B `]@sdZddlmZddlmZddlmZddlZddlmm Z ddl m Z ddl mZddlmZdd lmZdd lmZdd lmZd d ddgZe ZejZejZGdd d ejZGdddejZ Gdd d ej!Z"Gdddej#Z$dS)z+Affine layers for building neural networks.)absolute_import)division)print_functionN) distribution)normal)layers)util)variational_base) prefer_staticAffineAffineVariationalFlipout#AffineVariationalReparameterization(AffineVariationalReparameterizationLocalcs4eZdZdZddejejdddffdd ZZ S)r zBasic affine layer.Nc s|dkrtjgtjdntj|dgd}t|} t| dkrV||g} |g} tj} n2tj |||ggdd} tj ||ggdd} dd} t|} || | ||| | |\}}||_ t t |j ||| ||| d dS) akConstructs layer. Args: input_size: ... output_size: ... init_kernel_fn: ... Default value: `None` (i.e., `tfp.experimental.nn.initializers.glorot_uniform()`). init_bias_fn: ... Default value: `None` (i.e., `tf.initializers.zeros()`). make_kernel_bias_fn: ... Default value: `tfp.experimental.nn.util.make_kernel_bias`. dtype: ... Default value: `tf.float32`. batch_shape: ... Default value: `()`. activation_fn: ... Default value: `None`. name: ... Default value: `None` (i.e., `'Affine'`). N)dtype)shaper)ZaxiscSstjj||ddS)NT)Z adjoint_a)tfZlinalgZmatvec)xkrrj/home/dcms/DCMS/lib/python3.7/site-packages/tensorflow_probability/python/experimental/nn/affine_layers.pydz!Affine.__init__..)kernelbiasapply_kernel_fn activation_fnrname)nparrayint32r ZreshapesizerZget_static_valuematmulconcatZ_make_kernel_bias_fnsuperr __init__)self input_size output_sizeinit_kernel_fn init_bias_fnZmake_kernel_bias_fnrZ batch_shaperr batch_ndimsZ kernel_shapeZ bias_shaperrr) __class__rrr%1s4"    zAffine.__init__) __name__ __module__ __qualname____doc__ nn_util_libZmake_kernel_biasrfloat32r% __classcell__rr)r,rr .sc sDeZdZdZddejejejj e e j de dddf fdd ZZS)r aDensely-connected layer class with reparameterization estimator. This layer implements the Bayesian variational inference analogue to a dense layer by assuming the `kernel` and/or the `bias` are drawn from distributions. By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors, ```none kernel, bias ~ posterior outputs = matmul(inputs, kernel) + bias ``` It uses the reparameterization estimator [(Kingma and Welling, 2014)][1], which performs a Monte Carlo approximation of the distribution integrating over the `kernel` and `bias`. The arguments permit separate specification of the surrogate posterior (`q(W|x)`), prior (`p(W)`), and divergence for both the `kernel` and `bias` distributions. Upon being built, this layer adds losses (accessible via the `losses` property) representing the divergences of `kernel` and/or `bias` surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if `kl` is the sum of `losses` for each element of the batch, you should pass `kl / num_examples_per_epoch` to your optimizer). You can access the `kernel` and/or `bias` posterior and prior distributions after the layer is built via the `kernel_posterior`, `kernel_prior`, `bias_posterior` and `bias_prior` properties. #### Examples We illustrate a Bayesian neural network with [variational inference]( https://en.wikipedia.org/wiki/Variational_Bayesian_methods), assuming a dataset of images and length-10 one-hot `targets`. ```python import functools import tensorflow.compat.v2 as tf import tensorflow_probability as tfp import tensorflow_datasets as tfds tfb = tfp.bijectors tfd = tfp.distributions tfn = tfp.experimental.nn # 1 Prepare Dataset [train_dataset, eval_dataset], datasets_info = tfds.load( name='mnist', split=['train', 'test'], with_info=True, as_supervised=True, shuffle_files=True) def _preprocess(image, label): # image = image < tf.random.uniform(tf.shape(image)) # Randomly binarize. image = tf.cast(image, tf.float32) / 255. # Scale to unit interval. lo = 0.001 image = (1. - 2. * lo) * image + lo # Rescale to *open* unit interval. return image, label batch_size = 32 train_size = datasets_info.splits['train'].num_examples train_dataset = tfn.util.tune_dataset( train_dataset, batch_shape=(batch_size,), shuffle_size=int(train_size / 7), preprocess_fn=_preprocess) train_iter = iter(train_dataset) eval_iter = iter(eval_dataset) x, y = next(train_iter) evidence_shape = x.shape[1:] targets_shape = y.shape[1:] # 2 Specify Model BayesConv2D = functools.partial( tfn.ConvolutionVariationalReparameterization, rank=2, padding='same', filter_shape=5, # Use `he_uniform` because we'll use the `relu` family. init_kernel_fn=tf.initializers.he_uniform()) BayesAffine = functools.partial( tfn.AffineVariationalReparameterization, init_kernel_fn=tf.initializers.he_normal()) scale = tfp.util.TransformedVariable(1., tfb.Softplus()) bnn = tfn.Sequential([ BayesConv2D(evidence_shape[-1], 32, filter_shape=7, strides=2, activation_fn=tf.nn.leaky_relu), # [b, 14, 14, 32] tfn.util.flatten_rightmost(ndims=3), # [b, 14 * 14 * 32] BayesAffine(14 * 14 * 32, np.prod(target_shape) - 1), # [b, 9] tfn.Lambda( eval_fn=lambda loc: tfb.SoftmaxCentered()( tfd.Independent(tfd.Normal(loc, scale), reinterpreted_batch_ndims=1)), also_track=scale), # [b, 10] ], name='bayesian_neural_network') print(bnn.summary()) # 3 Train. def loss_fn(): x, y = next(train_iter) nll = -tf.reduce_mean(bnn(x).log_prob(y), axis=-1) kl = bnn.extra_loss / tf.cast(train_size, tf.float32) loss = nll + kl return loss, (nll, kl) opt = tf.optimizers.Adam() fit_op = tfn.util.make_fit_op(loss_fn, opt, bnn.trainable_variables) for _ in range(200): loss, (nll, kl), g = fit_op() ``` This example uses reparameterization gradients to minimize the Kullback-Leibler divergence up to a constant, also known as the negative Evidence Lower Bound. It consists of the sum of two terms: the expected negative log-likelihood, which we approximate via Monte Carlo; and the KL divergence, which is added via regularizer terms which are arguments to the layer. #### References [1]: Diederik Kingma and Max Welling. Auto-Encoding Variational Bayes. In _International Conference on Learning Representations_, 2014. https://arxiv.org/abs/1312.6114 Nc sh||_||_d}tt|j|||g|g||||| |||g|g||||| tj||| | | | | |d dS)amConstructs layer. Args: input_size: ... output_size: ... init_kernel_fn: ... Default value: `None` (i.e., `tfp.experimental.nn.initializers.glorot_uniform()`). init_bias_fn: ... Default value: `None` (i.e., `tf.initializers.zeros()`). make_posterior_fn: ... Default value: `tfp.experimental.nn.util.make_kernel_bias_posterior_mvn_diag`. make_prior_fn: ... Default value: `tfp.experimental.nn.util.make_kernel_bias_prior_spike_and_slab`. posterior_value_fn: ... Default valye: `tfd.Distribution.sample` unpack_weights_fn: Default value: `unpack_kernel_and_bias` dtype: ... Default value: `tf.float32`. penalty_weight: ... Default value: `None` (i.e., weight is `1`). posterior_penalty_fn: ... Default value: `kl_divergence_monte_carlo`. activation_fn: ... Default value: `None`. seed: ... Default value: `None` (i.e., no seed). name: ... Default value: `None` (i.e., `'AffineVariationalReparameterization'`). r) posteriorpriorrposterior_value_fnunpack_weights_fnrpenalty_weightposterior_penalty_fnrseedrN)_make_posterior_fn_make_prior_fnr$r r%rr")r&r'r(r)r*make_posterior_fn make_prior_fnr6r7rr8r9rr:rr+)r,rrr%s.5   z,AffineVariationalReparameterization.__init__)r-r.r/r0r1#make_kernel_bias_posterior_mvn_diag%make_kernel_bias_prior_spike_and_slabtfd Distributionsampleunpack_kernel_and_biasrr2kl_divergence_monte_carlor%r3rr)r,rr usc sDeZdZdZddejejejj e e j de dddf fdd ZZS)r a Densely-connected layer class with Flipout estimator. This layer implements the Bayesian variational inference analogue to a dense layer by assuming the `kernel` and/or the `bias` are drawn from distributions. By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors, ```none kernel, bias ~ posterior outputs = tf.linalg.matmul(inputs, kernel) + bias ``` It uses the Flipout estimator [(Wen et al., 2018)][1], which performs a Monte Carlo approximation of the distribution integrating over the `kernel` and `bias`. Flipout uses roughly twice as many floating point operations as the reparameterization estimator but has the advantage of significantly lower variance. The arguments permit separate specification of the surrogate posterior (`q(W|x)`), prior (`p(W)`), and divergence for both the `kernel` and `bias` distributions. Upon being built, this layer adds losses (accessible via the `losses` property) representing the divergences of `kernel` and/or `bias` surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if `kl` is the sum of `losses` for each element of the batch, you should pass `kl / num_examples_per_epoch` to your optimizer). #### Examples We illustrate a Bayesian neural network with [variational inference]( https://en.wikipedia.org/wiki/Variational_Bayesian_methods), assuming a dataset of images and length-10 one-hot `targets`. ```python # Using the following substitution, see: tfn = tfp.experimental.nn help(tfn.AffineVariationalReparameterization) BayesAffine = tfn.AffineVariationalFlipout ``` This example uses reparameterization gradients to minimize the Kullback-Leibler divergence up to a constant, also known as the negative Evidence Lower Bound. It consists of the sum of two terms: the expected negative log-likelihood, which we approximate via Monte Carlo; and the KL divergence, which is added via regularizer terms which are arguments to the layer. #### References [1]: Yeming Wen, Paul Vicol, Jimmy Ba, Dustin Tran, and Roger Grosse. Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches. In _International Conference on Learning Representations_, 2018. https://arxiv.org/abs/1803.04386 Nc sh||_||_d}tt|j|||g|g||||| |||g|g||||| tj||| | | | | |d dS)abConstructs layer. Args: input_size: ... output_size: ... init_kernel_fn: ... Default value: `None` (i.e., `tfp.experimental.nn.initializers.glorot_uniform()`). init_bias_fn: ... Default value: `None` (i.e., `tf.initializers.zeros()`). make_posterior_fn: ... Default value: `tfp.experimental.nn.util.make_kernel_bias_posterior_mvn_diag`. make_prior_fn: ... Default value: `tfp.experimental.nn.util.make_kernel_bias_prior_spike_and_slab`. posterior_value_fn: ... Default valye: `tfd.Distribution.sample` unpack_weights_fn: Default value: `unpack_kernel_and_bias` dtype: ... Default value: `tf.float32`. penalty_weight: ... Default value: `None` (i.e., weight is `1`). posterior_penalty_fn: ... Default value: `kl_divergence_monte_carlo`. activation_fn: ... Default value: `None`. seed: ... Default value: `None` (i.e., no seed). name: ... Default value: `None` (i.e., `'AffineVariationalFlipout'`). r) r4r5rr6r7rr8r9rr:rN)r;r<r$r r%rr")r&r'r(r)r*r=r>r6r7rr8r9rr:rr+)r,rrr%s.5   z!AffineVariationalFlipout.__init__)r-r.r/r0r1r?r@rArBrCrDrr2rEr%r3rr)r,rr Gs8c sXeZdZdZddejejejj e e j de dddf fdd ZeddZddZZS) ra Densely-connected layer class with local reparameterization estimator. This layer implements the Bayesian variational inference analogue to a dense layer by assuming the `kernel` and/or the `bias` are drawn from distributions. By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors, ```none kernel, bias ~ posterior outputs = matmul(inputs, kernel) + bias ``` It uses the local reparameterization estimator [(Kingma et al., 2015)][1], which performs a Monte Carlo approximation of the distribution on the hidden units induced by the `kernel` and `bias`. The default `kernel_posterior_fn` is a normal distribution which factorizes across all elements of the weight matrix and bias vector. Unlike [1]'s multiplicative parameterization, this distribution has trainable location and scale parameters which is known as an additive noise parameterization [(Molchanov et al., 2017)][2]. The arguments permit separate specification of the surrogate posterior (`q(W|x)`), prior (`p(W)`), and divergence for both the `kernel` and `bias` distributions. Upon being built, this layer adds losses (accessible via the `losses` property) representing the divergences of `kernel` and/or `bias` surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if `kl` is the sum of `losses` for each element of the batch, you should pass `kl / num_examples_per_epoch` to your optimizer). You can access the `kernel` and/or `bias` posterior and prior distributions after the layer is built via the `kernel_posterior`, `kernel_prior`, `bias_posterior` and `bias_prior` properties. #### Examples We illustrate a Bayesian neural network with [variational inference]( https://en.wikipedia.org/wiki/Variational_Bayesian_methods), assuming a dataset of images and length-10 one-hot `targets`. ```python # Using the following substitution, see: tfn = tfp.experimental.nn help(tfn.AffineVariationalReparameterization) BayesAffine = tfn.AffineVariationalReparameterizationLocal ``` This example uses reparameterization gradients to minimize the Kullback-Leibler divergence up to a constant, also known as the negative Evidence Lower Bound. It consists of the sum of two terms: the expected negative log-likelihood, which we approximate via Monte Carlo; and the KL divergence, which is added via regularizer terms which are arguments to the layer. #### References [1]: Diederik Kingma, Tim Salimans, and Max Welling. Variational Dropout and the Local Reparameterization Trick. In _Neural Information Processing Systems_, 2015. https://arxiv.org/abs/1506.02557 [2]: Dmitry Molchanov, Arsenii Ashukha, Dmitry Vetrov. Variational Dropout Sparsifies Deep Neural Networks. In _International Conference on Machine Learning_, 2017. https://arxiv.org/abs/1701.05369 Nc sh||_||_d}tt|j|||g|g||||| |||g|g||||| | | | || | |d ||_dS)abConstructs layer. Args: input_size: ... output_size: ... init_kernel_fn: ... Default value: `None` (i.e., `tfp.experimental.nn.initializers.glorot_uniform()`). init_bias_fn: ... Default value: `None` (i.e., `tf.initializers.zeros()`). make_posterior_fn: ... Default value: `tfp.experimental.nn.util.make_kernel_bias_posterior_mvn_diag`. make_prior_fn: ... Default value: `tfp.experimental.nn.util.make_kernel_bias_prior_spike_and_slab`. posterior_value_fn: ... Default valye: `tfd.Distribution.sample` unpack_weights_fn: Default value: `unpack_kernel_and_bias` dtype: ... Default value: `tf.float32`. penalty_weight: ... Default value: `None` (i.e., weight is `1`). posterior_penalty_fn: ... Default value: `kl_divergence_monte_carlo`. activation_fn: ... Default value: `None`. seed: ... Default value: `None` (i.e., no seed). name: ... Default value: `None` (i.e., `'AffineVariationalFlipout'`). r) r4r5rr8r9r6rr:rN)r;r<r$rr%_unpack_weights_fn)r&r'r(r)r*r=r>r6r7rr8r9rr:rr+)r,rrr%s,5   z1AffineVariationalReparameterizationLocal.__init__cCs|jS)N)rF)r&rrrr7]sz:AffineVariationalReparameterizationLocal.unpack_weights_fncCs||jj|dd\}}t|\}}t||}ttt|t|}||\} } | dk ryt|\} } d} Wnt k rd} YnX| r|| }tt|t| }n|| }t j ||dj | d}|jdk r||}|S)N)valuerTF)locscale)r:)r7r4Zsample_distributionsvi_libZget_spherical_normal_loc_scalerr"sqrtZsquare TypeError normal_libZNormalrCZ_seedr)r&rweightsZ kernel_distZ bias_distZ kernel_locZ kernel_scalerHrI_Z sampled_biasZbias_locZ bias_scaleZis_bias_spherical_normalyrrr_evalas,      z.AffineVariationalReparameterizationLocal._eval)r-r.r/r0r1r?r@rArBrCrDrr2rEr%propertyr7rQr3rr)r,rrs@: )%r0 __future__rrrnumpyrZtensorflow.compat.v2compatZv2rZ+tensorflow_probability.python.distributionsrZdistribution_librrMZ-tensorflow_probability.python.experimental.nnrZ layers_librr1r rJZ&tensorflow_probability.python.internalr __all__rArErDZKernelBiasLayerr Z,VariationalReparameterizationKernelBiasLayerr Z!VariationalFlipoutKernelBiasLayerr ZVariationalLayerrrrrrs2         G R