
|
|
def next(self):
|
|
# prepares the next epoch. returns whether or not to continue training.
|
|
if self.epoch + 1 >= self.epochs:
|
|
return False
|
|
if self.started:
|
|
self.epoch += 1
|
|
else:
|
|
self.started = True
|
|
self.epoch = self.epoch # poke property setter just in case
|
|
return True
|
|
|
|
def batch(self, progress): # TODO: rename
|
|
# interpolates rates between epochs.
|
|
# unlike epochs, we do not store batch number as a state.
|
|
# i.e. calling next() will not respect progress.
|
|
assert 0 <= progress <= 1
|
|
self.rate = self.rate_at(self._epoch + progress)
|
|
|
|
@property
|
|
def final_rate(self):
|
|
return self.rate_at(self.epochs - 1)
|
|
|
|
class AnnealingLearner(Learner):
|
|
def __init__(self, optim, epochs=100, rate=None, halve_every=10):
|
|
self.halve_every = _f(halve_every)
|
|
self.anneal = _f(0.5**(1/self.halve_every))
|
|
super().__init__(optim, epochs, rate)
|
|
|
|
def rate_at(self, epoch):
|
|
return self.start_rate * self.anneal**epoch
|
|
|
|
def cosmod(x):
|
|
# plot: https://www.desmos.com/calculator/hlgqmyswy2
|
|
return (_1 + np.cos((x % _1) * _pi)) * _inv2
|
|
|
|
class SGDR(Learner):
|
|
# Stochastic Gradient Descent with Restarts
|
|
# paper: https://arxiv.org/abs/1608.03983
|
|
# NOTE: this is missing a couple features.
|
|
|
|
per_batch = True
|
|
|
|
def __init__(self, optim, epochs=100, rate=None,
|
|
restarts=0, restart_decay=0.5, callback=None,
|
|
expando=None):
|
|
self.restart_epochs = int(epochs)
|
|
self.decay = _f(restart_decay)
|
|
self.restarts = int(restarts)
|
|
self.restart_callback = callback
|
|
# TODO: rename expando to something not insane
|
|
self.expando = expando if expando is not None else lambda i: 1
|
|
|
|
self.splits = []
|
|
epochs = 0
|
|
for i in range(0, self.restarts + 1):
|
|
split = epochs + int(self.restart_epochs * self.expando(i))
|
|
self.splits.append(split)
|
|
epochs = split
|
|
super().__init__(optim, epochs, rate)
|
|
|
|
def split_num(self, epoch):
|
|
shit = [0] + self.splits # hack
|
|
for i in range(0, len(self.splits)):
|
|
if epoch < self.splits[i]:
|
|
sub_epoch = epoch - shit[i]
|
|
next_restart = self.splits[i] - shit[i]
|
|
return i, sub_epoch, next_restart
|
|
raise Exception('this should never happen.')
|
|
|
|
def rate_at(self, epoch):
|
|
restart, sub_epoch, next_restart = self.split_num(epoch)
|
|
x = _f(sub_epoch) / _f(next_restart)
|
|
return self.start_rate * self.decay**_f(restart) * cosmod(x)
|
|
|
|
def next(self):
|
|
if not super().next():
|
|
return False
|
|
restart, sub_epoch, next_restart = self.split_num(self.epoch)
|
|
if restart > 0 and sub_epoch == 0:
|
|
if self.restart_callback is not None:
|
|
self.restart_callback(restart)
|
|
return True
|