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Module

[macro] defmodule

(defmodule (name ((&rest constructor-args) &rest attrs) &key (where nil) (direct-superclasses nil))
  (&rest slots)
  &key (documentation "") (impl nil) (forward nil) (backward nil))

Define a module named name.

In Caten, Module is a CLOS class that represents a set of Funcs and is defined as a subclass of Func itself. It is used to represent computational nodes that can be expressed through compositions of Funcs. Consequently, as a subclass of Func, Module utilizes the following three methods for manipulation:

[method] impl

(impl (op Module) &rest tensors)

  • tensors[list] a list of the input tensor.

In the impl method, please describe the process for constructing the computational graph of the Module using a combination of Func and Module. The computational graph must begin with the inputs. If there are multiple outputs, bind them with cl:values. If you need to record Tensors for the backward process, now is the time to do so.

[method] forward

(forward (op Module) &rest tensors)

  • tensors[List] a list of the input tensor.

In the forward method, describe the operation to create a Tensor after computation. Be aware of its lazy evaluation nature; do not perform the actual computation at this stage. The st macro in ShapeTracker is quite useful for creating the Tensor after the operation. If necessary, you may also include checks for additional attributes or slots here. If you specify ShapeTracker in :where, the defmodule macro will automatically generate the forward. Therefore, you must describe either :where or :forward.

[method] backward (optional)

(backward (op Module) prev-grad) -> (values input_1.grad input_2.grad ...)

  • prev-grad[Tensor]

In the backward method, describe the gradient computation for the Module using a combination of Func and Module. The arguments are fixed as (op prev-grad), where op = module instance, prev-grad is a tensor. If you need the value of the Tensor at the input stage for the gradient calculation, temporarily store it using the module-sv4bws accessor while calling the impl method. The compiler does not depend on module-sv4bws, so you are free to choose how to store the Tensor. In Caten, since save-for-backward is automatically determined, there is no need to be concerned about in-place operations.

Note that backward is optional. If it is not provided, AD will be applied based on the computational graph from impl.

[method] lower

The lower method is automatically written by the defmodule, so there is no need to consider it when describing the module. However, it is necessary to understand how it is lowered for when defining simplifiers for the Module.

lower produces the following node: (make-node :Graph (intern (symbol-name (symb 'graph/ name)) "KEYWORD") outputs inputs &rest attrs)

Nodes whose class is :Graph are completely eliminated during lower by impl.

Syntax

forward, backward, impl are described in one of the following format.

forward := ((op &rest args) &body body)
forward := (lambda (&rest args) &body body)
forward := fname

Effects

  • it defines a class named name.
  • it defines a function named name. it works as a constructor.

Arguments

  • name[symbol] the name of module
  • constructor-args[list] arguments for the constructor
  • attrs[list] define attrs for the lowered graph based on the constructor-args variables using the following format: (:key1 value1 :key1 value2 ...).
  • slots[list] slots for the defined class.
  • where[nil or string] ShapeTracker
  • documentation[string] documentation

Notes

  • The methods are called in the order of forward->impl->backward during compilation
  • impl is performed recursively, so modules must not be co-dependent within the impl method. (e.g.: do not define a module A that depends on B that depends on A ...)

Modules (built_in)

[function] !sum

(!sum x &key (axis t) (keepdims nil))

Compute the sum of the tensor.

lisp
CATEN-USER> (proceed (!sum (ax+b `(10 10) 1 0)))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (1 1) :id STC155728
   ((4950.0))
  :op #<PROCEEDNODE {10031A1833}>
  :requires-grad NIL
  :variables (VID154435)
  :tracker #<TRACKER :order={row(0 1)} :shape=(~1 ~1) :contiguous-p=T>}

[function] !mean

(!mean x &key (axis t) (keepdims nil))

Compute the mean of the tensor.

lisp
CATEN-USER> (proceed (!mean (ax+b `(10 10) 1 0)))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (1 1) :id STC157467
   ((49.5))
  :op #<PROCEEDNODE {100360BE83}>
  :requires-grad NIL
  :variables (VID155831)
  :tracker #<TRACKER :order={row(0 1)} :shape=(~1 ~1) :contiguous-p=T>}

[function] !max

(!max x &key (axis t) (keepdims nil))

Compute the maximum of the tensor.

lisp
CATEN-USER> (proceed (!max (ax+b `(10 10) 1 0)))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (1 1) :id STC159537
   ((99.0))
  :op #<PROCEEDNODE {1003B2D8C3}>
  :requires-grad NIL
  :variables (VID157570)
  :tracker #<TRACKER :order={row(0 1)} :shape=(~1 ~1) :contiguous-p=T>}

[function] !min

(!min x &key (axis t) (keepdims nil))

Compute the minimum of the tensor.

lisp
CATEN-USER> (proceed (!min (ax+b `(10 10) 1 0)))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (1 1) :id STC161625
   ((0.0))
  :op #<PROCEEDNODE {1004155583}>
  :requires-grad NIL
  :variables (VID159640)
  :tracker #<TRACKER :order={row(0 1)} :shape=(~1 ~1) :contiguous-p=T>}

[function] !matmul

(!matmul a b)

Performs matrix multiplication between the two tensors a and b.

lisp
CATEN-USER> (proceed (!matmul (rand `(32 64)) (rand `(64 128))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (32 128) :id STC166090
   ((16.115143  16.458525  16.092386  17.81228   13.661716  ~ 17.686089  18.038162  16.683573  16.274176  18.700905)
    (16.326677  15.621148  16.356201  17.916739  14.871678  ~ 18.09569   17.361448  15.73287   16.648724  18.704985)
    (16.722721  14.823622  14.077707  16.202015  13.752501  ~ 17.039087  16.04018   16.320084  16.388088  16.415977)
    (16.117361  16.602467  14.900114  16.754038  12.972164  ~ 15.914988  16.225424  14.572695  16.187672  17.73983)
    (15.025454  14.202459  13.762134  14.921074  12.034962  ~ 14.2497    14.7951    15.23291   14.765818  17.027578)
                                                        ...
    (14.671678  15.548787  14.961614  16.846735  14.662898  ~ 15.099126  15.20463   15.049035  16.246407  17.84826)
    (15.084174  14.32615   15.439503  17.32295   13.282019  ~ 16.467468  15.561042  15.09145   16.568888  16.251673)
    (15.426824  15.761291  14.47131   15.671989  13.309795  ~ 15.386046  15.088989  14.298187  14.939453  17.597435)
    (16.099691  15.497888  13.230323  15.339464  12.640831  ~ 16.377731  16.77367   15.217857  16.147154  15.99234)
    (14.86157   15.624828  13.565197  16.511955  13.524295  ~ 16.017046  14.623064  14.877545  16.962063  16.800804))
  :op #<PROCEEDNODE {1002ED0633}>
  :requires-grad NIL
  :variables (STC161638)
  :tracker #<TRACKER :order={row(0 1)} :shape=(32 128) :contiguous-p=T>}

[function] !sinh

(!sinh x)
lisp
CATEN-USER> (proceed (!sinh (randn `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC166854
   ((-0.6667148  -1.7986057  -0.16147432)
    (0.99311143  1.5690467   -0.45024085)
    (0.2741389   -0.84445757 3.6562643))
  :op #<PROCEEDNODE {1003399B73}>
  :requires-grad NIL
  :variables (STC166097)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !cosh

(!cosh x)
lisp
CATEN-USER> (proceed (!cosh (randn `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC167612
   ((1.1091444 12.141601 1.8187159)
    (1.0450624 1.0673907 2.024306)
    (1.0057459 11.280086 1.0366853))
  :op #<PROCEEDNODE {100372F103}>
  :requires-grad NIL
  :variables (STC166861)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !tanh

(!tanh x)
lisp
CATEN-USER> (proceed (!tanh (randn `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC170370
   ((0.48222518 0.83497787 0.15090048)
    (-0.6021365 -0.8142663 0.0836575)
    (0.90113175 0.5248045  0.26375103))
  :op #<PROCEEDNODE {1003FA9C23}>
  :requires-grad NIL
  :variables (STC167619)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !cos

(!cos x)
lisp
CATEN-USER> (proceed (!cos (randn `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC171055
   ((0.8741474   0.6821368   0.96187115)
    (0.9756673   -0.15136945 0.5390583)
    (0.7348094   0.56210893  0.9987133))
  :op #<PROCEEDNODE {1005563B83}>
  :requires-grad NIL
  :variables (STC170377)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !tan

(!tan x)
lisp
CATEN-USER> (proceed (!tan (randn `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC171779
   ((2.2656112    1.2551787    -52.0603)
    (0.11679068   0.27259648   0.0093172565)
    (0.26652285   -0.48955667  -2.6124444))
  :op #<PROCEEDNODE {1005BD7AB3}>
  :requires-grad NIL
  :variables (STC171062)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !log2

(!log2 x)
lisp
CATEN-USER> (proceed (!log2 (ax+b `(3 3) 1 0.1)))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC172535
   ((-3.321928  0.13750356 1.0703893)
    (1.6322682  2.0356238  2.3504972)
    (2.6088092  2.827819   3.017922))
  :op #<PROCEEDNODE {100719F343}>
  :requires-grad NIL
  :variables (STC171787)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !exp2

(!exp2 x)
lisp
CATEN-USER> (proceed (!exp2 (ax+b `(3 3) 1 0.1)))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC173274
   ((1.0717734 2.143547  4.2870936)
    (8.574187  17.148375 34.29675)
    (68.593475 137.18695 274.37408))
  :op #<PROCEEDNODE {10073224D3}>
  :requires-grad NIL
  :variables (STC172543)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !expt

(!expt base power)
Computes the power of base with power.

lisp
CATEN-USER> (proceed (!expt (ax+b `(3 3) 1 0.1) 2))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC175289
   ((0.010000001 1.21        4.4099994)
    (9.61        16.81       26.009998)
    (37.21       50.41       65.61001))
  :op #<PROCEEDNODE {10081FA423}>
  :requires-grad NIL
  :variables (STC173577)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !truncate

(!truncate x)
lisp
CATEN-USER> (proceed (!truncate (randn `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC175481
   ((0.0  0.0  0.0)
    (0.0  0.0  1.0)
    (0.0  0.0  -1.0))
  :op #<PROCEEDNODE {10090E3853}>
  :requires-grad NIL
  :variables (STC175296)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !ceiling

(!ceiling x)
lisp
CATEN-USER> (proceed (!ceiling (randn `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC176399
   ((1.0  -3.0 -1.0)
    (1.0  0.0  0.0)
    (0.0  0.0  0.0))
  :op #<PROCEEDNODE {10094B0D33}>
  :requires-grad NIL
  :variables (STC175488)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !floor

(!floor x)
lisp
CATEN-USER> (proceed (!floor (randn `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC177319
   ((-1.0 0.0  -2.0)
    (0.0  0.0  -2.0)
    (-1.0 -1.0 -1.0))
  :op #<PROCEEDNODE {1009A380A3}>
  :requires-grad NIL
  :variables (STC176406)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !triu

(!triu x &key (diagonal 0))

Returns the upper triangular part of the tensor (>= 2D) or batch of matrices input.

lisp
CATEN-USER> (proceed (!triu (rand `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC178677
   ((0.016040208 0.9379116   0.9069626)
    (0.0         0.90060127  0.21504083)
    (0.0         0.0         0.8353897))
  :op #<PROCEEDNODE {10018581F3}>
  :requires-grad NIL
  :variables (STC177326)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !tril

(!tril x &key (diagonal 0))

Returns the lower triangular part of the tensor (>= 2D) or batch of matrices input.

lisp
CATEN-USER> (proceed (!tril (rand `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC180043
   ((0.81040674 0.0        0.0)
    (0.5340498  0.44669133 0.0)
    (0.47975928 0.7199338  0.24915472))
  :op #<PROCEEDNODE {1001CD1FF3}>
  :requires-grad NIL
  :variables (STC178684)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !argmax

(!argmax x &key (axis -1) (keepdims nil))

Returns the indices of the maximum values along an axis.

lisp
CATEN-USER> (proceed (!argmax (rand `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[int64] :shape (3 1) :id STC186798
   ((1)
    (0)
    (1))
  :op #<PROCEEDNODE {1003760EE3}>
  :requires-grad NIL
  :variables (VID180145)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 ~1) :contiguous-p=T>}

[function] !argmin

(!argmin x &key (axis -1) (keepdims nil))

Returns the indices of the minimum values along an axis.

lisp
CATEN-USER> (proceed (!argmin (rand `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[int64] :shape (3 1) :id STC193742
   ((2)
    (1)
    (1))
  :op #<PROCEEDNODE {10072078D3}>
  :requires-grad NIL
  :variables (VID186900)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 ~1) :contiguous-p=T>}

[function] !clip

(!clip x min max)

!clip limits the given input within an interval. The interval is specified by the inputs 'min' and 'max'. min/max is either a number, a symbol, or a tensor.

The implementation follows the ONNX specification. https://github.com/onnx/onnx/blob/main/docs/Changelog.md#clip-13

lisp
CATEN-USER> (proceed (!clip (randn `(3 3)) -0.3 0.3))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC196335
   ((-0.3      0.3       0.3)
    (0.3       0.2180472 0.3)
    (0.3       -0.3      0.3))
  :op #<PROCEEDNODE {10090BBF73}>
  :requires-grad NIL
  :variables (STC193939)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !erf

(!erf x)
Computes the error function of x.

lisp
CATEN-USER> (proceed (!erf (randn `(3 3))))
Result
Result
{Tensor{LISPBUFFER}[float32] :shape (3 3) :id STC207681
   ((-0.5891361  -0.9240581  -0.08728349)
    (0.9355107   0.5068274   -0.44668216)
    (-0.76412225 -0.96422094 0.37599617))
  :op #<PROCEEDNODE {10031D7013}>
  :requires-grad NIL
  :variables (STC196342)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}