RealNVP affine coupling layer for vector-valued events

Real NVP models a normalizing flow on a D-dimensional distribution via a single D-d-dimensional conditional distribution (Dinh et al., 2017): y[d:D] = x[d:D] * tf.exp(log_scale_fn(x[0:d])) + shift_fn(x[0:d]) y[0:d] = x[0:d] The last D-d units are scaled and shifted based on the first d units only, while the first d units are 'masked' and left unchanged. Real NVP's shift_and_log_scale_fn computes vector-valued quantities. For scale-and-shift transforms that do not depend on any masked units, i.e. d=0, use the tfb_affine bijector with learned parameters instead. Masking is currently only supported for base distributions with event_ndims=1. For more sophisticated masking schemes like checkerboard or channel-wise masking (Papamakarios et al., 2016), use the tfb_permute bijector to re-order desired masked units into the first d units. For base distributions with event_ndims > 1, use the tfb_reshape bijector to flatten the event shape.

tfb_real_nvp(
  num_masked,
  shift_and_log_scale_fn,
  is_constant_jacobian = FALSE,
  validate_args = FALSE,
  name = NULL
)

Arguments

num_masked	integer indicating that the first d units of the event should be masked. Must be in the closed interval [1, D-1], where D is the event size of the base distribution.
shift_and_log_scale_fn	Function which computes shift and log_scale from both the forward domain (x) and the inverse domain (y). Calculation must respect the "autoregressive property". Suggested default: tfb_real_nvp_default_template(hidden_layers=...). Typically the function contains tf$Variables and is wrapped using tf$make_template. Returning NULL for either (both) shift, log_scale is equivalent to (but more efficient than) returning zero.
is_constant_jacobian	Logical, default: FALSE. When TRUE the implementation assumes log_scale does not depend on the forward domain (x) or inverse domain (y) values. (No validation is made; is_constant_jacobian=FALSE is always safe but possibly computationally inefficient.)
validate_args	Logical, default FALSE. Whether to validate input with asserts. If validate_args is FALSE, and the inputs are invalid, correct behavior is not guaranteed.
name	name prefixed to Ops created by this class.

Value

a bijector instance.

Details

Recall that the MAF bijector (Papamakarios et al., 2016) implements a normalizing flow via an autoregressive transformation. MAF and IAF have opposite computational tradeoffs - MAF can train all units in parallel but must sample units sequentially, while IAF must train units sequentially but can sample in parallel. In contrast, Real NVP can compute both forward and inverse computations in parallel. However, the lack of an autoregressive transformations makes it less expressive on a per-bijector basis.

A "valid" shift_and_log_scale_fn must compute each shift (aka loc or "mu" in Papamakarios et al. (2016) and log(scale) (aka "alpha" in Papamakarios et al. (2016)) such that each are broadcastable with the arguments to forward and inverse, i.e., such that the calculations in forward, inverse below are possible. For convenience, real_nvp_default_nvp is offered as a possible shift_and_log_scale_fn function.

NICE (Dinh et al., 2014) is a special case of the Real NVP bijector which discards the scale transformation, resulting in a constant-time inverse-log-determinant-Jacobian. To use a NICE bijector instead of Real NVP, shift_and_log_scale_fn should return (shift, NULL), and is_constant_jacobian should be set to TRUE in the RealNVP constructor. Calling tfb_real_nvp_default_template with shift_only=TRUE returns one such NICE-compatible shift_and_log_scale_fn.

Caching: the scalar input depth D of the base distribution is not known at construction time. The first call to any of forward(x), inverse(x), inverse_log_det_jacobian(x), or forward_log_det_jacobian(x) memoizes D, which is re-used in subsequent calls. This shape must be known prior to graph execution (which is the case if using tf$layers).

References

• George Papamakarios, Theo Pavlakou, and Iain Murray. Masked Autoregressive Flow for Density Estimation. In Neural Information Processing Systems, 2017.

• Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. Density Estimation using Real NVP. In International Conference on Learning Representations, 2017.

• Laurent Dinh, David Krueger, and Yoshua Bengio. NICE: Non-linear Independent Components Estimation.arXiv preprint arXiv:1410.8516,2014.

• Eric Jang. Normalizing Flows Tutorial, Part 2: Modern Normalizing Flows. Technical Report_, 2018.

See also

For usage examples see tfb_forward(), tfb_inverse(), tfb_inverse_log_det_jacobian().

Other bijectors: tfb_absolute_value(), tfb_affine_linear_operator(), tfb_affine_scalar(), tfb_affine(), tfb_ascending(), tfb_batch_normalization(), tfb_blockwise(), tfb_chain(), tfb_cholesky_outer_product(), tfb_cholesky_to_inv_cholesky(), tfb_correlation_cholesky(), tfb_cumsum(), tfb_discrete_cosine_transform(), tfb_expm1(), tfb_exp(), tfb_ffjord(), tfb_fill_scale_tri_l(), tfb_fill_triangular(), tfb_glow(), tfb_gompertz_cdf(), tfb_gumbel_cdf(), tfb_gumbel(), tfb_identity(), tfb_inline(), tfb_invert(), tfb_iterated_sigmoid_centered(), tfb_kumaraswamy_cdf(), tfb_kumaraswamy(), tfb_lambert_w_tail(), tfb_masked_autoregressive_default_template(), tfb_masked_autoregressive_flow(), tfb_masked_dense(), tfb_matrix_inverse_tri_l(), tfb_matvec_lu(), tfb_normal_cdf(), tfb_ordered(), tfb_pad(), tfb_permute(), tfb_power_transform(), tfb_rational_quadratic_spline(), tfb_rayleigh_cdf(), tfb_real_nvp_default_template(), tfb_reciprocal(), tfb_reshape(), tfb_scale_matvec_diag(), tfb_scale_matvec_linear_operator(), tfb_scale_matvec_lu(), tfb_scale_matvec_tri_l(), tfb_scale_tri_l(), tfb_scale(), tfb_shifted_gompertz_cdf(), tfb_shift(), tfb_sigmoid(), tfb_sinh_arcsinh(), tfb_sinh(), tfb_softmax_centered(), tfb_softplus(), tfb_softsign(), tfb_split(), tfb_square(), tfb_tanh(), tfb_transform_diagonal(), tfb_transpose(), tfb_weibull_cdf(), tfb_weibull()