tfb_ffjord | R Documentation |
This bijector implements a continuous dynamics transformation parameterized by a differential equation, where initial and terminal conditions correspond to domain (X) and image (Y) i.e.
tfb_ffjord( state_time_derivative_fn, ode_solve_fn = NULL, trace_augmentation_fn = tfp$bijectors$ffjord$trace_jacobian_hutchinson, initial_time = 0, final_time = 1, validate_args = FALSE, dtype = tf$float32, name = "ffjord" )
state_time_derivative_fn |
|
ode_solve_fn |
|
trace_augmentation_fn |
|
initial_time |
Scalar float representing time to which the |
final_time |
Scalar float representing time to which the |
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. |
dtype |
|
name |
name prefixed to Ops created by this class. |
d/dt[state(t)] = state_time_derivative_fn(t, state(t)) state(initial_time) = X state(final_time) = Y
For this transformation the value of log_det_jacobian
follows another
differential equation, reducing it to computation of the trace of the jacobian
along the trajectory
state_time_derivative = state_time_derivative_fn(t, state(t)) d/dt[log_det_jac(t)] = Tr(jacobian(state_time_derivative, state(t)))
FFJORD constructor takes two functions ode_solve_fn
and
trace_augmentation_fn
arguments that customize integration of the
differential equation and trace estimation.
Differential equation integration is performed by a call to ode_solve_fn
.
Custom ode_solve_fn
must accept the following arguments:
ode_fn(time, state): Differential equation to be solved.
initial_time: Scalar float or floating Tensor representing the initial time.
initial_state: Floating Tensor representing the initial state.
solution_times: 1D floating Tensor of solution times.
And return a Tensor of shape [solution_times$shape, initial_state$shape]
representing state values evaluated at solution_times
. In addition
ode_solve_fn
must support nested structures. For more details see the
interface of tfp$math$ode$Solver$solve()
.
Trace estimation is computed simultaneously with state_time_derivative
using augmented_state_time_derivative_fn
that is generated by
trace_augmentation_fn
. trace_augmentation_fn
takes
state_time_derivative_fn
, state.shape
and state.dtype
arguments and
returns a augmented_state_time_derivative_fn
callable that computes both
state_time_derivative
and unreduced trace_estimation
.
Custom ode_solve_fn
and trace_augmentation_fn
examples:
# custom_solver_fn: `function(f, t_initial, t_solutions, y_initial, ...)` # ... : Additional arguments to pass to custom_solver_fn. ode_solve_fn <- function(ode_fn, initial_time, initial_state, solution_times) { custom_solver_fn(ode_fn, initial_time, solution_times, initial_state, ...) } ffjord <- tfb_ffjord(state_time_derivative_fn, ode_solve_fn = ode_solve_fn)
# state_time_derivative_fn: `function(time, state)` # trace_jac_fn: `function(time, state)` unreduced jacobian trace function trace_augmentation_fn <- function(ode_fn, state_shape, state_dtype) { augmented_ode_fn <- function(time, state) { list(ode_fn(time, state), trace_jac_fn(time, state)) } augmented_ode_fn } ffjord <- tfb_ffjord(state_time_derivative_fn, trace_augmentation_fn = trace_augmentation_fn)
For more details on FFJORD and continous normalizing flows see Chen et al. (2018), Grathwol et al. (2018).
a bijector instance.
Chen, T. Q., Rubanova, Y., Bettencourt, J., & Duvenaud, D. K. (2018). Neural ordinary differential equations. In Advances in neural information processing systems (pp. 6571-6583)
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_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()
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