Scan - 21 vs 23

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1 1	Scan can be used to iterate over one or more scan_input tensors,
2 2	constructing zero or more scan_output tensors. It combines ideas from general recurrences,
3 3	functional programming constructs such as scan, fold, map, and zip, and is intended to enable
4 4	generalizations of RNN-like constructs for sequence-to-sequence processing.
5 5	Other tensors (referred to as state_variables here) can be used to carry a state
6 6	when iterating from one element to another (similar to hidden-state in RNNs, also referred
7 7	to as loop-carried dependences in the context of loops).
8 8	Many common usages involve a single scan_input tensor (where functionality
9 9	similar to scan, fold and map can be obtained). When more than one scan_input is used,
10 10	a behavior similar to zip is obtained.
11 11	The attribute body must be a graph, specifying the computation to be performed in
12 12	every iteration. It takes as input the current values of the state_variables and
13 13	the current iterated element of the scan_inputs. It must return the (updated) values
14 14	of the state_variables and zero or more scan_output_element tensors. The values of the
15 15	scan_output_element tensors are concatenated over all the iterations to produce the
16 16	scan_output values of the scan construct (similar to the concatenated intermediate
17 17	hidden-state values of RNN-like constructs). All the output tensors (state_variables as
18 18	well as scan_output_element tensors) are required to have the same shape in each iteration
19 19	of the loop (a restriction imposed to enable efficient memory allocation).
20 20	Note that the iterated element passed to the body subgraph does not have a sequence
21 21	axis. It will have a rank one less than the rank of the corresponding scan_input.
22 22	The scan operation returns the final values of the state_variables as well as the
23 23	scan_outputs.
24 24	The optional attribute scan_input_directions specifies the direction (forward or backward)
25 25	for each scan input. If this attribute is omitted, all sequences are scanned in the forward
26 26	direction. A bidirectional scan may be performed by specifying the same tensor input twice
27 27	in the scan_inputs, once with a forward direction, and once with a backward direction.
28 28	The scan_output of the operation is produced by concatenating the scan_output_element
29 29	values produced by the body in each iteration. The optional attribute scan_output_directions
30 30	specifies the direction in which scan_output is constructed (by appending or prepending the
31 31	scan_output_element to scan_output in each iteration) for each scan_output. If this attribute
32 32	is omitted, the scan_output_element is appended to the scan_output in each iteration.
33 33	The optional attribute scan_input_axes specifies the axis to be scanned for each scan_input.
34 34	If omitted, every scan_input will be scanned in axis 0. For example, if axis 0 is the
35 35	batch axis and axis 1 is the time axis (to be scanned), specify an axis value of 1.
36 36	Note that scanning a non-zero axis may be less efficient than scanning axis zero.
37 37	The optional attribute scan_output_axes specifies the axis along which the scan_outputs
38 38	are accumulated for each scan_output. For example, if axis 1 is the time axis (to be
39 39	scanned) for both inputs and outputs, specify a scan_input axis and scan_output axis
40 40	value of 1.
41 41	Note that because of the ONNX restriction that only the last parameter of an operator can
42 42	be variadic, the initial-states and scan-inputs are listed together as one input parameter.
43 43	Similarly, the final-states and scan-outputs are listed together as one output parameter.
44 44	The attribute num_scan_inputs indicates the number M of scan-inputs.
45 45	The behavior of
46 46	Scan <
47 47	num_scan_inputs = m,
48 48	body = loop-body,
49 49	scan_input_axes = [axis_1, ..., axis_m]
50 50	> (init_1, ..., init_n, scan_1, ..., scan_m)
51 51	is equivalent to the following pseudo-code:
52 52	// scan_i.shape[axis_i] denotes the (max) sequence-length of scan_i
53 53	// scan_i.shape[axis_i] is required to be equal to scan_j.shape[axis_j] for all i,j.
54 54	sequence_length = scan_1.shape[axis_1];
55 55	// initialize state-variables
56 56	st_1 = init_1; ... st_n = init_n;
57 57	// initialize scan-output variables: [] denotes an empty tensor
58 58	scan_out_1 = []; ...; scan_out_k = [];
59 59	// identify number of iterations:
60 60	// execute loop
61 61	for (int t = 0; t < sequence_length; ++t) {
62 62	// generate the scan-input elements: the notation T<axis=k>[t] indicates the sub-tensor
63 63	// of rank one less than T obtained by indexing T at position t along axis k.
64 64	si_1 = scan_1<axis=axis_1>[t];
65 65	... ;
66 66	si_m = scan_m<axis=axis_m>[t];
67 67	// execute loop-body
68 68	st_1, ..., st_n, so_1, ..., so_k = loop-body(st_1, ..., st_n, si_1, ..., si_m)
69 69	// accumulate the scan-output elements
70 70	scan_out_1 = Concat<axis=0>(scan_out_1, so_1); ... ; scan_out_k = Concat<axis=0>(scan_out_k, so_k);
71 71	}
72 72	return st_1, ..., st_n, scan_out_1, ..., scan_out_k;
73 73	*Sample usage: Encoding RNN using a Scan*
74 74	The following example shows how a simple RNN over an input tensor %X, with weight tensor %Wi,
75 75	recurrence weight tensor %Ri, bias tensors %Wbi and %Rbi, and initial hidden-state %H_0 can
76 76	be encoded as a ScanLoop. Note that the loop-body is a nested graph, and it directly computes
77 77	%Wi, %Ri, %Wbi, and %Rbi (typically constants or initializers in the body graph). If these
78 78	values are computed in the outer graph, they need to be passed in as extra state_variables.
79 79	graph rnn-encoding {
80 80	%H_0 = ...
81 81	%X = ...
82 82	%Y_h, %Y = Scan[body = <graph rnn-cell-1>, num_scan_inputs=1](%H_0, %X)
83 83	return %Y, %Y_h
84 84	}
85 85	graph rnn-cell-1 (
86 86	%H_tminus1[FLOAT, tensor]
87 87	%X_t[FLOAT, tensor]
88 88	) {
89 89	%Wi = ...
90 90	%Ri = ...
91 91	%Wbi = ...
92 92	%Rbi = ...
93 93	%t1 = X_t * (Wi^T)
94 94	%t2 = H_tminus1*(Ri^T)
95 95	%t3 = Add(%t1, %t2)
96 96	%t4 = Add(%t3, %Wbi)
97 97	%t5 = Add(%t4, %Rbi)
98 98	%Ht = Tanh(%t5)
99 99	%Accumulate = Identity(%Ht)
100 100	return %Ht, %Accumulate
101 101	}
102 102	### Attributes
103 103	* **body - GRAPH** (required) :
104 104	The graph run each iteration. It has N+M inputs: (loop state variables..., scan_input_elts...). It has N+K outputs: (loop state variables..., scan_output_elts...). Each scan_output is created by concatenating the value of the specified scan_output_elt value at the end of each iteration of the loop. It is an error if the dimensions of these values change across loop iterations.
105 105	* **num_scan_inputs - INT** (required) :
106 106	An attribute specifying the number of scan_inputs M.
107 107	* **scan_input_axes - INTS** :
108 108	An optional list of M flags. The i-th element of the list specifies the axis to be scanned (the sequence axis) for the i-th scan_input. If omitted, 0 will be used as the scan axis for every scan_input. Negative value for an axis means counting dimensions from the back. Accepted range is [-r, r-1] where r = rank(input).
109 109	* **scan_input_directions - INTS** :
110 110	An optional list of M flags. The i-th element of the list specifies the direction to be scanned for the i-th scan_input tensor: 0 indicates forward direction and 1 indicates reverse direction. If omitted, all scan_input tensors will be scanned in the forward direction.
111 111	* **scan_output_axes - INTS** :
112 112	An optional list of K flags. The i-th element of the list specifies the axis for the i-th scan_output. The scan outputs are accumulated along the specified axis. If omitted, 0 will be used as the scan axis for every scan_output. Negative value for an axis means counting dimensions from the back. Accepted range is [-r, r-1].
113 113	* **scan_output_directions - INTS** :
114 114	An optional list of K flags, one for each scan_output. The i-th element of the list specifies whether the i-th scan_output should be constructed by appending or prepending a new value in each iteration: 0 indicates appending and 1 indicates prepending. If omitted, all scan_output tensors will be produced by appending a value in each iteration.
115 115	### Inputs
116 116	Between 1 and 2147483647 inputs.
117 117	- **initial_state_and_scan_inputs** (variadic) - **V**:
118 118	Initial values of the loop's N state variables followed by M scan_inputs
119 119	### Outputs
120 120	Between 1 and 2147483647 outputs.
121 121	- **final_state_and_scan_outputs** (variadic) - **V**:
122 122	Final values of the loop's N state variables followed by K scan_outputs
123 123	### Type Constraints
124	- * **V** in ( tensor(bfloat16), tensor(bool), tensor(complex128), tensor(complex64), tensor(double), tensor(float), tensor(float16), tensor(float8e4m3fn), tensor(float8e4m3fnuz), tensor(float8e5m2), tensor(float8e5m2fnuz), tensor(int16), tensor(int32), tensor(int4), tensor(int64), tensor(int8), tensor(string), tensor(uint16), tensor(uint32), tensor(uint4), tensor(uint64), tensor(uint8) ):
124	+ * **V** in ( tensor(bfloat16), tensor(bool), tensor(complex128), tensor(complex64), tensor(double), tensor(float), tensor(float16), tensor(float4e2m1), tensor(float8e4m3fn), tensor(float8e4m3fnuz), tensor(float8e5m2), tensor(float8e5m2fnuz), tensor(int16), tensor(int32), tensor(int4), tensor(int64), tensor(int8), tensor(string), tensor(uint16), tensor(uint32), tensor(uint4), tensor(uint64), tensor(uint8) ):
125	- All Tensor types up to IRv10.? ^
125	+ All Tensor types up to IRv11.? ^