-
-
Notifications
You must be signed in to change notification settings - Fork 611
/
recurrent.jl
507 lines (385 loc) · 15.6 KB
/
recurrent.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
gate(h, n) = (1:h) .+ h*(n-1)
gate(x::AbstractVector, h, n) = @view x[gate(h,n)]
gate(x::AbstractMatrix, h, n) = view(x, gate(h,n), :)
# AD-friendly helper for dividing monolithic RNN params into equally sized gates
multigate(x::AbstractArray, h, ::Val{N}) where N = ntuple(n -> gate(x,h,n), N)
function ChainRulesCore.rrule(::typeof(multigate), x::AbstractArray, h, c)
function multigate_pullback(dy)
dx = map!(zero, similar(x, float(eltype(x)), axes(x)), x)
foreach(multigate(dx, h, c), unthunk(dy)) do dxᵢ, dyᵢ
dyᵢ isa AbstractZero && return
@. dxᵢ += dyᵢ
end
return (NoTangent(), dx, NoTangent(), NoTangent())
end
return multigate(x, h, c), multigate_pullback
end
# Type stable and AD-friendly helper for iterating over the last dimension of an array
function eachlastdim(A::AbstractArray{T,N}) where {T,N}
inds_before = ntuple(_ -> :, N-1)
return (view(A, inds_before..., i) for i in axes(A, N))
end
# adapted from https://github.com/JuliaDiff/ChainRules.jl/blob/f13e0a45d10bb13f48d6208e9c9d5b4a52b96732/src/rulesets/Base/indexing.jl#L77
function ∇eachlastdim(dys_raw, x::AbstractArray{T, N}) where {T, N}
dys = unthunk(dys_raw)
i1 = findfirst(dy -> dy isa AbstractArray, dys)
if isnothing(i1) # all slices are Zero!
return fill!(similar(x, T, axes(x)), zero(T))
end
# The whole point of this gradient is that we can allocate one `dx` array:
dx = similar(x, T, axes(x))::AbstractArray
for i in axes(x, N)
slice = selectdim(dx, N, i)
if dys[i] isa AbstractZero
fill!(slice, zero(eltype(slice)))
else
copyto!(slice, dys[i])
end
end
return ProjectTo(x)(dx)
end
function ChainRulesCore.rrule(::typeof(eachlastdim), x::AbstractArray{T,N}) where {T,N}
lastdims(dy) = (NoTangent(), ∇eachlastdim(unthunk(dy), x))
collect(eachlastdim(x)), lastdims
end
reshape_cell_output(h, x) = reshape(h, :, size(x)[2:end]...)
# Stateful recurrence
"""
Recur(cell)
`Recur` takes a recurrent cell and makes it stateful, managing the hidden state
in the background. `cell` should be a model of the form:
h, y = cell(h, x...)
For example, here's a recurrent network that keeps a running total of its inputs:
# Examples
```jldoctest
julia> accum(h, x) = (h + x, x)
accum (generic function with 1 method)
julia> rnn = Flux.Recur(accum, 0)
Recur(accum)
julia> rnn(2)
2
julia> rnn(3)
3
julia> rnn.state
5
```
Folding over a 3d Array of dimensions `(features, batch, time)` is also supported:
```jldoctest
julia> accum(h, x) = (h .+ x, x)
accum (generic function with 1 method)
julia> rnn = Flux.Recur(accum, zeros(Int, 1, 1))
Recur(accum)
julia> rnn([2])
1-element Vector{Int64}:
2
julia> rnn([3])
1-element Vector{Int64}:
3
julia> rnn.state
1×1 Matrix{Int64}:
5
julia> out = rnn(reshape(1:10, 1, 1, :)); # apply to a sequence of (features, batch, time)
julia> out |> size
(1, 1, 10)
julia> vec(out)
10-element Vector{Int64}:
1
2
3
4
5
6
7
8
9
10
julia> rnn.state
1×1 Matrix{Int64}:
60
```
"""
mutable struct Recur{T,S}
cell::T
state::S
end
function (m::Recur)(x)
m.state, y = m.cell(m.state, x)
return y
end
@functor Recur
trainable(a::Recur) = (; cell = a.cell)
Base.show(io::IO, m::Recur) = print(io, "Recur(", m.cell, ")")
"""
reset!(rnn)
Reset the hidden state of a recurrent layer back to its original value.
Assuming you have a `Recur` layer `rnn`, this is roughly equivalent to:
rnn.state = hidden(rnn.cell)
# Examples
```jldoctest
julia> r = Flux.RNNCell(relu, ones(1,1), zeros(1,1), ones(1,1), zeros(1,1)); # users should use the RNN wrapper struct instead
julia> y = Flux.Recur(r, ones(1,1));
julia> y.state
1×1 Matrix{Float64}:
1.0
julia> y(ones(1,1)) # relu(1*1 + 1)
1×1 Matrix{Float64}:
2.0
julia> y.state
1×1 Matrix{Float64}:
2.0
julia> Flux.reset!(y)
1×1 Matrix{Float64}:
0.0
julia> y.state
1×1 Matrix{Float64}:
0.0
```
"""
reset!(m::Recur) = (m.state = m.cell.state0)
reset!(m) = foreach(reset!, functor(m)[1])
flip(f, xs) = reverse([f(x) for x in reverse(xs)])
function (m::Recur)(x::AbstractArray{T, 3}) where T
h = [m(x_t) for x_t in eachlastdim(x)]
sze = size(h[1])
reshape(reduce(hcat, h), sze[1], sze[2], length(h))
end
# Vanilla RNN
struct RNNCell{F,I,H,V,S}
σ::F
Wi::I
Wh::H
b::V
state0::S
end
RNNCell((in, out)::Pair, σ=tanh; init=Flux.glorot_uniform, initb=zeros32, init_state=zeros32) =
RNNCell(σ, init(out, in), init(out, out), initb(out), init_state(out,1))
function (m::RNNCell{F,I,H,V,<:AbstractMatrix{T}})(h, x::Union{AbstractVecOrMat{<:AbstractFloat},OneHotArray}) where {F,I,H,V,T}
Wi, Wh, b = m.Wi, m.Wh, m.b
_size_check(m, x, 1 => size(Wi,2))
σ = NNlib.fast_act(m.σ, x)
xT = _match_eltype(m, T, x)
h = σ.(Wi*xT .+ Wh*h .+ b)
return h, reshape_cell_output(h, x)
end
@functor RNNCell
function Base.show(io::IO, l::RNNCell)
print(io, "RNNCell(", size(l.Wi, 2), " => ", size(l.Wi, 1))
l.σ == identity || print(io, ", ", l.σ)
print(io, ")")
end
"""
RNN(in => out, σ = tanh)
The most basic recurrent layer; essentially acts as a `Dense` layer, but with the
output fed back into the input each time step.
The arguments `in` and `out` describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length `in` or a batch of vectors represented as a `in x B` matrix and outputs a vector of length `out` or a batch of vectors of size `out x B`.
This constructor is syntactic sugar for `Recur(RNNCell(a...))`, and so RNNs are stateful. Note that the state shape can change depending on the inputs, and so it is good to `reset!` the model between inference calls if the batch size changes. See the examples below.
# Examples
```jldoctest
julia> r = RNN(3 => 5)
Recur(
RNNCell(3 => 5, tanh), # 50 parameters
) # Total: 4 trainable arrays, 50 parameters,
# plus 1 non-trainable, 5 parameters, summarysize 432 bytes.
julia> r(rand(Float32, 3)) |> size
(5,)
julia> Flux.reset!(r);
julia> r(rand(Float32, 3, 10)) |> size # batch size of 10
(5, 10)
```
!!! warning "Batch size changes"
Failing to call `reset!` when the input batch size changes can lead to unexpected behavior. See the following example:
```julia
julia> r = RNN(3 => 5)
Recur(
RNNCell(3 => 5, tanh), # 50 parameters
) # Total: 4 trainable arrays, 50 parameters,
# plus 1 non-trainable, 5 parameters, summarysize 432 bytes.
julia> r.state |> size
(5, 1)
julia> r(rand(Float32, 3)) |> size
(5,)
julia> r.state |> size
(5, 1)
julia> r(rand(Float32, 3, 10)) |> size # batch size of 10
(5, 10)
julia> r.state |> size # state shape has changed
(5, 10)
julia> r(rand(Float32, 3)) |> size # erroneously outputs a length 5*10 = 50 vector.
(50,)
```
# Note:
`RNNCell`s can be constructed directly by specifying the non-linear function, the `Wi` and `Wh` internal matrices, a bias vector `b`, and a learnable initial state `state0`. The `Wi` and `Wh` matrices do not need to be the same type, but if `Wh` is `dxd`, then `Wi` should be of shape `dxN`.
```julia
julia> using LinearAlgebra
julia> r = Flux.Recur(Flux.RNNCell(tanh, rand(5, 4), Tridiagonal(rand(5, 5)), rand(5), rand(5, 1)))
julia> r(rand(4, 10)) |> size # batch size of 10
(5, 10)
```
"""
RNN(a...; ka...) = Recur(RNNCell(a...; ka...))
Recur(m::RNNCell) = Recur(m, m.state0)
# LSTM
struct LSTMCell{I,H,V,S}
Wi::I
Wh::H
b::V
state0::S
end
function LSTMCell((in, out)::Pair;
init = glorot_uniform,
initb = zeros32,
init_state = zeros32)
cell = LSTMCell(init(out * 4, in), init(out * 4, out), initb(out * 4), (init_state(out,1), init_state(out,1)))
cell.b[gate(out, 2)] .= 1
return cell
end
function (m::LSTMCell{I,H,V,<:NTuple{2,AbstractMatrix{T}}})((h, c), x::Union{AbstractVecOrMat{<:AbstractFloat},OneHotArray}) where {I,H,V,T}
_size_check(m, x, 1 => size(m.Wi,2))
b, o = m.b, size(h, 1)
xT = _match_eltype(m, T, x)
g = muladd(m.Wi, xT, muladd(m.Wh, h, b))
input, forget, cell, output = multigate(g, o, Val(4))
c′ = @. sigmoid_fast(forget) * c + sigmoid_fast(input) * tanh_fast(cell)
h′ = @. sigmoid_fast(output) * tanh_fast(c′)
return (h′, c′), reshape_cell_output(h′, x)
end
@functor LSTMCell
Base.show(io::IO, l::LSTMCell) =
print(io, "LSTMCell(", size(l.Wi, 2), " => ", size(l.Wi, 1)÷4, ")")
"""
LSTM(in => out)
[Long Short Term Memory](https://www.researchgate.net/publication/13853244_Long_Short-term_Memory)
recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.
The arguments `in` and `out` describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length `in` or a batch of vectors represented as a `in x B` matrix and outputs a vector of length `out` or a batch of vectors of size `out x B`.
This constructor is syntactic sugar for `Recur(LSTMCell(a...))`, and so LSTMs are stateful. Note that the state shape can change depending on the inputs, and so it is good to `reset!` the model between inference calls if the batch size changes. See the examples below.
See [this article](https://colah.github.io/posts/2015-08-Understanding-LSTMs/)
for a good overview of the internals.
# Examples
```jldoctest
julia> l = LSTM(3 => 5)
Recur(
LSTMCell(3 => 5), # 190 parameters
) # Total: 5 trainable arrays, 190 parameters,
# plus 2 non-trainable, 10 parameters, summarysize 1.062 KiB.
julia> l(rand(Float32, 3)) |> size
(5,)
julia> Flux.reset!(l);
julia> l(rand(Float32, 3, 10)) |> size # batch size of 10
(5, 10)
```
!!! warning "Batch size changes"
Failing to call `reset!` when the input batch size changes can lead to unexpected behavior. See the example in [`RNN`](@ref).
# Note:
`LSTMCell`s can be constructed directly by specifying the non-linear function, the `Wi` and `Wh` internal matrices, a bias vector `b`, and a learnable initial state `state0`. The `Wi` and `Wh` matrices do not need to be the same type. See the example in [`RNN`](@ref).
"""
LSTM(a...; ka...) = Recur(LSTMCell(a...; ka...))
Recur(m::LSTMCell) = Recur(m, m.state0)
# GRU
function _gru_output(gxs, ghs, bs)
r = @. sigmoid_fast(gxs[1] + ghs[1] + bs[1])
z = @. sigmoid_fast(gxs[2] + ghs[2] + bs[2])
return r, z
end
struct GRUCell{I,H,V,S}
Wi::I
Wh::H
b::V
state0::S
end
GRUCell((in, out)::Pair; init = glorot_uniform, initb = zeros32, init_state = zeros32) =
GRUCell(init(out * 3, in), init(out * 3, out), initb(out * 3), init_state(out,1))
function (m::GRUCell{I,H,V,<:AbstractMatrix{T}})(h, x::Union{AbstractVecOrMat{<:AbstractFloat},OneHotArray}) where {I,H,V,T}
_size_check(m, x, 1 => size(m.Wi,2))
Wi, Wh, b, o = m.Wi, m.Wh, m.b, size(h, 1)
xT = _match_eltype(m, T, x)
gxs, ghs, bs = multigate(Wi*xT, o, Val(3)), multigate(Wh*h, o, Val(3)), multigate(b, o, Val(3))
r, z = _gru_output(gxs, ghs, bs)
h̃ = @. tanh_fast(gxs[3] + r * ghs[3] + bs[3])
h′ = @. (1 - z) * h̃ + z * h
return h′, reshape_cell_output(h′, x)
end
@functor GRUCell
Base.show(io::IO, l::GRUCell) =
print(io, "GRUCell(", size(l.Wi, 2), " => ", size(l.Wi, 1)÷3, ")")
"""
GRU(in => out)
[Gated Recurrent Unit](https://arxiv.org/abs/1406.1078v1) layer. Behaves like an
RNN but generally exhibits a longer memory span over sequences. This implements
the variant proposed in v1 of the referenced paper.
The integer arguments `in` and `out` describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length `in` or a batch of vectors represented as a `in x B` matrix and outputs a vector of length `out` or a batch of vectors of size `out x B`.
This constructor is syntactic sugar for `Recur(GRUCell(a...))`, and so GRUs are stateful. Note that the state shape can change depending on the inputs, and so it is good to `reset!` the model between inference calls if the batch size changes. See the examples below.
See [this article](https://colah.github.io/posts/2015-08-Understanding-LSTMs/)
for a good overview of the internals.
# Examples
```jldoctest
julia> g = GRU(3 => 5)
Recur(
GRUCell(3 => 5), # 140 parameters
) # Total: 4 trainable arrays, 140 parameters,
# plus 1 non-trainable, 5 parameters, summarysize 792 bytes.
julia> g(rand(Float32, 3)) |> size
(5,)
julia> Flux.reset!(g);
julia> g(rand(Float32, 3, 10)) |> size # batch size of 10
(5, 10)
```
!!! warning "Batch size changes"
Failing to call `reset!` when the input batch size changes can lead to unexpected behavior. See the example in [`RNN`](@ref).
# Note:
`GRUCell`s can be constructed directly by specifying the non-linear function, the `Wi` and `Wh` internal matrices, a bias vector `b`, and a learnable initial state `state0`. The `Wi` and `Wh` matrices do not need to be the same type. See the example in [`RNN`](@ref).
"""
GRU(a...; ka...) = Recur(GRUCell(a...; ka...))
Recur(m::GRUCell) = Recur(m, m.state0)
# GRU v3
struct GRUv3Cell{I,H,V,HH,S}
Wi::I
Wh::H
b::V
Wh_h̃::HH
state0::S
end
GRUv3Cell((in, out)::Pair; init = glorot_uniform, initb = zeros32, init_state = zeros32) =
GRUv3Cell(init(out * 3, in), init(out * 2, out), initb(out * 3),
init(out, out), init_state(out,1))
function (m::GRUv3Cell{I,H,V,HH,<:AbstractMatrix{T}})(h, x::Union{AbstractVecOrMat{<:AbstractFloat},OneHotArray}) where {I,H,V,HH,T}
_size_check(m, x, 1 => size(m.Wi,2))
Wi, Wh, b, Wh_h̃, o = m.Wi, m.Wh, m.b, m.Wh_h̃, size(h, 1)
xT = _match_eltype(m, T, x)
gxs, ghs, bs = multigate(Wi*xT, o, Val(3)), multigate(Wh*h, o, Val(2)), multigate(b, o, Val(3))
r, z = _gru_output(gxs, ghs, bs)
h̃ = tanh_fast.(gxs[3] .+ (Wh_h̃ * (r .* h)) .+ bs[3])
h′ = @. (1 - z) * h̃ + z * h
return h′, reshape_cell_output(h′, x)
end
@functor GRUv3Cell
Base.show(io::IO, l::GRUv3Cell) =
print(io, "GRUv3Cell(", size(l.Wi, 2), " => ", size(l.Wi, 1)÷3, ")")
"""
GRUv3(in => out)
[Gated Recurrent Unit](https://arxiv.org/abs/1406.1078v3) layer. Behaves like an
RNN but generally exhibits a longer memory span over sequences. This implements
the variant proposed in v3 of the referenced paper.
The arguments `in` and `out` describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length `in` or a batch of vectors represented as a `in x B` matrix and outputs a vector of length `out` or a batch of vectors of size `out x B`.
This constructor is syntactic sugar for `Recur(GRUv3Cell(a...))`, and so GRUv3s are stateful. Note that the state shape can change depending on the inputs, and so it is good to `reset!` the model between inference calls if the batch size changes. See the examples below.
See [this article](https://colah.github.io/posts/2015-08-Understanding-LSTMs/)
for a good overview of the internals.
# Examples
```jldoctest
julia> g = GRUv3(3 => 5)
Recur(
GRUv3Cell(3 => 5), # 140 parameters
) # Total: 5 trainable arrays, 140 parameters,
# plus 1 non-trainable, 5 parameters, summarysize 848 bytes.
julia> g(rand(Float32, 3)) |> size
(5,)
julia> Flux.reset!(g);
julia> g(rand(Float32, 3, 10)) |> size # batch size of 10
(5, 10)
```
!!! warning "Batch size changes"
Failing to call `reset!` when the input batch size changes can lead to unexpected behavior. See the example in [`RNN`](@ref).
# Note:
`GRUv3Cell`s can be constructed directly by specifying the non-linear function, the `Wi`, `Wh`, and `Wh_h` internal matrices, a bias vector `b`, and a learnable initial state `state0`. The `Wi`, `Wh`, and `Wh_h` matrices do not need to be the same type. See the example in [`RNN`](@ref).
"""
GRUv3(a...; ka...) = Recur(GRUv3Cell(a...; ka...))
Recur(m::GRUv3Cell) = Recur(m, m.state0)