-
-
Notifications
You must be signed in to change notification settings - Fork 610
/
basic.jl
928 lines (719 loc) · 29.6 KB
/
basic.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
"""
Chain(layers...)
Chain(name = layer, ...)
Collects multiple layers / functions to be called in sequence
on a given input. Supports indexing and slicing, `m[2]` or `m[1:end-1]`,
and if names are given, `m[:name] == m[1]` etc.
# Examples
```jldoctest
julia> m = Chain(x -> x^2, x -> x+1);
julia> m(5) == 26
true
julia> m = Chain(Dense(10 => 5, tanh), Dense(5 => 2));
julia> x = rand32(10, 32);
julia> m(x) == m[2](m[1](x))
true
julia> m2 = Chain(enc = Chain(Flux.flatten, Dense(10 => 5, tanh)),
dec = Dense(5 => 2));
julia> m2(x) == (m2[:dec] ∘ m2[:enc])(x)
true
```
A chain may be called with multiple arguments, which is equivalent to calling it
with one tuple of these arguments. Such a tuple is understood by [`Parallel`](@ref)
to mean the same as several arguments:
```jldoctest
julia> Chain(println, println)(1, 2, 3) # three arguments become a tuple
(1, 2, 3)
nothing
julia> Chain(x->@show(x), Parallel(+, inv, abs2))(4, 5) # returns 1/4 + 5^2
x = (4, 5)
25.25
```
For large models, there is a special type-unstable path which can reduce compilation
times. This can be used by supplying a vector of layers `Chain([layer1, layer2, ...])`.
This feature is somewhat experimental, beware!
"""
struct Chain{T<:Union{Tuple, NamedTuple, AbstractVector}}
layers::T
end
Chain(xs...) = Chain(xs)
function Chain(; kw...)
:layers in keys(kw) && throw(ArgumentError("a Chain cannot have a named layer called `layers`"))
isempty(kw) && return Chain(())
Chain(values(kw))
end
@forward Chain.layers Base.getindex, Base.length, Base.first, Base.last,
Base.iterate, Base.lastindex, Base.keys, Base.firstindex
@layer Chain
(c::Chain)(x) = _applychain(c.layers, x)
(c::Chain)(x, ys...) = _applychain(c.layers, (x, ys...))
@generated function _applychain(layers::Tuple{Vararg{Any,N}}, x) where {N}
symbols = vcat(:x, [gensym() for _ in 1:N])
calls = [:($(symbols[i+1]) = layers[$i]($(symbols[i]))) for i in 1:N]
Expr(:block, calls...)
end
_applychain(layers::NamedTuple, x) = _applychain(Tuple(layers), x)
function _applychain(layers::AbstractVector, x) # type-unstable path, helps compile times
for f in layers
x = f(x)
end
return x
end
# An easy error to make is to pass result of explicit gradient(...), not gradient(...)[1]
# Can't catch every case, but can catch many simple Flux models:
function Optimisers.update!(opt, model::Chain, grads::Tuple)
# Zygote will make a NamedTuple{(:layers,)} for the gradient of Chain, Diffractor a Tangent
@warn """explicit `update!(opt, model, grad)` wants the gradient for the model alone,
not the whole tuple from `gradient(m -> loss(m, x, y), model)`. You probably want `grads[1]`."""
return Optimisers.update!(opt, model, grads[1])
end
Base.getindex(c::Chain, i::AbstractArray) = Chain(c.layers[i])
Base.getindex(c::Chain{<:NamedTuple}, i::AbstractArray) =
Chain(NamedTuple{keys(c)[i]}(Tuple(c.layers)[i]))
function Base.show(io::IO, c::Chain)
print(io, "Chain(")
_show_layers(io, c.layers)
print(io, ")")
end
_show_layers(io, layers::Tuple) = join(io, layers, ", ")
_show_layers(io, layers::NamedTuple) = join(io, [lazy"$k = $v" for (k, v) in pairs(layers)], ", ")
_show_layers(io, layers::AbstractVector) = (print(io, "["); join(io, layers, ", "); print(io, "]"))
# This is a temporary and naive implementation
# it might be replaced in the future for better performance
# see issue https://github.com/FluxML/Flux.jl/issues/702
# Johnny Chen -- @johnnychen94
# only slightly changed to better handle interaction with Zygote @dsweber2
"""
activations(c::Chain, input)
Like calling a `Chain`, but saves the result of each layer as an output.
# Examples
```jldoctest
julia> using Flux: activations
julia> c = Chain(x -> x + 1, x -> x * 2, x -> x ^ 3);
julia> activations(c, 1)
(2, 4, 64)
```
"""
activations(c::Chain, input) = _extraChain(Tuple(c.layers), input)
# Calculates the forward results of each layer provided in a `Tuple` with `x` as model input.
function _extraChain(fs::Tuple, x)
res = first(fs)(x)
return (res, _extraChain(Base.tail(fs), res)...)
end
_extraChain(::Tuple{}, x) = ()
"""
Dense(in => out, σ=identity; bias=true, init=glorot_uniform)
Dense(W::AbstractMatrix, [bias, σ])
Create a traditional fully connected layer, whose forward pass is given by:
y = σ.(W * x .+ bias)
The input `x` should be a vector of length `in`, or batch of vectors represented
as an `in × N` matrix, or any array with `size(x,1) == in`.
The out `y` will be a vector of length `out`, or a batch with
`size(y) == (out, size(x)[2:end]...)`
Keyword `bias=false` will switch off trainable bias for the layer.
The initialisation of the weight matrix is `W = init(out, in)`, calling the function
given to keyword `init`, with default [`glorot_uniform`](@ref Flux.glorot_uniform).
The weight matrix and/or the bias vector (of length `out`) may also be provided explicitly.
# Examples
```jldoctest
julia> model = Dense(5 => 2)
Dense(5 => 2) # 12 parameters
julia> model(rand32(5, 64)) |> size
(2, 64)
julia> model(rand32(5, 6, 4, 64)) |> size # treated as three batch dimensions
(2, 6, 4, 64)
julia> model2 = Dense(ones(2, 5), false, tanh) # using provided weight matrix
Dense(5 => 2, tanh; bias=false) # 10 parameters
julia> model2(ones(5))
2-element Vector{Float64}:
0.9999092042625951
0.9999092042625951
julia> Flux.trainables(model2) # no trainable bias
1-element Vector{AbstractArray}:
[1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0]
```
"""
struct Dense{F, M<:AbstractMatrix, B}
weight::M
bias::B
σ::F
function Dense(W::M, bias = true, σ::F = identity) where {M<:AbstractMatrix, F}
b = create_bias(W, bias, size(W,1))
new{F,M,typeof(b)}(W, b, σ)
end
end
function Dense((in, out)::Pair{<:Integer, <:Integer}, σ = identity;
init = glorot_uniform, bias = true)
Dense(init(out, in), bias, σ)
end
@layer Dense
function (a::Dense)(x::AbstractVecOrMat)
_size_check(a, x, 1 => size(a.weight, 2))
xT = _match_eltype(a, x) # fixes Float64 input, etc.
return NNlib.bias_act!(a.σ, a.weight * xT, a.bias) # does σ.(W*x .+ b), with fast paths
end
function (a::Dense)(x::AbstractArray)
_size_check(a, x, 1 => size(a.weight, 2))
reshape(a(reshape(x, size(x,1), :)), :, size(x)[2:end]...)
end
function Base.show(io::IO, l::Dense)
print(io, "Dense(", size(l.weight, 2), " => ", size(l.weight, 1))
l.σ == identity || print(io, ", ", l.σ)
l.bias == false && print(io, "; bias=false")
print(io, ")")
end
Dense(W::LinearAlgebra.Diagonal, bias = true, σ = identity) =
Scale(W.diag, bias, σ)
function _size_check(layer, x::AbstractArray, (d, n)::Pair)
0 < d <= ndims(x) || throw(DimensionMismatch(string("layer ", layer,
" expects ndims(input) >= ", d, ", but got ", summary(x))))
size(x, d) == n || throw(DimensionMismatch(string("layer ", layer,
lazy" expects size(input, $d) == $n, but got ", summary(x))))
end
ChainRulesCore.@non_differentiable _size_check(::Any...)
"""
Scale(size::Integer..., σ=identity; bias=true, init=ones32)
Scale(scale::AbstractArray, [bias, σ])
Create an element-wise layer, whose forward pass is given by:
y = σ.(scale .* x .+ bias)
This uses `.*` instead of matrix multiplication `*` of [`Dense`](@ref).
The learnable scale & bias are initialised `init(size...)` and `zeros32(size...)`,
with `init=ones32` by default. You may specify the function `init`,
turn off trainable bias with `bias=false`, or provide the array(s) explicitly.
Used by [`LayerNorm`](@ref) with `affine=true`.
# Examples
```jldoctest
julia> a = Flux.Scale(2)
Scale(2) # 4 parameters
julia> Flux.trainables(a)
2-element Vector{AbstractArray}:
Float32[1.0, 1.0]
Float32[0.0, 0.0]
julia> a([1 2 3])
2×3 Matrix{Float32}:
1.0 2.0 3.0
1.0 2.0 3.0
julia> b = Flux.Scale(Float32[1 2 3 4], false, abs2)
Scale(1, 4, abs2; bias=false) # 4 parameters
julia> b([1, 10])
2×4 Matrix{Float32}:
1.0 4.0 9.0 16.0
100.0 400.0 900.0 1600.0
julia> Flux.trainables(b)
1-element Vector{AbstractArray}:
Float32[1.0 2.0 3.0 4.0]
```
"""
struct Scale{F, A<:AbstractArray, B}
scale::A
bias::B
σ::F
function Scale(scale::A, bias::B = true, σ::F = identity) where {A<:AbstractArray, B<:Union{Bool, AbstractArray}, F}
b = create_bias(scale, bias, size(scale)...)
new{F, A, typeof(b)}(scale, b, σ)
end
end
Scale(s1::Integer, s23::Integer...; bias = true, init = ones32, _act = identity) = Scale(init(s1, s23...), bias, _act)
Scale(size_act...; bias = true, init = ones32) = Scale(size_act[1:end-1]...; bias, init, _act = size_act[end])
@layer Scale
function (a::Scale)(x::AbstractArray)
σ = NNlib.fast_act(a.σ, x) # replaces tanh => tanh_fast, etc
σ.(a.scale .* x .+ a.bias)
end
function Base.show(io::IO, l::Scale)
print(io, "Scale(", join(size(l.scale), ", "))
l.σ == identity || print(io, ", ", l.σ)
l.bias == false && print(io, "; bias=false")
print(io, ")")
end
"""
Maxout(layers...)
Maxout(f, n_alts)
This contains a number of internal layers, each of which receives the same input.
Its output is the elementwise maximum of the internal layers' outputs.
Instead of defining layers individually, you can provide a zero-argument function
which constructs them, and the number to construct.
Maxout over linear dense layers satisfies the universal approximation theorem.
See Goodfellow, Warde-Farley, Mirza, Courville & Bengio "Maxout Networks"
[https://arxiv.org/abs/1302.4389](https://arxiv.org/abs/1302.4389).
See also [`Parallel`](@ref) to reduce with other operators.
# Examples
```jldoctest
julia> m = Maxout(x -> abs2.(x), x -> x .* 3);
julia> m([-2 -1 0 1 2])
1×5 Matrix{Int64}:
4 1 0 3 6
julia> m3 = Maxout(() -> Dense(5 => 7, tanh), 3)
Maxout(
Dense(5 => 7, tanh), # 42 parameters
Dense(5 => 7, tanh), # 42 parameters
Dense(5 => 7, tanh), # 42 parameters
) # Total: 6 arrays, 126 parameters, 816 bytes.
julia> Flux.outputsize(m3, (5, 11))
(7, 11)
```
"""
struct Maxout{T<:Tuple}
layers::T
end
Maxout(layers...) = Maxout(layers)
Maxout(f::Function, n_alts::Integer) = Maxout((f() for _ in 1:n_alts)...)
@layer Maxout
function (mo::Maxout)(input::AbstractArray)
# Perhaps surprisingly, pairwise max broadcast is often faster,
# even with Zygote. See #698 and #1794
mapreduce(f -> f(input), (acc, out) -> max.(acc, out), mo.layers)
end
function Base.show(io::IO, mo::Maxout)
print(io, "Maxout(")
_show_layers(io, mo.layers)
print(io, ")")
end
"""
SkipConnection(layer, connection)
Create a skip connection which consists of a layer or `Chain` of consecutive
layers and a shortcut connection linking the block's input to the output
through a user-supplied 2-argument callable. The first argument to the callable
will be propagated through the given `layer` while the second is the unchanged,
"skipped" input.
The simplest "ResNet"-type connection is just `SkipConnection(layer, +)`.
Here is a more complicated example:
```jldoctest
julia> m = Conv((3,3), 4 => 7, pad=(1,1));
julia> x = ones(Float32, 5, 5, 4, 10);
julia> size(m(x)) == (5, 5, 7, 10)
true
julia> sm = SkipConnection(m, (mx, x) -> cat(mx, x, dims=3));
julia> size(sm(x)) == (5, 5, 11, 10)
true
```
See also [`Parallel`](@ref), [`Maxout`](@ref).
"""
struct SkipConnection{T,F}
layers::T
connection::F #user can pass arbitrary connections here, such as (a,b) -> a + b
end
@layer SkipConnection
function (skip::SkipConnection)(input)
skip.connection(skip.layers(input), input)
end
function Base.show(io::IO, b::SkipConnection)
print(io, "SkipConnection(", b.layers, ", ", b.connection, ")")
end
"""
Bilinear((in1, in2) => out, σ=identity; bias=true, init=glorot_uniform)
Bilinear(W::AbstractArray, [bias, σ])
Creates a layer which is fully connected between two inputs and the output, and otherwise similar to [`Dense`](@ref).
Its output, given vectors `x` & `y`, is another vector `z` with,
for all `i ∈ 1:out`:
z[i] = σ(x' * W[i,:,:] * y + bias[i])
If `x` and `y` are matrices, then each column of the output `z = B(x, y)` is of this form,
with `B` the Bilinear layer.
If the second input `y` is not given, it is taken to be equal to `x`, i.e. `B(x) == B(x, x)`
The two inputs may also be provided as a tuple, `B((x, y)) == B(x, y)`,
which is accepted as the input to a `Chain`.
If the two input sizes are the same, `in1 == in2`, then you may write `Bilinear(in => out, σ)`.
The initialisation works as for [`Dense`](@ref) layer, with `W = init(out, in1, in2)`.
By default the bias vector is `zeros(Float32, out)`, option `bias=false` will switch off
trainable bias. Either of these may be provided explicitly.
# Examples
```jldoctest
julia> x, y = randn(Float32, 5, 32), randn(Float32, 5, 32);
julia> B = Flux.Bilinear((5, 5) => 7)
Bilinear(5 => 7) # 182 parameters
julia> B(x) |> size # interactions based on one input
(7, 32)
julia> B(x,y) == B((x,y)) # two inputs, may be given as a tuple
true
julia> sc = SkipConnection(
Chain(Dense(5 => 20, tanh), Dense(20 => 9, tanh)),
Flux.Bilinear((9, 5) => 3, bias=false),
); # used as the recombinator, with skip as the second input
julia> sc(x) |> size
(3, 32)
julia> Flux.Bilinear(rand(4,8,16), false, tanh) # first dim of weight is the output
Bilinear((8, 16) => 4, tanh; bias=false) # 512 parameters
```
"""
struct Bilinear{F,A,B}
weight::A
bias::B
σ::F
function Bilinear(W::A, bias = true, σ::F = identity) where {A<:AbstractArray, F}
ndims(A) == 3 || throw(ArgumentError("expected a 3-array of weights"))
b = create_bias(W, bias, size(W,1))
new{F,A,typeof(b)}(W, b, σ)
end
end
@layer Bilinear
function Bilinear(((in1, in2), out)::Pair{<:Tuple, <:Integer}, σ = identity;
bias = true, init = glorot_uniform)
Bilinear(init(out, in1, in2), bias, σ)
end
Bilinear((in12, out)::Pair{<:Integer, <:Integer}, σ = identity; kw...) = Bilinear((in12, in12) => out, σ; kw...)
function (a::Bilinear)(x::AbstractMatrix, y::AbstractMatrix)
W, b, σ = a.weight, a.bias, a.σ
d_z, d_x, d_y = size(W)
d_x == size(x,1) && d_y == size(y,1) || throw(DimensionMismatch("number of rows in data must match W"))
size(x,2) == size(y,2) || throw(DimensionMismatch("Data inputs must agree on number of columns, got $(size(x,2)) and $(size(y,2))"))
# @einsum Wy[o,i,s] := W[o,i,j] * y[j,s]
Wy = reshape(reshape(W, (:, d_y)) * y, (d_z, d_x, :))
# @einsum Z[o,s] := Wy[o,i,s] * x[i,s]
Wyx = batched_mul(Wy, reshape(x, (d_x, 1, :)))
Z = reshape(Wyx, (d_z, :))
# @einsum out[o,s] := σ(Z[o,i] + b[o])
NNlib.bias_act!(σ, Z, b) # σ.(Z .+ b)
end
(a::Bilinear)(x::AbstractVecOrMat) = a(x, x)
(a::Bilinear)(x::AbstractVector, y::AbstractVector) = vec(a(reshape(x, :,1), reshape(y, :,1)))
(a::Bilinear)(x::NTuple{2, AbstractArray}) = a(x[1], x[2])
function Base.show(io::IO, l::Bilinear)
if size(l.weight, 2) == size(l.weight, 3)
print(io, "Bilinear(", size(l.weight, 2), " => ", size(l.weight, 1))
else
print(io, "Bilinear((", size(l.weight, 2), ", ", size(l.weight, 3), ") => ", size(l.weight, 1))
end
l.σ == identity || print(io, ", ", l.σ)
l.bias === false && print(io, "; bias=false")
print(io, ")")
end
"""
Parallel(connection, layers...)
Parallel(connection; name = layer, ...)
Create a layer which passes an input array to each path in
`layers`, before reducing the output with `connection`.
Obeys the similar rules to broadcasting:
* Called with one input `x`, this is equivalent to `connection([l(x) for l in layers]...)`.
* With multiple `inputs` and just one layer, it is instead `connection([layer(x) for x in inputs]...)`.
* With multiple inputs and multiple layers, one input is passed to each layer,
thus `Parallel(+, f, g)(x, y) = f(x) + g(y)`.
Like [`Chain`](@ref), its sub-layers may be given names using the keyword constructor.
These can be accessed by indexing: `m[1] == m[:name]` is the first layer.
See also [`SkipConnection`](@ref) which is `Parallel` with one `identity`,
and [`Maxout`](@ref) which reduces by broadcasting `max`.
# Examples
```jldoctest
julia> p = Parallel(+, abs2, sqrt);
julia> p(3, 4) # == 3^2 + √4, two functions two inputs
11.0
julia> p((3, 4)) # tuple is always splatted
11.0
julia> p(4) # == 4^2 + √4, one input used twice
18.0
julia> Parallel(hcat, inv)(1, 2, 4) # one function three inputs
1×3 Matrix{Float64}:
1.0 0.5 0.25
```
With Flux layers:
```jldoctest
julia> model = Chain(Dense(3 => 5),
Parallel(vcat, Dense(5 => 4), Chain(Dense(5 => 7), Dense(7 => 4))),
Dense(8 => 17));
julia> model(rand32(3)) |> size
(17,)
julia> model2 = Parallel(+; α = Dense(10 => 2, tanh), β = Dense(5 => 2))
Parallel(
+,
α = Dense(10 => 2, tanh), # 22 parameters
β = Dense(5 => 2), # 12 parameters
) # Total: 4 arrays, 34 parameters, 344 bytes.
julia> model2(rand32(10), rand32(5)) |> size
(2,)
julia> model2[:α](rand32(10)) |> size
(2,)
julia> model2[:β] == model2[2]
true
```
"""
struct Parallel{F, T<:Union{Tuple, NamedTuple}}
connection::F
layers::T
end
_ParallelONE{T} = Parallel{T, <:Union{Tuple{Any}, NamedTuple{<:Any, <:Tuple{Any}}}}
Parallel(connection, layers...) = Parallel(connection, layers)
function Parallel(connection; kw...)
layers = NamedTuple(kw)
if :layers in keys(layers) || :connection in keys(layers)
throw(ArgumentError("a Parallel layer cannot have a named sub-layer called `connection` or `layers`"))
end
Parallel(connection, layers)
end
Parallel(connection, layers::Union{Tuple{}, @NamedTuple{}}) =
throw(ArgumentError("cannot construct a Parallel layer with no sub-layers"))
@layer Parallel
(m::Parallel)(x) = m.connection(map(f -> f(x), Tuple(m.layers))...) # one argument
function _parallel_check(layers, xs)
nl = length(layers)
@assert nl > 1 # dispatch handles nl==1 cases
nx = length(xs)
if (nl != nx)
throw(ArgumentError(lazy"Parallel with $nl > 1 sub-layers can take one input or $nl inputs, but got $nx inputs"))
end
end
ChainRulesCore.@non_differentiable _parallel_check(nl, nx)
function (m::Parallel)(x, ys...)
xs = (x, ys...)
_parallel_check(m.layers, xs)
m.connection(map(|>, xs, Tuple(m.layers))...) # multiple arguments & multiple layers
end
(m::_ParallelONE)(x, ys...) =
m.connection(map(z -> only(m.layers)(z), (x, ys...))...) # multiple arguments, one layer
(m::Parallel)(xs::Tuple) = m(xs...) # tuple is always splatted
(m::_ParallelONE)(xs::Tuple) = m(xs...) # solves an ambiguity
(m::Parallel)() = throw(ArgumentError("Parallel layer cannot take 0 inputs"))
Base.getindex(m::Parallel, i) = m.layers[i]
Base.getindex(m::Parallel, i::AbstractVector) = Parallel(m.connection, m.layers[i])
Base.getindex(m::Parallel{<:Any, <:NamedTuple}, i::AbstractVector) =
Parallel(m.connection, NamedTuple{keys(m)[i]}(Tuple(m.layers)[i]))
Base.keys(m::Parallel) = keys(getfield(m, :layers))
function Base.show(io::IO, m::Parallel)
print(io, "Parallel(", m.connection, ", ")
_show_layers(io, m.layers)
print(io, ")")
end
"""
PairwiseFusion(connection, layers...)
## Arguments
- `connection`: A function taking 2 inputs and combining them into a single output
- `layers`: The layers whose outputs are combined
## Inputs
This layer behaves differently based on input type:
1. If input `x` is a tuple of length N (or the input is `xs` with N `x`'s), matching the number of `layers`,
then each layer receives a new input `x[i]` combined with the previous output `y[i-1]` using `connection`.
Thus `(y1, y2, y3) = PairwiseFusion(connection, layer1, layer2, layer3)((x1, x2, x3))`
may be drawn as:
```
x1 → layer1 → y1 ↘
connection → layer2 → y2 ↘
x2 ↗ connection → layer3 → y3
x3 ↗
```
... or written as:
```julia
y1 = layer1(x1)
y2 = layer2(connection(y1, x2))
y3 = layer3(connection(y2, x3))
```
2. With just one input, each layer receives the same `x` combined with the previous output.
Thus `y = PairwiseFusion(connection, layers...)(x)` obeys:
```julia
y[1] == layers[1](x)
for i in 2:length(layers)
y[i] == connection(layers[i](y[i-1]), x)
end
```
## Returns
A tuple of length N with the output of each fusion ((`y1`, `y2`, ..., `yN`) in the example above).
"""
struct PairwiseFusion{F, T<:Union{Tuple, NamedTuple}}
connection::F
layers::T
end
PairwiseFusion(connection, layers...) = PairwiseFusion(connection, layers)
function PairwiseFusion(connection; kw...)
layers = NamedTuple(kw)
if :layers in keys(layers) || :connection in keys(layers)
throw(ArgumentError("a PairwiseFusion layer cannot have a named sub-layer called `connection` or `layers`"))
end
isempty(layers) && return PairwiseFusion(connection, ())
PairwiseFusion(connection, layers)
end
function _pairwise_check(x, layers, T)
lx = length(x)
N = length(layers)
if T <: Tuple && lx != N
throw(ArgumentError(lazy"PairwiseFusion with $N sub-layers can take one input or $N inputs, but got $lx inputs"))
end
end
ChainRulesCore.@non_differentiable _pairwise_check(lx, N, T)
function (m::PairwiseFusion)(x::T) where {T}
_pairwise_check(x, m.layers, T)
applypairwisefusion(m.layers, m.connection, x)
end
(m::PairwiseFusion)(xs...) = m(xs)
@generated function applypairwisefusion(layers::Tuple{Vararg{Any,N}}, connection, x::T) where {N, T}
y_symbols = [gensym() for _ in 1:(N + 1)]
getinput(i) = T <: Tuple ? :(x[$i]) : :x
calls = [:($(y_symbols[N + 1]) = $(getinput(1)))]
for i in 1:N - 1
push!(calls, quote
$(y_symbols[i]) = layers[$i]($(y_symbols[N + 1]))
$(y_symbols[N + 1]) = connection($(y_symbols[i]), $(getinput(i + 1)))
end)
end
push!(calls, :($(y_symbols[N]) = layers[$N]($(y_symbols[N + 1]))))
push!(calls, :(return tuple($(Tuple(y_symbols[1:N])...))))
return Expr(:block, calls...)
end
applypairwisefusion(layers::NamedTuple, connection, x) = applypairwisefusion(Tuple(layers), connection, x)
@layer PairwiseFusion
Base.getindex(m::PairwiseFusion, i) = m.layers[i]
Base.getindex(m::PairwiseFusion, i::AbstractVector) = PairwiseFusion(m.connection, m.layers[i])
Base.getindex(m::PairwiseFusion{<:Any, <:NamedTuple}, i::AbstractVector) =
PairwiseFusion(m.connection, NamedTuple{keys(m)[i]}(Tuple(m.layers)[i]))
Base.keys(m::PairwiseFusion) = keys(getfield(m, :layers))
function Base.show(io::IO, m::PairwiseFusion)
print(io, "PairwiseFusion(", m.connection, ", ")
_show_layers(io, m.layers)
print(io, ")")
end
"""
Embedding(in => out; init=randn32)
A lookup table that stores embeddings of dimension `out`
for a vocabulary of size `in`, as a trainable matrix.
This layer is often used to store word embeddings and retrieve them using indices.
The input to the layer can be a vocabulary index in `1:in`, an array of indices,
or the corresponding [`onehot encoding`](@ref OneHotArrays.onehotbatch).
For indices `x`, the result is of size `(out, size(x)...)`, allowing several batch dimensions.
For one-hot `ohx`, the result is of size `(out, size(ohx)[2:end]...)`.
# Examples
```jldoctest
julia> emb = Embedding(26 => 4, init=Flux.identity_init(gain=22))
Embedding(26 => 4) # 104 parameters
julia> emb(2) # one column of e.weight (here not random!)
4-element Vector{Float32}:
0.0
22.0
0.0
0.0
julia> emb([3, 1, 20, 14, 4, 15, 7]) # vocabulary indices, in 1:26
4×7 Matrix{Float32}:
0.0 22.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
22.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 22.0 0.0 0.0
julia> ans == emb(Flux.onehotbatch("cat&dog", 'a':'z', 'n'))
true
julia> emb(rand(1:26, (10, 1, 12))) |> size # three batch dimensions
(4, 10, 1, 12)
```
"""
struct Embedding{W<:AbstractMatrix}
weight::W
end
@layer Embedding
Embedding((in, out)::Pair{<:Integer, <:Integer}; init = randn32) = Embedding(init(out, in))
(m::Embedding)(x::Integer) = m.weight[:, x]
(m::Embedding)(x::AbstractVector) = NNlib.gather(m.weight, x)
(m::Embedding)(x::AbstractArray) = reshape(m(vec(x)), :, size(x)...)
(m::Embedding)(x::AbstractVector{Bool}) = m.weight * x # usually OneHotVector
(m::Embedding)(x::AbstractMatrix{Bool}) = m.weight * x # usually OneHotMatrix
(m::Embedding)(x::AbstractArray{Bool}) = reshape(m(reshape(x, size(x,1), :)), :, size(x)[2:end]...)
function Base.show(io::IO, m::Embedding)
print(io, "Embedding(", size(m.weight, 2), " => ", size(m.weight, 1), ")")
end
"""
_splitat(data::AbstractVector, at::AbstractVector{Int})
Partitions `data` into a vector of views.
Each index `i in at` specifies that a view starts with `data[i]`.
These indices must be strictly increasing, and start at `1`.
The resulting views do not overlap, and are never empty.
The last view always ends with `data[end]`.
### Example
```jldoctest
julia> Flux._splitat(collect('A':'Z'), [1, 3, 4, 13])
4-element Vector{SubArray{Char, 1, Vector{Char}, Tuple{UnitRange{Int64}}, true}}:
['A', 'B']
['C']
['D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L']
['M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z']
```
"""
function _splitat(data::AbstractVector, at::AbstractVector{<:Integer})
at[begin] == firstindex(data) || throw(ArgumentError("The first element in `at` must be 1."))
at[end] <= lastindex(data) || throw(ArgumentError("The last element in `at` must be at most the length of `data`."))
issorted(at, lt = <=) || throw(ArgumentError("`at` must be monotonically increasing with no duplicates."))
iplus = vcat(at, lastindex(data)+1)
return [view(data, iplus[n]:(iplus[n+1]-1)) for n in eachindex(at)]
end
"""
EmbeddingBag(in => out, reduction=mean; init=Flux.randn32)
A lookup table that stores embeddings of dimension `out` for a vocabulary of size `in`.
Differs from [`Embedding`](@ref) in that, instead of acting on a single vocabulary index,
it always acts a vector of indices which it calls a "bag".
Their individual embedding vectors are reduced to one, using `mean` or some other function.
Instead of acting on one "bag", such as `x::Vector{Int}`, the layer can also act on several:
* Acting on a vector of "bags", it produces a matrix whose columns are the reduced vectors.
More generally on `x::Array{Vector{Int}}`, its output is of size `(out, size(x)...)`.
* Any higher-rank array of integers is interpreted as a collection of "bags" each along the first dimension.
Thus the output is `mapslices(e, x; dims=1)` when `e::EmbeddingBag` and `x::Array{Int,N}`.
This method is more efficient, but requires that all "bags" have the same length.
* A vector of "bags" may also be produced by splitting a vector of indices at specified points.
For this case the layer takes two inputs, both vectors of integers. See details below.
The "bag" may equivalently be represented as a `OneHotMatrix`. A collection of these,
or one higher-rank `OneHotArray`, again produce a stack of embeddings. See details below.
# Examples
```jldoctest ebag
julia> vocab_size = 26; # embed into 3 dimensions, with non-random vectors:
julia> eb = EmbeddingBag(vocab_size => 3, init=Flux.identity_init(gain=100))
EmbeddingBag(26 => 3) # 78 parameters
julia> eb([2]) # one bag of 1 item
3-element Vector{Float32}:
0.0
100.0
0.0
julia> eb([3,3,1]) # one bag of 3 items, one mean embedding
3-element Vector{Float32}:
33.333332
0.0
66.666664
julia> eb([[3,1,3], [2,1]]) # two bags
3×2 Matrix{Float32}:
33.3333 50.0
0.0 50.0
66.6667 0.0
julia> eb([1 1 1 1; 1 2 3 4]) # 4 bags each of 2 items, eachcol([1 1 1 1; 1 2 3 4])
3×4 Matrix{Float32}:
100.0 50.0 50.0 50.0
0.0 50.0 0.0 0.0
0.0 0.0 50.0 0.0
julia> eb(rand(1:26, 10, 5, 5)) |> size # 25 bags each of 10 items
(3, 5, 5)
```
Another way to specify "many bags of many items" is to provide a vector `data` (each in `1:in`)
and a vector `at` stating where to split that up into "bags".
The first bag starts with `data[at[1]]`, the second at `data[at[2]]`, and so on,
with no overlaps and nothing left out (thus it requires `at[1]==1`).
```jldoctest ebag
julia> data = [11, 1, 12, 2, 13, 3, 14];
julia> data[1:3], data[4:end]
([11, 1, 12], [2, 13, 3, 14])
julia> eb(data, [1, 4]) # two bags, of 3 and 4 items
3×2 Matrix{Float32}:
33.3333 0.0
0.0 25.0
0.0 25.0
```
Finally, each bag may also be also be represented as a [`OneHotMatrix`](@ref OneHotArrays.onehotbatch).
```jldoctest ebag
julia> eb(Flux.onehotbatch("bba", 'a':'z')) # same as [2,2,1], one bag of 3 items
3-element Vector{Float32}:
33.333332
66.666664
0.0
julia> eb([Flux.onehotbatch("bba", 'a':'z'), Flux.onehotbatch("cc", 'a':'z')]) # two bags
3×2 Matrix{Float32}:
33.3333 0.0
66.6667 0.0
0.0 100.0
```
"""
struct EmbeddingBag{F, W<:AbstractMatrix}
weight::W
reduction::F
end
@layer EmbeddingBag
EmbeddingBag((in, out)::Pair{<:Integer, <:Integer}, reduction::Function = mean; init = randn32) = EmbeddingBag(init(out, in), reduction)
EmbeddingBag(weight::AbstractMatrix) = EmbeddingBag(weight, mean)
(m::EmbeddingBag)(data::AbstractVector, at::AbstractVector) = m(_splitat(data, at))
(m::EmbeddingBag)(inds::AbstractArray{<:Integer}) = dropdims(m.reduction(Embedding(m.weight)(inds), dims=2), dims=2)
(m::EmbeddingBag)(ind::Integer) = error("EmbeddingBag expects an array of indices, not just one")
(m::EmbeddingBag)(hot::AbstractArray{Bool}) = dropdims(m.reduction(Embedding(m.weight)(hot), dims=2), dims=2)
(m::EmbeddingBag)(hot::AbstractVector{Bool}) = error("EmbeddingBag not defined for a one-hot vector")
# These two could be stack(m, bags), but no AD support yet. (Gradient for weight quite inefficient here.)
(m::EmbeddingBag)(bags::AbstractVector{<:AbstractVector}) = reduce(hcat, m.(bags))
(m::EmbeddingBag)(bags::AbstractArray{<:AbstractVector}) = reshape(m(vec(bags)), :, size(bags)...)
(m::EmbeddingBag)(bags::AbstractArray{<:AbstractMatrix{Bool}}) = reshape(reduce(hcat, m.(vec(bags))), :, size(bags)...)
function Base.show(io::IO, m::EmbeddingBag)
print(io, "EmbeddingBag(", size(m.weight, 2), " => ", size(m.weight, 1), ")")
end