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Fix complexities #166

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Fix complexities #166

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86625f6
more detailed complexities
Bihaqo Jan 6, 2019
25835c4
fix the code to actually get the advertaised complexity
Bihaqo Jan 6, 2019
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22 changes: 13 additions & 9 deletions t3f/riemannian.py
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Original file line number Diff line number Diff line change
Expand Up @@ -389,12 +389,16 @@ def project_matmul(what, where, matrix):
a TensorTrain with the TT-ranks equal 2 * tangent_space_tens.get_tt_ranks()

Complexity:
O(d r_where^3 m) for orthogonalizing the TT-cores of where
O(d r_where^3 m) for orthogonalizing the TT-cores
+O(batch_size d R r_what r_where (n r_what + n m R + m r_where))
d is the number of TT-cores (what.ndims());
r_what is the largest TT-rank of what max(what.get_tt_rank())
r_where is the largest TT-rank of where
matrix is of TT-rank R and of raw-shape (m, m, ..., m) x (n, n, ..., n).
or equivalently
O(d r_where^3 m)
+O(batch_size d R^3 r_what r_where n m R)
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This is wrong

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O(batch_size d R^2 r_what r_where n m)

given that m r_where < n m R and n r_what < n m R, where
d is the number of TT-cores (what.ndims());
r_what is the largest TT-rank of what (max(what.get_tt_rank()))
r_where is the largest TT-rank of where
matrix is of TT-rank R and of raw-shape (m, m, ..., m) x (n, n, ..., n).
"""

if not isinstance(where, TensorTrain):
Expand Down Expand Up @@ -446,8 +450,8 @@ def project_matmul(what, where, matrix):
tens_core = what.tt_cores[core_idx]
right_tang_core = right_tangent_space_tens.tt_cores[core_idx]
matrix_core = matrix.tt_cores[core_idx]
rhs[core_idx] = tf.einsum('bije,cikf,sdef,sajkd->sabc', matrix_core,
right_tang_core, rhs[core_idx + 1], tens_core)
rhs[core_idx] = tf.einsum('cikf,sdef,bije,sajkd->sabc', right_tang_core,
rhs[core_idx + 1], matrix_core, tens_core)
# Prepare lhs vectors.
# lhs[core_idx] is of size
# batch_size x tangent_tt_ranks[core_idx] x matrix_tt_ranks[core_idx] x tensor_tt_ranks[core_idx]
Expand All @@ -458,8 +462,8 @@ def project_matmul(what, where, matrix):
left_tang_core = left_tangent_space_tens.tt_cores[core_idx]
matrix_core = matrix.tt_cores[core_idx]
# TODO: brutforce order of indices in lhs??
lhs[core_idx + 1] = tf.einsum('bije,aikd,sabc,scjkf->sdef', matrix_core,
left_tang_core, lhs[core_idx], tens_core)
lhs[core_idx + 1] = tf.einsum('aikd,sabc,bije,scjkf->sdef', left_tang_core,
lhs[core_idx], matrix_core, tens_core)

# Left to right sweep.
res_cores_list = []
Expand Down