Python tensor.sqrt函数代码示例

    def get_updates_adadelta(grads,params,decay=0.95):
        decay = constantX(decay)
        print 'build updates with adadelta'
        for param, grad in zip(params, grads):
            # mean_squared_grad := E[g^2]_{t-1}
            mean_square_grad = sharedX(numpy.zeros(param.get_value().shape, dtype=floatX))
            # mean_square_dx := E[(\Delta x)^2]_{t-1}
            mean_square_dx = sharedX(numpy.zeros(param.get_value().shape, dtype=floatX))
            if param.name is not None:
                mean_square_grad.name = 'mean_square_grad_' + param.name
                mean_square_dx.name = 'mean_square_dx_' + param.name

            # Accumulate gradient
            new_mean_squared_grad = \
                    decay * mean_square_grad +\
                    (1. - decay) * T.sqr(grad)
            # Compute update
            epsilon = constantX(1e-7)
            rms_dx_tm1 = T.sqrt(mean_square_dx + epsilon)
            rms_grad_t = T.sqrt(new_mean_squared_grad + epsilon)
            delta_x_t = - rms_dx_tm1 / rms_grad_t * grad

            # Accumulate updates
            new_mean_square_dx = \
                    decay * mean_square_dx + \
                    (1. - decay) * T.sqr(delta_x_t)

            # Apply update
            updates[mean_square_grad] = new_mean_squared_grad
            updates[mean_square_dx] = new_mean_square_dx
            updates[param] = param + delta_x_t

def adadelta(lr,tparams,grads,x,mask,y,cost):
    zipped_grads = [theano.shared(p.get_value() * numpy_floatX(0.),
                                  name='%s_grad' % k)
                    for k, p in tparams.items()]
    running_up2 = [theano.shared(p.get_value() * numpy_floatX(0.),
                                 name='%s_rup2' % k)
                   for k, p in tparams.items()]
    running_grads2 = [theano.shared(p.get_value() * numpy_floatX(0.),
                                    name='%s_rgrad2' % k)
                      for k, p in tparams.items()]

    zgup = [(zg, g) for zg, g in zip(zipped_grads, grads)]
    rg2up = [(rg2, 0.95 * rg2 + 0.05 * (g ** 2))
             for rg2, g in zip(running_grads2, grads)]

    f_grad_shared = theano.function([x, mask, y], cost, updates=zgup + rg2up,
                                    name='adadelta_f_grad_shared')

    updir = [-T.sqrt(ru2 + 1e-6) / T.sqrt(rg2 + 1e-6) * zg
             for zg, ru2, rg2 in zip(zipped_grads,
                                     running_up2,
                                     running_grads2)]
    ru2up = [(ru2, 0.95 * ru2 + 0.05 * (ud ** 2))
             for ru2, ud in zip(running_up2, updir)]
    #梯度更新字典
    param_up = [(p, p + ud) for p, ud in zip(tparams.values(), updir)]

    f_update = theano.function([lr], [], updates=ru2up + param_up,
                               on_unused_input='ignore',
                               name='adadelta_f_update')

    return f_grad_shared, f_update

  def buildUpdatesSimpleMomentum(self, batchTrainer, momentum,
                  batchLearningRate, error):

    deltaParams = T.grad(error, batchTrainer.params)
    updates = []
    parametersTuples = zip(batchTrainer.params,
                           deltaParams,
                           batchTrainer.oldUpdates,
                           batchTrainer.oldMeanSquare,
                           batchTrainer.hasNormConstraint)

    for param, delta, oldUpdate, oldMeanSquare, hasNormConstraint in parametersTuples:
      paramUpdate = momentum * oldUpdate
      if self.rmsprop:
        meanSquare = 0.9 * oldMeanSquare + 0.1 * delta ** 2
        paramUpdate += - batchLearningRate * delta / T.sqrt(meanSquare + 1e-8)
        updates.append((oldMeanSquare, meanSquare))
      else:
        paramUpdate += - batchLearningRate * delta

      newParam = param + paramUpdate

      if self.normConstraint is not None and hasNormConstraint:
        norms = SquaredElementWiseNorm(newParam)
        rescaled = norms > self.normConstraint
        factors = T.ones(norms.shape, dtype=theanoFloat) / T.sqrt(norms) * np.sqrt(self.normConstraint, dtype='float32') - 1.0
        replaceNewParam = (factors * rescaled) * newParam
        replaceNewParam += newParam
        newParam = replaceNewParam
        # paramUpdate = newParam - param

      updates.append((param, newParam))
      updates.append((oldUpdate, paramUpdate))

    return updates

def batchnorm(X, rescale=None, reshift=None, u=None, s=None, e=1e-8):
    """
    batchnorm with support for not using scale and shift parameters
    as well as inference values (u and s) and partial batchnorm (via a)
    will detect and use convolutional or fully connected version
    """
    g = rescale
    b = reshift
    if X.ndim == 4:
        if u is not None and s is not None:
            # use normalization params given a priori
            b_u = u.dimshuffle('x', 0, 'x', 'x')
            b_s = s.dimshuffle('x', 0, 'x', 'x')
        else:
            # compute normalization params from input
            b_u = T.mean(X, axis=[0, 2, 3]).dimshuffle('x', 0, 'x', 'x')
            b_s = T.mean(T.sqr(X - b_u), axis=[0, 2, 3]).dimshuffle('x', 0, 'x', 'x')
        # batch normalize
        X = (X - b_u) / T.sqrt(b_s + e)
        if g is not None and b is not None:
            # apply rescale and reshift
            X = X*T.exp(0.2*g.dimshuffle('x', 0, 'x', 'x')) + b.dimshuffle('x', 0, 'x', 'x')
    elif X.ndim == 2:
        if u is None and s is None:
            # compute normalization params from input
            u = T.mean(X, axis=0)
            s = T.mean(T.sqr(X - u), axis=0)
        # batch normalize
        X = (X - u) / T.sqrt(s + e)
        if g is not None and b is not None:
            # apply rescale and reshift
            X = X*T.exp(0.2*g) + b
    else:
        raise NotImplementedError
    return X

    def get_mu_sigma(self, X_noisy, t):
        """
        Generate mu and sigma for one step in the reverse trajectory,
        starting from a minibatch of images X_noisy, and at timestep t.
        """
        Z = self.mlp.apply(X_noisy)
        mu_coeff, beta_coeff = self.temporal_readout(Z, t)
        # reverse variance is perturbation around forward variance
        beta_forward = self.get_beta_forward(t)
        # make impact of beta_coeff scaled appropriately with mu_coeff
        beta_coeff_scaled = beta_coeff / np.sqrt(self.trajectory_length).astype(theano.config.floatX)
        beta_reverse = T.nnet.sigmoid(beta_coeff_scaled + util.logit(beta_forward))
        # # reverse mean is decay towards mu_coeff
        # mu = (X_noisy - mu_coeff)*T.sqrt(1. - beta_reverse) + mu_coeff
        # reverse mean is a perturbation around the mean under forward
        # process


        # # DEBUG -- use these lines to test objective is 0 for isotropic Gaussian model
        # beta_reverse = beta_forward
        # mu_coeff = mu_coeff*0


        mu = X_noisy*T.sqrt(1. - beta_forward) + mu_coeff*T.sqrt(beta_forward)
        sigma = T.sqrt(beta_reverse)
        mu.name = 'mu p'
        sigma.name = 'sigma p'
        return mu, sigma

    def sample_s_given_ghv(self, g_sample, h_sample, v_sample, rng=None, size=None):
        """
        Generates sample from p(s | g, h, v)
        """
        s_mean = self.s_given_ghv(g_sample, h_sample, v_sample)
        
        rng = self.theano_rng if rng is None else rng
        size = size if size else self.batch_size

        if self.flags['truncate_s']:
            s_sample = truncated.truncated_normal(
                    size=(size, self.n_s),
                    avg = s_mean, 
                    std = T.sqrt(1./self.alpha_prec),
                    lbound = self.truncation_bound['s'],
                    ubound = self.truncation_bound['s'],
                    theano_rng = rng,
                    dtype=floatX)
        else: 
            s_sample = rng.normal(
                    size=(size, self.n_s),
                    avg = s_mean, 
                    std = T.sqrt(1./self.alpha_prec),
                    dtype=floatX)
        return s_sample

def adadelta(lr, tparams, grads, inp, cost):
    zipped_grads = [theano.shared(p.get_value() * numpy.float32(0.),
                                  name='%s_grad' % k)
                    for k, p in tparams.iteritems()]
    running_up2 = [theano.shared(p.get_value() * numpy.float32(0.),
                                 name='%s_rup2' % k)
                   for k, p in tparams.iteritems()]
    running_grads2 = [theano.shared(p.get_value() * numpy.float32(0.),
                                    name='%s_rgrad2' % k)
                      for k, p in tparams.iteritems()]

    zgup = [(zg, g) for zg, g in zip(zipped_grads, grads)]
    rg2up = [(rg2, 0.95 * rg2 + 0.05 * (g ** 2))
             for rg2, g in zip(running_grads2, grads)]

    f_grad_shared = theano.function(inp, cost, updates=zgup+rg2up,
                                    profile=profile)

    updir = [-tensor.sqrt(ru2 + 1e-6) / tensor.sqrt(rg2 + 1e-6) * zg
             for zg, ru2, rg2 in zip(zipped_grads, running_up2,
                                     running_grads2)]
    ru2up = [(ru2, 0.95 * ru2 + 0.05 * (ud ** 2))
             for ru2, ud in zip(running_up2, updir)]
    param_up = [(p, p + ud) for p, ud in zip(itemlist(tparams), updir)]

    f_update = theano.function([lr], [], updates=ru2up+param_up,
                               on_unused_input='ignore', profile=profile)

    return f_grad_shared, f_update

    def ADAMopt(self, tVars, loss, lr, momentum=0):

        i = T.iscalar('i'); lr = T.fscalar('lr');
        grads = T.grad(loss, tVars)
        '''ADAM Code from
            https://github.com/danfischetti/deep-recurrent-attentive-writer/blob/master/DRAW/adam.py
        '''
        self.m = [theano.shared(name = 'm', \
                value = np.zeros(param.get_value().shape,dtype=theano.config.floatX)) for param in model.params]
        self.v = [theano.shared(name = 'v', \
        	value = np.zeros(param.get_value().shape,dtype=theano.config.floatX)) for param in model.params]
        self.t = theano.shared(name = 't',value = np.asarray(1).astype(theano.config.floatX))
        updates = [(self.t,self.t+1)]

        for param, gparam,m,v in zip(model.params, gparams, self.m, self.v):

            b1_t = 1-(1-beta1)*(l**(self.t-1))
            m_t = b1_t*gparam + (1-b1_t)*m
            updates.append((m,m_t))
            v_t = beta2*(gparam**2)+(1-beta2)*v
            updates.append((v,v_t))
            m_t_bias = m_t/(1-(1-beta1)**self.t)
            v_t_bias = v_t/(1-(1-beta2)**self.t)
            if param.get_value().ndim == 1:
                updates.append((param,param - 5*lr*m_t_bias/(T.sqrt(v_t_bias)+epsilon)))
            else:
                updates.append((param,param - lr*m_t_bias/(T.sqrt(v_t_bias)+epsilon)))

        return theano.function([], loss, updates=updates)

 def applyConstraint(self, param):
     if param.ndim != 4 and param.ndim != 2:
         warnings.warn("Norm constraints are normally applied to matrices"
                       +" or 4-dimensional tensors, but currently got "
                       +"%d dimensions, please make sure this is the desired"
                       +" parameter to apply norm constraints" % param.ndim)
         
     needFlip = False
     if param.ndim == 4: # a hack for conv layer filters
         prevShape = param.shape
         # conv layer filter shape is (nChannelOut, nChannelIn, r, c)
         param = param.flatten(2)
         # now it is (nout, nin), which is different from (nin, nout) 
         # from fulling connected networks, so need to flip here
         needFlip = True
     
     if needFlip:
         col_norm = T.sqrt(T.sum(T.sqr(param), axis=1, keepdims=True))
     else:
         col_norm = T.sqrt(T.sum(T.sqr(param), axis=0, keepdims=True))
         
     param /= (col_norm+1e-7)
     param *= self.norm
     
     if needFlip:
         param = param.reshape(prevShape)
                     
     return param

    def get_updates(self, params, loss):
        grads = self.get_gradients(loss, params)
        accumulators = [shared_zeros(p.get_value().shape) for p in params]
        delta_accumulators = [shared_zeros(p.get_value().shape) for p in params]
        self.updates = []
        n_step = theano.shared(1.0)
        self.updates.append((n_step, n_step + 1))

        for p, g, a, d_a in zip(params, grads, accumulators, delta_accumulators):
            g_noise = self.rng.normal(p.shape, 0, T.sqrt(n_step ** - 0.55), dtype='float32')
            g_deviated = g + g_noise

            new_a = self.rho * a + (1 - self.rho) * g_deviated ** 2  # update accumulator
            self.updates.append((a, new_a))

            # use the new accumulator and the *old* delta_accumulator
            update = g_deviated * T.sqrt(d_a + self.epsilon) / T.sqrt(new_a +
                                                             self.epsilon)

            new_p = p - self.lr * update
            self.updates.append((p, new_p))

            # update delta_accumulator
            new_d_a = self.rho * d_a + (1 - self.rho) * update ** 2
            self.updates.append((d_a, new_d_a))
        return self.updates

    def forward(self,input_org,train=True,update_batch_stat=True,finetune=False):
        print "Layer/BatchNormalization"
        ldim,cdim,rdim = self._internal_shape(input_org)
        input = input_org.reshape((ldim,cdim,rdim))
        if (train):
            mean = T.mean(input, axis=(0, 2), keepdims=True )
            var = T.mean((input-mean)**2, axis=(0, 2), keepdims=True)

            if(update_batch_stat):
                finetune_N = theano.clone(self.finetune_N, share_inputs=False)
                if(finetune):
                    finetune_N.default_update = finetune_N+1
                    ratio = T.cast(1-1.0/(finetune_N+1),theano.config.floatX)
                else:
                    finetune_N.default_update = 0
                    ratio = self.moving_avg_ratio
                m = ldim*rdim
                scale = T.cast(m/(m-1.0),theano.config.floatX)
                est_mean = theano.clone(self.est_mean, share_inputs=False)
                est_var = theano.clone(self.est_var, share_inputs=False)
                est_mean.default_update = T.cast(ratio*self.est_mean + (1-ratio)*mean,theano.config.floatX)
                est_var.default_update = T.cast(ratio*self.est_var + (1-ratio)*scale*var,theano.config.floatX)
                mean += 0 * est_mean
                var += 0 * est_var
            output = self._pbc(self.gamma) * (input - self._pbc(mean)) \
                     / T.sqrt(1e-6+self._pbc(var)) + self._pbc(self.beta)

        else:
            output = self._pbc(self.gamma) * (input - self._pbc(self.est_mean)) \
                     / T.sqrt(1e-6+self._pbc(self.est_var)) + self._pbc(self.beta)

        return output.reshape(input_org.shape)

def AdadeltaUpdate(params,cost,stepSize=1.0,rho=0.95,epsilon=1e-6,norm_lim=9):
    updates=OrderedDict({})
    exp_sqr_grads=OrderedDict({})
    exp_sqr_update=OrderedDict({})
    g_params=[]
    for param in params:
        empty=np.zeros_like(param.get_value())
        exp_sqr_grads[param]=theano.shared(value=as_floatX(empty),name='exp_grad_%s'%param.name)
        exp_sqr_update[param]=theano.shared(value=as_floatX(empty),name='exp_grad_%s'%param.name)
        gp=T.grad(cost,param)
        g_params.append(gp)
    for param,gp in zip(params,g_params):
        exp_sg=exp_sqr_grads[param]
        exp_su=exp_sqr_update[param]
        update_exp_sg=rho*exp_sg+(1-rho)*T.sqr(gp)#????
        updates[exp_sg]=update_exp_sg
        
        step=-(T.sqrt(exp_su+epsilon)/T.sqrt(update_exp_sg+epsilon))*gp
        stepped_param=param+step*stepSize
        
        update_exp_su=rho*exp_su+(1-rho)*T.sqr(step)
        updates[exp_su]=update_exp_su

        if param.get_value(borrow=True).ndim==2 and param.name!='wordVec':
            col_norms=T.sqrt(T.sum(T.sqr(stepped_param),axis=0))
            desired_norms=T.clip(col_norms,0,T.sqrt(norm_lim))#???
            scale=desired_norms/(1e-7+col_norms)
            updates[param]=stepped_param*scale
        else:
            updates[param]=stepped_param
    return updates

def make_functions(inputs,outputs,params,grads,lr):
	shapes = [ p.get_value().shape for p in params ]
	acc_grads = [ theano.shared(np.zeros(s,dtype=np.float32)) for s in shapes ]
	count = theano.shared(np.float32(0))
	acc_update = [ (a,a+g) for a,g in zip(acc_grads,grads) ] + [ (count,count + 1.) ]

#	deltas = acc_grads
	deltas	  = [ ag / count for ag in acc_grads ]
	grads_norms = [ T.sqrt(T.sum(g**2)) for g in deltas ]
	deltas	  = [ T.switch(T.gt(n,1.),1.*g/n,g) for n,g in zip(grads_norms,deltas) ]
	
#	param_update = [ (p, p - lr * g) for p,g in zip(params,deltas) ]
	param_update = updates.adadelta(params,deltas,learning_rate=lr) # ,learning_rate=lr,rho=np.float32(0.95)

	clear_update = [ 
			(a,np.zeros(s,dtype=np.float32)) 
			for a,s in zip(acc_grads,shapes) 
			] + [ (count,0) ]
	acc = theano.function(
			inputs  = inputs,
			outputs = [outputs,output_ans[ans_lbl]],
			updates = acc_update,
			on_unused_input='warn',
#			mode=theano.compile.MonitorMode(post_func=detect_nan)
		)
	update = theano.function(
			inputs=[lr],
			updates = param_update + clear_update,
			outputs = [ T.sqrt(T.sum(T.sqr(w))) for w in deltas ],
			on_unused_input='warn',
#			mode=theano.compile.MonitorMode(post_func=detect_nan)
		)
	return acc,update

 def __init__(self, vocab_size, dim, lr=0.5):
     W = np.asarray(np.random.rand(vocab_size, dim),
                    dtype=theano.config.floatX) / float(dim)
     W1 = np.asarray((np.random.rand(vocab_size, dim)),
                     dtype=theano.config.floatX) / float(dim)
     self.W = theano.shared(W, name='W', borrow=True)
     self.W1 = theano.shared(W1, name='W1', borrow=True)
     gW = np.asarray(np.ones((vocab_size, dim)), dtype=theano.config.floatX)
     gW1 = np.asarray(
         np.ones((vocab_size, dim)), dtype=theano.config.floatX)
     self.gW = theano.shared(gW, name='gW', borrow=True)
     self.gW1 = theano.shared(gW1, name='gW1', borrow=True)
     X = T.vector()
     fX = T.vector()
     ind_W = T.ivector()
     ind_W1 = T.ivector()
     w = self.W[ind_W, :]
     w1 = self.W1[ind_W1, :]
     cost = T.sum(fX * ((T.sum(w * w1, axis=1) - X) ** 2))
     grad = T.clip(T.grad(cost, [w, w1]), -5.0, 5.0)
     updates1 = [(self.gW, T.inc_subtensor(self.gW[ind_W, :],
                                           grad[0] ** 2))]
     updates2 = [(self.gW1, T.inc_subtensor(self.gW1[ind_W1, :],
                                            grad[1] ** 2))]
     updates3 = [(self.W, T.inc_subtensor(self.W[ind_W, :],
                                          - (lr / T.sqrt(self.gW[ind_W, :])) *
                                          grad[0]))]
     updates4 = [(self.W1, T.inc_subtensor(self.W1[ind_W1, :],
                                           - (lr / T.sqrt(self.gW1[ind_W1, :])) *
                                           grad[1]))]
     updates = updates1 + updates2 + updates3 + updates4
     self.cost_fn = theano.function(
         inputs=[ind_W, ind_W1, X, fX], outputs=cost, updates=updates)

    def _get_model_updates(self):
        alpha = self.params['optimizer/learning_rate']

        updates = dict()
        for name, param in self.network.params.items():
            gradient = self.params[name + '_gradient']
            ms_gradient = self.params[name + '_mean_sqr_gradient']
            ms_velocity = self.params[name + '_mean_sqr_velocity']
            # rms_velocity quantity lags behind rms_gradient by 1 time step,
            # due to the recurrence relationship for velocity.
            rms_gradient = tensor.sqrt(ms_gradient + self._epsilon)
            rms_velocity = tensor.sqrt(ms_velocity + self._epsilon)
            velocity = -gradient * rms_velocity / rms_gradient
            updates[name] = velocity
        self._normalize(updates)

        result = []
        for name, param in self.network.params.items():
            update = updates[name]
            ms_velocity = self.params[name + '_mean_sqr_velocity']
            ms_velocity_new = self._gamma * ms_velocity + \
                              (1.0 - self._gamma) * tensor.sqr(update)
            param_new = param + alpha * update
            result.append((ms_velocity, ms_velocity_new))
            result.append((param, param_new))
        return result