ComputesY = g(X) = DCT(X), where DCT type is indicated by the type arg

The discrete cosine transform efficiently applies a unitary DCT operator. This can be useful for mixing and decorrelating across the innermost event dimension. The inverse X = g^{-1}(Y) = IDCT(Y), where IDCT is DCT-III for type==2. This bijector can be interleaved with Affine bijectors to build a cascade of structured efficient linear layers as in Moczulski et al., 2016. Note that the operator applied is orthonormal (i.e. norm='ortho').

tfb_discrete_cosine_transform(
  validate_args = FALSE,
  dct_type = 2,
  name = "dct"
)

Arguments

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.
dct_type	integer, the DCT type performed by the forward transformation. Currently, only 2 and 3 are supported.
name	name prefixed to Ops created by this class.

Value

a bijector instance.

References

• Moczulski M, Denil M, Appleyard J, de Freitas N. ACDC: A structured efficient linear layer. In International Conference on Learning Representations, 2016.

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_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_real_nvp(), 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()