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Tensor library for Gleam/BEAM with a pure Gleam API, zero-copy views, and optional native acceleration
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src/viva_tensor@autograd.erl
-module(viva_tensor@autograd).
-compile([no_auto_import, nowarn_unused_vars, nowarn_unused_function, nowarn_nomatch, inline]).
-define(FILEPATH, "src/viva_tensor/autograd.gleam").
-export([new_tape/0, new_variable/2, sequence/2, add/3, sub/3, mul/3, mean/2, matmul/3, transpose/2, relu/2, backward/2]).
-export_type([tape/0, variable/0, traced/1]).
-if(?OTP_RELEASE >= 27).
-define(MODULEDOC(Str), -moduledoc(Str)).
-define(DOC(Str), -doc(Str)).
-else.
-define(MODULEDOC(Str), -compile([])).
-define(DOC(Str), -compile([])).
-endif.
-type tape() :: {tape,
integer(),
gleam@dict:dict(integer(), fun((viva_tensor@tensor:tensor()) -> list({integer(),
viva_tensor@tensor:tensor()})))}.
-type variable() :: {variable, integer(), viva_tensor@tensor:tensor()}.
-type traced(FFK) :: {traced, FFK, tape()}.
-file("src/viva_tensor/autograd.gleam", 39).
?DOC(" Creates a new empty tape\n").
-spec new_tape() -> tape().
new_tape() ->
{tape, 0, maps:new()}.
-file("src/viva_tensor/autograd.gleam", 44).
?DOC(" Registers a new variable (leaf node) in the graph\n").
-spec new_variable(tape(), viva_tensor@tensor:tensor()) -> traced(variable()).
new_variable(Tape, Data) ->
Id = erlang:element(2, Tape),
Var = {variable, Id, Data},
New_tape = {tape, Id + 1, erlang:element(3, Tape)},
{traced, Var, New_tape}.
-file("src/viva_tensor/autograd.gleam", 57).
?DOC(
" Operation sequencing (Monadic Pipe)\n"
" Allows chaining layers: x |> sequence(layer1) |> sequence(layer2)\n"
).
-spec sequence(
{ok, traced(variable())} | {error, FFO},
fun((tape(), variable()) -> {ok, traced(variable())} | {error, FFO})
) -> {ok, traced(variable())} | {error, FFO}.
sequence(Input, Layer_fn) ->
gleam@result:'try'(
Input,
fun(_use0) ->
{traced, Var, Tape} = _use0,
Layer_fn(Tape, Var)
end
).
-file("src/viva_tensor/autograd.gleam", 66).
?DOC(" Traced addition: c = a + b (supports broadcasting)\n").
-spec add(tape(), variable(), variable()) -> {ok, traced(variable())} |
{error, viva_tensor@tensor:tensor_error()}.
add(Tape, A, B) ->
gleam@result:'try'(
viva_tensor@tensor:add_broadcast(
erlang:element(3, A),
erlang:element(3, B)
),
fun(Res_data) ->
Res_id = erlang:element(2, Tape),
Backward = fun(Grad) ->
Grad_a = case erlang:element(3, Grad) =:= erlang:element(
3,
erlang:element(3, A)
) of
true ->
Grad;
false ->
Res@1 = case viva_tensor@tensor:sum_axis(Grad, 0) of
{ok, Res} -> Res;
_assert_fail ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"add"/utf8>>,
line => 83,
value => _assert_fail,
start => 2548,
'end' => 2593,
pattern_start => 2559,
pattern_end => 2566})
end,
Res@1
end,
Grad_b = case erlang:element(3, Grad) =:= erlang:element(
3,
erlang:element(3, B)
) of
true ->
Grad;
false ->
Res@3 = case viva_tensor@tensor:sum_axis(Grad, 0) of
{ok, Res@2} -> Res@2;
_assert_fail@1 ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"add"/utf8>>,
line => 91,
value => _assert_fail@1,
start => 2716,
'end' => 2761,
pattern_start => 2727,
pattern_end => 2734})
end,
Res@3
end,
[{erlang:element(2, A), Grad_a}, {erlang:element(2, B), Grad_b}]
end,
New_ops = gleam@dict:insert(
erlang:element(3, Tape),
Res_id,
Backward
),
New_tape = {tape, Res_id + 1, New_ops},
{ok, {traced, {variable, Res_id, Res_data}, New_tape}}
end
).
-file("src/viva_tensor/autograd.gleam", 106).
?DOC(" Traced subtraction: c = a - b\n").
-spec sub(tape(), variable(), variable()) -> {ok, traced(variable())} |
{error, viva_tensor@tensor:tensor_error()}.
sub(Tape, A, B) ->
gleam@result:'try'(
viva_tensor@tensor:sub(erlang:element(3, A), erlang:element(3, B)),
fun(Res_data) ->
Res_id = erlang:element(2, Tape),
Backward = fun(Grad) ->
Neg_grad = viva_tensor@tensor:negate(Grad),
[{erlang:element(2, A), Grad}, {erlang:element(2, B), Neg_grad}]
end,
New_ops = gleam@dict:insert(
erlang:element(3, Tape),
Res_id,
Backward
),
New_tape = {tape, Res_id + 1, New_ops},
{ok, {traced, {variable, Res_id, Res_data}, New_tape}}
end
).
-file("src/viva_tensor/autograd.gleam", 130).
?DOC(" Traced Element-wise Multiplication: c = a * b\n").
-spec mul(tape(), variable(), variable()) -> {ok, traced(variable())} |
{error, viva_tensor@tensor:tensor_error()}.
mul(Tape, A, B) ->
gleam@result:'try'(
viva_tensor@tensor:mul(erlang:element(3, A), erlang:element(3, B)),
fun(Res_data) ->
Res_id = erlang:element(2, Tape),
Backward = fun(Grad) ->
Grad_a@1 = case viva_tensor@tensor:mul(
Grad,
erlang:element(3, B)
) of
{ok, Grad_a} -> Grad_a;
_assert_fail ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"mul"/utf8>>,
line => 144,
value => _assert_fail,
start => 4043,
'end' => 4091,
pattern_start => 4054,
pattern_end => 4064})
end,
Grad_b@1 = case viva_tensor@tensor:mul(
Grad,
erlang:element(3, A)
) of
{ok, Grad_b} -> Grad_b;
_assert_fail@1 ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"mul"/utf8>>,
line => 145,
value => _assert_fail@1,
start => 4096,
'end' => 4144,
pattern_start => 4107,
pattern_end => 4117})
end,
[{erlang:element(2, A), Grad_a@1},
{erlang:element(2, B), Grad_b@1}]
end,
New_ops = gleam@dict:insert(
erlang:element(3, Tape),
Res_id,
Backward
),
New_tape = {tape, Res_id + 1, New_ops},
{ok, {traced, {variable, Res_id, Res_data}, New_tape}}
end
).
-file("src/viva_tensor/autograd.gleam", 157).
?DOC(
" Traced Mean (Reduce Mean): y = mean(x)\n"
" Returns a scalar Tensor (rank 0 or 1 depending on base implementation, here we force 1)\n"
).
-spec mean(tape(), variable()) -> traced(variable()).
mean(Tape, A) ->
Val = viva_tensor@tensor:mean(erlang:element(3, A)),
Res_data = viva_tensor@tensor:from_list([Val]),
Res_id = erlang:element(2, Tape),
Backward = fun(Grad) ->
N = begin
_pipe = viva_tensor@tensor:size(erlang:element(3, A)),
erlang:float(_pipe)
end,
Grad_val = begin
_pipe@1 = viva_tensor@tensor:to_list(Grad),
_pipe@2 = gleam@list:first(_pipe@1),
gleam@result:unwrap(_pipe@2, 1.0)
end,
Scaled_grad_val = case N of
+0.0 -> +0.0;
-0.0 -> -0.0;
Gleam@denominator -> Grad_val / Gleam@denominator
end,
Grad_input = viva_tensor@tensor:fill(
erlang:element(3, erlang:element(3, A)),
Scaled_grad_val
),
[{erlang:element(2, A), Grad_input}]
end,
New_ops = gleam@dict:insert(erlang:element(3, Tape), Res_id, Backward),
New_tape = {tape, Res_id + 1, New_ops},
{traced, {variable, Res_id, Res_data}, New_tape}.
-file("src/viva_tensor/autograd.gleam", 185).
?DOC(" Traced Matrix Multiplication: c = a @ b\n").
-spec matmul(tape(), variable(), variable()) -> {ok, traced(variable())} |
{error, viva_tensor@tensor:tensor_error()}.
matmul(Tape, A, B) ->
gleam@result:'try'(
viva_tensor@tensor:matmul(erlang:element(3, A), erlang:element(3, B)),
fun(Res_data) ->
Res_id = erlang:element(2, Tape),
Backward = fun(Grad) ->
Bt@1 = case viva_tensor@tensor:transpose(erlang:element(3, B)) of
{ok, Bt} -> Bt;
_assert_fail ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"matmul"/utf8>>,
line => 199,
value => _assert_fail,
start => 5862,
'end' => 5906,
pattern_start => 5873,
pattern_end => 5879})
end,
At@1 = case viva_tensor@tensor:transpose(erlang:element(3, A)) of
{ok, At} -> At;
_assert_fail@1 ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"matmul"/utf8>>,
line => 200,
value => _assert_fail@1,
start => 5911,
'end' => 5955,
pattern_start => 5922,
pattern_end => 5928})
end,
Grad_a@1 = case viva_tensor@tensor:matmul(Grad, Bt@1) of
{ok, Grad_a} -> Grad_a;
_assert_fail@2 ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"matmul"/utf8>>,
line => 202,
value => _assert_fail@2,
start => 5961,
'end' => 6008,
pattern_start => 5972,
pattern_end => 5982})
end,
Grad_b@1 = case viva_tensor@tensor:matmul(At@1, Grad) of
{ok, Grad_b} -> Grad_b;
_assert_fail@3 ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"matmul"/utf8>>,
line => 203,
value => _assert_fail@3,
start => 6013,
'end' => 6060,
pattern_start => 6024,
pattern_end => 6034})
end,
[{erlang:element(2, A), Grad_a@1},
{erlang:element(2, B), Grad_b@1}]
end,
New_ops = gleam@dict:insert(
erlang:element(3, Tape),
Res_id,
Backward
),
New_tape = {tape, Res_id + 1, New_ops},
{ok, {traced, {variable, Res_id, Res_data}, New_tape}}
end
).
-file("src/viva_tensor/autograd.gleam", 215).
?DOC(" Traced Transpose: c = a.T\n").
-spec transpose(tape(), variable()) -> {ok, traced(variable())} |
{error, viva_tensor@tensor:tensor_error()}.
transpose(Tape, A) ->
gleam@result:'try'(
viva_tensor@tensor:transpose(erlang:element(3, A)),
fun(Res_data) ->
Res_id = erlang:element(2, Tape),
Backward = fun(Grad) ->
Grad_t@1 = case viva_tensor@tensor:transpose(Grad) of
{ok, Grad_t} -> Grad_t;
_assert_fail ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"transpose"/utf8>>,
line => 225,
value => _assert_fail,
start => 6606,
'end' => 6652,
pattern_start => 6617,
pattern_end => 6627})
end,
[{erlang:element(2, A), Grad_t@1}]
end,
New_ops = gleam@dict:insert(
erlang:element(3, Tape),
Res_id,
Backward
),
New_tape = {tape, Res_id + 1, New_ops},
{ok, {traced, {variable, Res_id, Res_data}, New_tape}}
end
).
-file("src/viva_tensor/autograd.gleam", 236).
?DOC(" Traced ReLU\n").
-spec relu(tape(), variable()) -> traced(variable()).
relu(Tape, A) ->
Res_data = viva_tensor@tensor:map(
erlang:element(3, A),
fun(X) -> case X > +0.0 of
true ->
X;
false ->
+0.0
end end
),
Res_id = erlang:element(2, Tape),
Backward = fun(Grad) ->
Mask = viva_tensor@tensor:map(
erlang:element(3, A),
fun(X@1) -> case X@1 > +0.0 of
true ->
1.0;
false ->
+0.0
end end
),
Grad_a@1 = case viva_tensor@tensor:mul(Grad, Mask) of
{ok, Grad_a} -> Grad_a;
_assert_fail ->
erlang:error(#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"relu"/utf8>>,
line => 256,
value => _assert_fail,
start => 7346,
'end' => 7392,
pattern_start => 7357,
pattern_end => 7367})
end,
[{erlang:element(2, A), Grad_a@1}]
end,
New_ops = gleam@dict:insert(erlang:element(3, Tape), Res_id, Backward),
New_tape = {tape, Res_id + 1, New_ops},
{traced, {variable, Res_id, Res_data}, New_tape}.
-file("src/viva_tensor/autograd.gleam", 331).
-spec string_shape(list(integer())) -> binary().
string_shape(Shape) ->
<<<<"["/utf8,
(gleam@string:join(
gleam@list:map(Shape, fun erlang:integer_to_binary/1),
<<", "/utf8>>
))/binary>>/binary,
"]"/utf8>>.
-file("src/viva_tensor/autograd.gleam", 272).
?DOC(
" Executes backpropagation starting from a scalar variable (loss).\n"
" Returns a Map of NodeId -> Gradient (Tensor)\n"
).
-spec backward(tape(), variable()) -> {ok,
gleam@dict:dict(integer(), viva_tensor@tensor:tensor())} |
{error, binary()}.
backward(Tape, Loss) ->
Initial_grad = viva_tensor@tensor:ones(
erlang:element(3, erlang:element(3, Loss))
),
Initial_grads = maps:from_list([{erlang:element(2, Loss), Initial_grad}]),
All_ids = gleam@list:range(erlang:element(2, Tape) - 1, 0),
Final_grads = gleam@list:fold(
All_ids,
Initial_grads,
fun(Grads, Current_id) ->
case gleam_stdlib:map_get(Grads, Current_id) of
{error, _} ->
Grads;
{ok, Current_grad} ->
case gleam_stdlib:map_get(
erlang:element(3, Tape),
Current_id
) of
{error, _} ->
Grads;
{ok, Back_fn} ->
Parent_grads = Back_fn(Current_grad),
gleam@list:fold(
Parent_grads,
Grads,
fun(Acc_grads, Pair) ->
{Pid, Pgrad} = Pair,
case gleam_stdlib:map_get(Acc_grads, Pid) of
{error, _} ->
gleam@dict:insert(
Acc_grads,
Pid,
Pgrad
);
{ok, Existing} ->
case erlang:element(3, Existing) =:= erlang:element(
3,
Pgrad
) of
true ->
Sum@1 = case viva_tensor@tensor:add(
Existing,
Pgrad
) of
{ok, Sum} -> Sum;
_assert_fail ->
erlang:error(
#{gleam_error => let_assert,
message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"backward"/utf8>>,
line => 305,
value => _assert_fail,
start => 9387,
'end' => 9435,
pattern_start => 9398,
pattern_end => 9405}
)
end,
gleam@dict:insert(
Acc_grads,
Pid,
Sum@1
);
false ->
Msg = <<<<<<<<<<"ShapeMismatch at node "/utf8,
(erlang:integer_to_binary(
Pid
))/binary>>/binary,
": existing="/utf8>>/binary,
(string_shape(
erlang:element(
3,
Existing
)
))/binary>>/binary,
", new="/utf8>>/binary,
(string_shape(
erlang:element(
3,
Pgrad
)
))/binary>>,
erlang:error(
#{gleam_error => panic,
message => Msg,
file => <<?FILEPATH/utf8>>,
module => <<"viva_tensor/autograd"/utf8>>,
function => <<"backward"/utf8>>,
line => 316}
)
end
end
end
)
end
end
end
),
{ok, Final_grads}.