| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | module athena__orthogonal_nop_block | ||
| 2 | !! Module containing implementation of an Orthogonal Neural Operator layer | ||
| 3 | !! | ||
| 4 | !! This module implements the Orthogonal Neural Operator (ONO) from | ||
| 5 | !! "Improved Operator Learning by Orthogonal Attention" (Luo et al., 2024). | ||
| 6 | !! | ||
| 7 | !! The ONO layer uses an orthogonal attention kernel to approximate the | ||
| 8 | !! integral operator. It combines: | ||
| 9 | !! 1. A learned orthogonal basis for efficient attention (k << N) | ||
| 10 | !! 2. A spectral pathway through the orthogonal basis | ||
| 11 | !! 3. A local affine bypass | ||
| 12 | !! | ||
| 13 | !! The layer computes: | ||
| 14 | !! \[ | ||
| 15 | !! \mathbf{v} = \sigma\!\bigl( | ||
| 16 | !! \mathbf{W}_V\,\mathbf{\Phi}\,(\mathbf{\Phi}^T\,\mathbf{u}) | ||
| 17 | !! + \mathbf{W}\,\mathbf{u} | ||
| 18 | !! + \mathbf{b}\bigr) | ||
| 19 | !! \] | ||
| 20 | !! | ||
| 21 | !! where \(\mathbf{\Phi} \in \mathbb{R}^{n_{in} \times k}\) is obtained | ||
| 22 | !! by QR/Gram-Schmidt orthogonalisation of learnable basis weights | ||
| 23 | !! \(\mathbf{B}\). | ||
| 24 | !! | ||
| 25 | !! Parameters (learnable): | ||
| 26 | !! - \(\mathbf{R} \in \mathbb{R}^{k \times k}\) spectral mixing | ||
| 27 | !! - \(\mathbf{B} \in \mathbb{R}^{n_{in} \times k}\) basis (orthogonalised) | ||
| 28 | !! - \(\mathbf{W} \in \mathbb{R}^{n_{out} \times n_{in}}\) bypass | ||
| 29 | !! - \(\mathbf{b} \in \mathbb{R}^{n_{out}}\) bias (optional) | ||
| 30 | !! | ||
| 31 | !! The spectral path is: decode( R * encode(u) ) | ||
| 32 | !! encode = Phi^T @ u [k, batch] | ||
| 33 | !! mix = R @ encoded [k, batch] | ||
| 34 | !! decode = Phi @ mix [n_in, batch] | ||
| 35 | !! | ||
| 36 | !! Then a linear projection to the output: W_out @ decode -> [n_out, batch] | ||
| 37 | !! Plus bypass: W @ u -> [n_out, batch] | ||
| 38 | use coreutils, only: real32, stop_program | ||
| 39 | use athena__base_layer, only: learnable_layer_type, base_layer_type | ||
| 40 | use athena__misc_types, only: base_actv_type, base_init_type, & | ||
| 41 | onnx_attribute_type | ||
| 42 | use diffstruc, only: array_type, matmul, operator(+) | ||
| 43 | use athena__diffstruc_extd, only: ono_encode, ono_decode | ||
| 44 | implicit none | ||
| 45 | public :: read_orthogonal_nop_block | ||
| 46 | |||
| 47 | |||
| 48 | type, extends(learnable_layer_type) :: orthogonal_nop_block_type | ||
| 49 | !! Type for an Orthogonal Neural Operator layer | ||
| 50 | integer :: num_inputs = 0 | ||
| 51 | !! Number of inputs (discretisation points) | ||
| 52 | integer :: num_outputs = 0 | ||
| 53 | !! Number of outputs (discretisation points) | ||
| 54 | integer :: num_basis = 0 | ||
| 55 | !! Number of orthogonal basis functions (k) | ||
| 56 | type(array_type), dimension(1) :: z | ||
| 57 | !! Temporary array for pre-activation values | ||
| 58 | contains | ||
| 59 | procedure, pass(this) :: get_num_params => get_num_params_ono | ||
| 60 | procedure, pass(this) :: set_hyperparams => set_hyperparams_ono | ||
| 61 | procedure, pass(this) :: init => init_ono | ||
| 62 | procedure, pass(this) :: print_to_unit => print_to_unit_ono | ||
| 63 | procedure, pass(this) :: read => read_ono | ||
| 64 | |||
| 65 | procedure, pass(this) :: forward => forward_ono | ||
| 66 | procedure, pass(this) :: get_bases => get_bases_ono | ||
| 67 | procedure, pass(this) :: get_orthogonality_metric | ||
| 68 | procedure, pass(this) :: get_attributes => get_attributes_ono | ||
| 69 | |||
| 70 | final :: finalise_ono | ||
| 71 | end type orthogonal_nop_block_type | ||
| 72 | |||
| 73 | interface orthogonal_nop_block_type | ||
| 74 | module function layer_setup( & | ||
| 75 | num_outputs, num_basis, & | ||
| 76 | num_inputs, use_bias, & | ||
| 77 | activation, & | ||
| 78 | kernel_initialiser, bias_initialiser, verbose & | ||
| 79 | ) result(layer) | ||
| 80 | integer, intent(in) :: num_outputs | ||
| 81 | integer, intent(in) :: num_basis | ||
| 82 | integer, optional, intent(in) :: num_inputs | ||
| 83 | logical, optional, intent(in) :: use_bias | ||
| 84 | class(*), optional, intent(in) :: activation | ||
| 85 | class(*), optional, intent(in) :: kernel_initialiser, bias_initialiser | ||
| 86 | integer, optional, intent(in) :: verbose | ||
| 87 | type(orthogonal_nop_block_type) :: layer | ||
| 88 | end function layer_setup | ||
| 89 | end interface orthogonal_nop_block_type | ||
| 90 | |||
| 91 | |||
| 92 | |||
| 93 | contains | ||
| 94 | |||
| 95 | !############################################################################### | ||
| 96 | 16 | subroutine finalise_ono(this) | |
| 97 | !! Finalise the orthogonal neural operator block | ||
| 98 | implicit none | ||
| 99 | |||
| 100 | ! Arguments | ||
| 101 | type(orthogonal_nop_block_type), intent(inout) :: this | ||
| 102 | !! Layer instance to release | ||
| 103 | |||
| 104 |
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16 | if(allocated(this%input_shape)) deallocate(this%input_shape) |
| 105 |
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16 | if(allocated(this%output)) deallocate(this%output) |
| 106 |
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16 | if(this%z(1)%allocated) call this%z(1)%deallocate() |
| 107 | |||
| 108 | 16 | end subroutine finalise_ono | |
| 109 | !############################################################################### | ||
| 110 | |||
| 111 | |||
| 112 | !############################################################################### | ||
| 113 | 11 | pure function get_num_params_ono(this) result(num_params) | |
| 114 | !! Return the number of learnable parameters for the block | ||
| 115 | implicit none | ||
| 116 | |||
| 117 | ! Arguments | ||
| 118 | class(orthogonal_nop_block_type), intent(in) :: this | ||
| 119 | !! Layer instance | ||
| 120 | integer :: num_params | ||
| 121 | !! Total number of learnable parameters | ||
| 122 | |||
| 123 | ! R: num_basis^2 (spectral mixing) | ||
| 124 | ! B: num_inputs * num_basis (basis weights) | ||
| 125 | ! W_out: num_outputs * num_inputs (output projection / bypass) | ||
| 126 | ! b: num_outputs (optional) | ||
| 127 | num_params = this%num_basis * this%num_basis + & | ||
| 128 | this%num_inputs * this%num_basis + & | ||
| 129 | 11 | this%num_outputs * this%num_inputs | |
| 130 |
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11 | if(this%use_bias) num_params = num_params + this%num_outputs |
| 131 | |||
| 132 | 11 | end function get_num_params_ono | |
| 133 | !############################################################################### | ||
| 134 | |||
| 135 | |||
| 136 | !############################################################################### | ||
| 137 | 11 | module function layer_setup( & | |
| 138 | num_outputs, num_basis, & | ||
| 139 | num_inputs, use_bias, & | ||
| 140 | activation, & | ||
| 141 | kernel_initialiser, bias_initialiser, verbose & | ||
| 142 |
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22 | ) result(layer) |
| 143 | use athena__activation, only: activation_setup | ||
| 144 | use athena__initialiser, only: initialiser_setup | ||
| 145 | implicit none | ||
| 146 | |||
| 147 | ! Arguments | ||
| 148 | integer, intent(in) :: num_outputs | ||
| 149 | !! Number of output features | ||
| 150 | integer, intent(in) :: num_basis | ||
| 151 | !! Number of orthogonal basis vectors | ||
| 152 | integer, optional, intent(in) :: num_inputs | ||
| 153 | !! Number of input features when known at construction time | ||
| 154 | logical, optional, intent(in) :: use_bias | ||
| 155 | !! Whether to allocate a bias term | ||
| 156 | class(*), optional, intent(in) :: activation | ||
| 157 | !! Activation function specification | ||
| 158 | class(*), optional, intent(in) :: kernel_initialiser, bias_initialiser | ||
| 159 | !! Kernel and bias initialiser specifications | ||
| 160 | integer, optional, intent(in) :: verbose | ||
| 161 | !! Verbosity level | ||
| 162 | |||
| 163 | type(orthogonal_nop_block_type) :: layer | ||
| 164 | !! Constructed orthogonal neural operator block | ||
| 165 | |||
| 166 | ! Local variables | ||
| 167 | integer :: verbose_ = 0 | ||
| 168 | !! Effective verbosity level | ||
| 169 | logical :: use_bias_ = .true. | ||
| 170 | !! Effective bias flag | ||
| 171 | 33 | class(base_actv_type), allocatable :: activation_ | |
| 172 | !! Materialised activation object | ||
| 173 | 11 | class(base_init_type), allocatable :: kernel_initialiser_, bias_initialiser_ | |
| 174 | !! Materialised kernel and bias initialisers | ||
| 175 | |||
| 176 |
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11 | if(present(verbose)) verbose_ = verbose |
| 177 |
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11 | if(present(use_bias)) use_bias_ = use_bias |
| 178 | |||
| 179 |
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11 | if(present(activation))then |
| 180 |
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7 | activation_ = activation_setup(activation) |
| 181 | else | ||
| 182 |
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4 | activation_ = activation_setup("none") |
| 183 | end if | ||
| 184 | |||
| 185 |
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11 | if(present(kernel_initialiser))then |
| 186 | ✗ | kernel_initialiser_ = initialiser_setup(kernel_initialiser) | |
| 187 | end if | ||
| 188 |
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11 | if(present(bias_initialiser))then |
| 189 | ✗ | bias_initialiser_ = initialiser_setup(bias_initialiser) | |
| 190 | end if | ||
| 191 | |||
| 192 | call layer%set_hyperparams( & | ||
| 193 | num_outputs = num_outputs, & | ||
| 194 | num_basis = num_basis, & | ||
| 195 | use_bias = use_bias_, & | ||
| 196 | activation = activation_, & | ||
| 197 | kernel_initialiser = kernel_initialiser_, & | ||
| 198 | bias_initialiser = bias_initialiser_, & | ||
| 199 | verbose = verbose_ & | ||
| 200 | 11 | ) | |
| 201 | |||
| 202 |
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20 | if(present(num_inputs)) call layer%init(input_shape=[num_inputs]) |
| 203 | |||
| 204 |
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33 | end function layer_setup |
| 205 | !############################################################################### | ||
| 206 | |||
| 207 | |||
| 208 | !############################################################################### | ||
| 209 | 12 | subroutine set_hyperparams_ono( & | |
| 210 | this, num_outputs, num_basis, & | ||
| 211 | use_bias, & | ||
| 212 | activation, & | ||
| 213 | kernel_initialiser, bias_initialiser, & | ||
| 214 | verbose & | ||
| 215 | ) | ||
| 216 | use athena__activation, only: activation_setup | ||
| 217 | use athena__initialiser, only: get_default_initialiser, initialiser_setup | ||
| 218 | implicit none | ||
| 219 | |||
| 220 | ! Arguments | ||
| 221 | class(orthogonal_nop_block_type), intent(inout) :: this | ||
| 222 | !! Layer instance to configure | ||
| 223 | integer, intent(in) :: num_outputs | ||
| 224 | !! Number of output features | ||
| 225 | integer, intent(in) :: num_basis | ||
| 226 | !! Number of orthogonal basis vectors | ||
| 227 | logical, intent(in) :: use_bias | ||
| 228 | !! Whether to use a bias term | ||
| 229 | class(base_actv_type), allocatable, intent(in) :: activation | ||
| 230 | !! Activation function object | ||
| 231 | class(base_init_type), allocatable, intent(in) :: & | ||
| 232 | kernel_initialiser, bias_initialiser | ||
| 233 | !! Kernel and bias initialiser objects | ||
| 234 | integer, optional, intent(in) :: verbose | ||
| 235 | !! Verbosity level | ||
| 236 | |||
| 237 | ! Local variables | ||
| 238 | character(len=256) :: buffer | ||
| 239 | !! Buffer for default initialiser lookup | ||
| 240 | |||
| 241 |
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12 | this%name = "orthogonal_nop" |
| 242 | 12 | this%type = "nop" | |
| 243 | 12 | this%input_rank = 1 | |
| 244 | 12 | this%output_rank = 1 | |
| 245 | 12 | this%use_bias = use_bias | |
| 246 | 12 | this%num_outputs = num_outputs | |
| 247 | 12 | this%num_basis = num_basis | |
| 248 | |||
| 249 |
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12 | if(allocated(this%activation)) deallocate(this%activation) |
| 250 |
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12 | if(.not.allocated(activation))then |
| 251 | ✗ | this%activation = activation_setup("none") | |
| 252 | else | ||
| 253 |
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12 | allocate(this%activation, source=activation) |
| 254 | end if | ||
| 255 |
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12 | if(allocated(this%kernel_init)) deallocate(this%kernel_init) |
| 256 |
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12 | if(.not.allocated(kernel_initialiser))then |
| 257 |
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11 | buffer = get_default_initialiser(this%activation%name) |
| 258 |
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11 | this%kernel_init = initialiser_setup(buffer) |
| 259 | else | ||
| 260 |
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1 | allocate(this%kernel_init, source=kernel_initialiser) |
| 261 | end if | ||
| 262 |
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12 | if(allocated(this%bias_init)) deallocate(this%bias_init) |
| 263 |
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12 | if(.not.allocated(bias_initialiser))then |
| 264 | buffer = get_default_initialiser( & | ||
| 265 | this%activation%name, & | ||
| 266 | is_bias=.true. & | ||
| 267 |
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11 | ) |
| 268 |
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11 | this%bias_init = initialiser_setup(buffer) |
| 269 | else | ||
| 270 |
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1 | allocate(this%bias_init, source=bias_initialiser) |
| 271 | end if | ||
| 272 | |||
| 273 |
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12 | if(present(verbose))then |
| 274 |
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12 | if(abs(verbose).gt.0)then |
| 275 | write(*,'("ORTHOGONAL_NOP activation: ",A)') & | ||
| 276 | ✗ | trim(this%activation%name) | |
| 277 | end if | ||
| 278 | end if | ||
| 279 | |||
| 280 | 12 | end subroutine set_hyperparams_ono | |
| 281 | !############################################################################### | ||
| 282 | |||
| 283 | |||
| 284 | !############################################################################### | ||
| 285 |
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11 | subroutine init_ono(this, input_shape, verbose) |
| 286 | !! Initialise parameter storage and output buffers for the block | ||
| 287 | implicit none | ||
| 288 | |||
| 289 | ! Arguments | ||
| 290 | class(orthogonal_nop_block_type), intent(inout) :: this | ||
| 291 | !! Layer instance to initialise | ||
| 292 | integer, dimension(:), intent(in) :: input_shape | ||
| 293 | !! Input shape used to infer num_inputs | ||
| 294 | integer, optional, intent(in) :: verbose | ||
| 295 | !! Verbosity level | ||
| 296 | |||
| 297 | ! Local variables | ||
| 298 | integer :: num_inputs | ||
| 299 | !! Effective fan-in size used for initialisation | ||
| 300 | integer :: verbose_ = 0 | ||
| 301 | !! Effective verbosity level | ||
| 302 | |||
| 303 |
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11 | if(present(verbose)) verbose_ = verbose |
| 304 | |||
| 305 | |||
| 306 | !--------------------------------------------------------------------------- | ||
| 307 | ! Set shapes | ||
| 308 | !--------------------------------------------------------------------------- | ||
| 309 |
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11 | if(.not.allocated(this%input_shape)) call this%set_shape(input_shape) |
| 310 |
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11 | this%num_inputs = this%input_shape(1) |
| 311 |
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22 | this%output_shape = [this%num_outputs] |
| 312 | 11 | this%num_params = this%get_num_params() | |
| 313 | |||
| 314 | |||
| 315 | !--------------------------------------------------------------------------- | ||
| 316 | ! Allocate learnable parameters | ||
| 317 | ! | ||
| 318 | ! params(1): R spectral mixing [num_basis x num_basis] | ||
| 319 | ! params(2): B basis weights [num_inputs x num_basis] | ||
| 320 | ! params(3): W bypass/output weights [num_outputs x num_inputs] | ||
| 321 | ! params(4): b bias [num_outputs] (optional) | ||
| 322 | !--------------------------------------------------------------------------- | ||
| 323 |
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11 | allocate(this%weight_shape(2,3)) |
| 324 |
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33 | this%weight_shape(:,1) = [ this%num_basis, this%num_basis ] |
| 325 |
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33 | this%weight_shape(:,2) = [ this%num_inputs, this%num_basis ] |
| 326 |
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33 | this%weight_shape(:,3) = [ this%num_outputs, this%num_inputs ] |
| 327 | |||
| 328 |
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11 | if(this%use_bias)then |
| 329 |
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18 | this%bias_shape = [ this%num_outputs ] |
| 330 |
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45 | allocate(this%params(4)) |
| 331 | else | ||
| 332 |
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8 | allocate(this%params(3)) |
| 333 | end if | ||
| 334 | |||
| 335 | 11 | num_inputs = this%num_inputs | |
| 336 |
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11 | if(this%use_bias) num_inputs = this%num_inputs + 1 |
| 337 | |||
| 338 | ! R: spectral mixing weights | ||
| 339 |
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44 | call this%params(1)%allocate([this%num_basis, this%num_basis, 1]) |
| 340 |
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11 | call this%params(1)%set_requires_grad(.true.) |
| 341 |
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11 | this%params(1)%fix_pointer = .true. |
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11 | this%params(1)%is_sample_dependent = .false. |
| 343 |
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11 | this%params(1)%is_temporary = .false. |
| 344 | |||
| 345 | ! B: basis weights (stored flat for Gram-Schmidt, but allocated shaped) | ||
| 346 |
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44 | call this%params(2)%allocate([this%num_inputs, this%num_basis, 1]) |
| 347 |
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11 | call this%params(2)%set_requires_grad(.true.) |
| 348 |
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11 | this%params(2)%fix_pointer = .true. |
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11 | this%params(2)%is_sample_dependent = .false. |
| 350 |
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11 | this%params(2)%is_temporary = .false. |
| 351 | |||
| 352 | ! W: bypass/output weights | ||
| 353 |
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44 | call this%params(3)%allocate([this%num_outputs, this%num_inputs, 1]) |
| 354 |
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11 | call this%params(3)%set_requires_grad(.true.) |
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11 | this%params(3)%fix_pointer = .true. |
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11 | this%params(3)%is_sample_dependent = .false. |
| 357 |
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11 | this%params(3)%is_temporary = .false. |
| 358 | |||
| 359 |
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11 | if(this%use_bias)then |
| 360 |
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36 | call this%params(4)%allocate([this%bias_shape, 1]) |
| 361 |
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9 | call this%params(4)%set_requires_grad(.true.) |
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9 | this%params(4)%fix_pointer = .true. |
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9 | this%params(4)%is_sample_dependent = .false. |
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9 | this%params(4)%is_temporary = .false. |
| 365 | end if | ||
| 366 | |||
| 367 | |||
| 368 | !--------------------------------------------------------------------------- | ||
| 369 | ! Initialise learnable parameters | ||
| 370 | !--------------------------------------------------------------------------- | ||
| 371 | call this%kernel_init%initialise( & | ||
| 372 | 110 | this%params(1)%val(:,1), & | |
| 373 | fan_in = this%num_basis, fan_out = this%num_basis, & | ||
| 374 | spacing = [ this%num_basis ] & | ||
| 375 |
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22 | ) |
| 376 | call this%kernel_init%initialise( & | ||
| 377 | 110 | this%params(2)%val(:,1), & | |
| 378 | fan_in = this%num_inputs, fan_out = this%num_basis, & | ||
| 379 | spacing = [ this%num_inputs ] & | ||
| 380 |
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22 | ) |
| 381 | call this%kernel_init%initialise( & | ||
| 382 | 110 | this%params(3)%val(:,1), & | |
| 383 | fan_in = num_inputs, fan_out = this%num_outputs, & | ||
| 384 | spacing = [ this%num_outputs ] & | ||
| 385 |
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22 | ) |
| 386 |
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11 | if(this%use_bias)then |
| 387 | call this%bias_init%initialise( & | ||
| 388 | 90 | this%params(4)%val(:,1), & | |
| 389 | fan_in = num_inputs, fan_out = this%num_outputs & | ||
| 390 |
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9 | ) |
| 391 | end if | ||
| 392 | |||
| 393 | |||
| 394 | !--------------------------------------------------------------------------- | ||
| 395 | ! Allocate output arrays | ||
| 396 | !--------------------------------------------------------------------------- | ||
| 397 |
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11 | if(allocated(this%output)) deallocate(this%output) |
| 398 |
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|
33 | allocate(this%output(1,1)) |
| 399 |
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11 | if(this%z(1)%allocated) call this%z(1)%deallocate() |
| 400 | |||
| 401 | 11 | end subroutine init_ono | |
| 402 | !############################################################################### | ||
| 403 | |||
| 404 | |||
| 405 | !############################################################################### | ||
| 406 | 1 | function get_bases_ono(this) result(phi) | |
| 407 | !! Orthogonalise the basis matrix B using modified Gram-Schmidt | ||
| 408 | implicit none | ||
| 409 | |||
| 410 | ! Arguments | ||
| 411 | class(orthogonal_nop_block_type), intent(in) :: this | ||
| 412 | !! Layer instance providing basis parameters | ||
| 413 | type(array_type) :: phi | ||
| 414 | !! Orthogonalised basis matrix packed in an array_type | ||
| 415 | |||
| 416 | ! Local variables | ||
| 417 | integer :: n, k, i, j | ||
| 418 | !! Basis dimensions and Gram-Schmidt loop indices | ||
| 419 | 1 | real(real32), allocatable :: B(:,:), Q(:,:) | |
| 420 | !! Raw basis matrix and orthogonalised copy | ||
| 421 | real(real32) :: norm_val, proj | ||
| 422 | !! Gram-Schmidt norm and projection scalars | ||
| 423 | |||
| 424 | 1 | n = this%num_inputs | |
| 425 | 1 | k = this%num_basis | |
| 426 | |||
| 427 |
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|
1 | allocate(B(n, k), Q(n, k)) |
| 428 | |||
| 429 | ! Reshape B from flat params(2) into [n, k] | ||
| 430 |
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3 | B = reshape(this%params(2)%val(:,1), [n, k]) |
| 431 | |||
| 432 | ! Modified Gram-Schmidt orthogonalisation | ||
| 433 |
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28 | Q = B |
| 434 |
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4 | do j = 1, k |
| 435 |
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6 | do i = 1, j - 1 |
| 436 |
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|
27 | proj = dot_product(Q(:,i), Q(:,j)) |
| 437 |
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|
30 | Q(:,j) = Q(:,j) - proj * Q(:,i) |
| 438 | end do | ||
| 439 |
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27 | norm_val = sqrt(dot_product(Q(:,j), Q(:,j))) |
| 440 |
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4 | if(norm_val .gt. 1.0e-12_real32)then |
| 441 |
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|
27 | Q(:,j) = Q(:,j) / norm_val |
| 442 | else | ||
| 443 | ✗ | Q(:,j) = 0.0_real32 | |
| 444 | end if | ||
| 445 | end do | ||
| 446 | |||
| 447 | ! Store phi [n x k] | ||
| 448 |
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4 | call phi%allocate([n, k, 1]) |
| 449 | 1 | phi%is_sample_dependent = .false. | |
| 450 | 1 | phi%requires_grad = .false. | |
| 451 | 1 | phi%fix_pointer = .true. | |
| 452 | 1 | phi%is_temporary = .false. | |
| 453 |
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|
26 | phi%val(:,1) = reshape(Q, [n * k]) |
| 454 | |||
| 455 |
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1 | deallocate(B, Q) |
| 456 | |||
| 457 |
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|
2 | end function get_bases_ono |
| 458 | !############################################################################### | ||
| 459 | |||
| 460 | |||
| 461 | !############################################################################### | ||
| 462 | 1 | function get_orthogonality_metric(this) result(metric) | |
| 463 | !! Compute max(|Phi^T @ Phi - I|) as a measure of basis orthogonality | ||
| 464 | implicit none | ||
| 465 | |||
| 466 | ! Arguments | ||
| 467 | class(orthogonal_nop_block_type), intent(in) :: this | ||
| 468 | !! Layer instance providing basis parameters | ||
| 469 | real(real32) :: metric | ||
| 470 | !! Maximum absolute deviation from orthogonality | ||
| 471 | |||
| 472 | ! Local variables | ||
| 473 | integer :: n, k, i, j | ||
| 474 | !! Matrix dimensions and traversal indices | ||
| 475 | 1 | real(real32), allocatable :: basis_matrix(:,:), orthogonal_basis(:,:) | |
| 476 | !! Raw basis weights and orthogonalised basis matrix | ||
| 477 | real(real32) :: norm_val, projection, val | ||
| 478 | !! Gram-Schmidt scalars and current absolute deviation entry | ||
| 479 | |||
| 480 | 1 | n = this%num_inputs | |
| 481 | 1 | k = this%num_basis | |
| 482 | |||
| 483 |
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1 | allocate(basis_matrix(n, k), orthogonal_basis(n, k)) |
| 484 |
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3 | basis_matrix = reshape(this%params(2)%val(:,1), [n, k]) |
| 485 |
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28 | orthogonal_basis = basis_matrix |
| 486 | |||
| 487 |
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4 | do j = 1, k |
| 488 |
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6 | do i = 1, j - 1 |
| 489 |
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27 | projection = dot_product(orthogonal_basis(:,i), orthogonal_basis(:,j)) |
| 490 | ✗ | orthogonal_basis(:,j) = orthogonal_basis(:,j) - & | |
| 491 |
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|
30 | projection * orthogonal_basis(:,i) |
| 492 | end do | ||
| 493 | norm_val = sqrt(dot_product( & | ||
| 494 |
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27 | orthogonal_basis(:,j), orthogonal_basis(:,j))) |
| 495 |
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4 | if(norm_val .gt. 1.0e-12_real32)then |
| 496 |
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|
27 | orthogonal_basis(:,j) = orthogonal_basis(:,j) / norm_val |
| 497 | else | ||
| 498 | ✗ | orthogonal_basis(:,j) = 0.0_real32 | |
| 499 | end if | ||
| 500 | end do | ||
| 501 | |||
| 502 | ! max(|Q^T Q - I|) | ||
| 503 | 1 | metric = 0.0_real32 | |
| 504 |
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4 | do j = 1, k |
| 505 |
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13 | do i = 1, k |
| 506 |
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81 | val = dot_product(orthogonal_basis(:,i), orthogonal_basis(:,j)) |
| 507 |
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9 | if(i .eq. j)then |
| 508 | 3 | val = abs(val - 1.0_real32) | |
| 509 | else | ||
| 510 | 6 | val = abs(val) | |
| 511 | end if | ||
| 512 |
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12 | if(val .gt. metric) metric = val |
| 513 | end do | ||
| 514 | end do | ||
| 515 | |||
| 516 |
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1 | deallocate(basis_matrix, orthogonal_basis) |
| 517 | |||
| 518 |
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1 | end function get_orthogonality_metric |
| 519 | !############################################################################### | ||
| 520 | |||
| 521 | |||
| 522 | !############################################################################### | ||
| 523 | 1 | subroutine print_to_unit_ono(this, unit) | |
| 524 | !! Print orthogonal neural operator settings and parameters to a unit | ||
| 525 | use coreutils, only: to_upper | ||
| 526 | implicit none | ||
| 527 | |||
| 528 | ! Arguments | ||
| 529 | class(orthogonal_nop_block_type), intent(in) :: this | ||
| 530 | !! Layer instance to print | ||
| 531 | integer, intent(in) :: unit | ||
| 532 | !! Output unit number | ||
| 533 | |||
| 534 | 1 | write(unit,'(3X,"NUM_INPUTS = ",I0)') this%num_inputs | |
| 535 | 1 | write(unit,'(3X,"NUM_OUTPUTS = ",I0)') this%num_outputs | |
| 536 | 1 | write(unit,'(3X,"NUM_BASIS = ",I0)') this%num_basis | |
| 537 | 1 | write(unit,'(3X,"USE_BIAS = ",L1)') this%use_bias | |
| 538 |
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1 | if(this%activation%name .ne. 'none')then |
| 539 | 1 | call this%activation%print_to_unit(unit) | |
| 540 | end if | ||
| 541 | |||
| 542 | 1 | write(unit,'("WEIGHTS")') | |
| 543 |
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5 | write(unit,'(5(E16.8E2))') this%params(1)%val(:,1) ! R |
| 544 |
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11 | write(unit,'(5(E16.8E2))') this%params(2)%val(:,1) ! B |
| 545 |
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16 | write(unit,'(5(E16.8E2))') this%params(3)%val(:,1) ! W |
| 546 |
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1 | if(this%use_bias)then |
| 547 |
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4 | write(unit,'(5(E16.8E2))') this%params(4)%val(:,1) ! b |
| 548 | end if | ||
| 549 | 1 | write(unit,'("END WEIGHTS")') | |
| 550 | |||
| 551 | 1 | end subroutine print_to_unit_ono | |
| 552 | !############################################################################### | ||
| 553 | |||
| 554 | |||
| 555 | !############################################################################### | ||
| 556 | 1 | subroutine read_ono(this, unit, verbose) | |
| 557 | use athena__tools_infile, only: assign_val, assign_vec, move | ||
| 558 | use coreutils, only: to_lower, to_upper, icount | ||
| 559 | use athena__activation, only: read_activation | ||
| 560 | use athena__initialiser, only: initialiser_setup | ||
| 561 | implicit none | ||
| 562 | |||
| 563 | ! Arguments | ||
| 564 | class(orthogonal_nop_block_type), intent(inout) :: this | ||
| 565 | !! Layer instance to populate from file data | ||
| 566 | integer, intent(in) :: unit | ||
| 567 | !! Input unit number | ||
| 568 | integer, optional, intent(in) :: verbose | ||
| 569 | !! Verbosity level | ||
| 570 | |||
| 571 | ! Local variables | ||
| 572 | integer :: stat, verbose_ = 0 | ||
| 573 | !! I/O status and effective verbosity level | ||
| 574 | integer :: j, k, c, itmp1, iline | ||
| 575 | !! Loop counters and parser scratch integers | ||
| 576 | integer :: num_inputs, num_outputs, num_basis | ||
| 577 | !! Parsed layer dimensions | ||
| 578 | logical :: use_bias = .true. | ||
| 579 | !! Parsed bias flag | ||
| 580 | character(14) :: kernel_initialiser_name='', bias_initialiser_name='' | ||
| 581 | !! Parsed initialiser names | ||
| 582 | 3 | class(base_actv_type), allocatable :: activation | |
| 583 | !! Parsed activation object | ||
| 584 | 5 | class(base_init_type), allocatable :: kernel_initialiser, bias_initialiser | |
| 585 | !! Parsed initialiser objects | ||
| 586 | character(256) :: buffer, tag, err_msg | ||
| 587 | !! Input buffer, parsed tag and formatted error message | ||
| 588 | 1 | real(real32), allocatable, dimension(:) :: data_list | |
| 589 | !! Temporary storage for flattened parameter blocks | ||
| 590 | integer :: param_line, final_line, num_vals | ||
| 591 | !! Weights-section line markers and current block size | ||
| 592 | |||
| 593 |
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1 | if(present(verbose)) verbose_ = verbose |
| 594 | |||
| 595 | 1 | iline = 0 | |
| 596 | 1 | param_line = 0 | |
| 597 | 1 | final_line = 0 | |
| 598 | 14 | tag_loop: do | |
| 599 | 15 | read(unit,'(A)',iostat=stat) buffer | |
| 600 |
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15 | if(stat.ne.0)then |
| 601 | write(err_msg,'("file encountered error (EoF?) before END ",A)') & | ||
| 602 | ✗ | to_upper(this%name) | |
| 603 | ✗ | call stop_program(err_msg) | |
| 604 | ✗ | return | |
| 605 | end if | ||
| 606 |
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15 | if(trim(adjustl(buffer)).eq."") cycle tag_loop |
| 607 | |||
| 608 |
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30 | if(trim(adjustl(buffer)).eq."END "//to_upper(trim(this%name)))then |
| 609 | 1 | final_line = iline | |
| 610 | 1 | backspace(unit) | |
| 611 | 15 | exit tag_loop | |
| 612 | end if | ||
| 613 | 14 | iline = iline + 1 | |
| 614 | |||
| 615 |
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14 | tag=trim(adjustl(buffer)) |
| 616 |
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14 | if(scan(buffer,"=").ne.0) tag=trim(tag(:scan(tag,"=")-1)) |
| 617 | |||
| 618 | 28 | select case(trim(tag)) | |
| 619 | case("NUM_INPUTS") | ||
| 620 | 2 | call assign_val(buffer, num_inputs, itmp1) | |
| 621 | case("NUM_OUTPUTS") | ||
| 622 | 2 | call assign_val(buffer, num_outputs, itmp1) | |
| 623 | case("NUM_BASIS") | ||
| 624 | 2 | call assign_val(buffer, num_basis, itmp1) | |
| 625 | case("USE_BIAS") | ||
| 626 | 2 | call assign_val(buffer, use_bias, itmp1) | |
| 627 | case("ACTIVATION") | ||
| 628 | 1 | iline = iline - 1 | |
| 629 | 1 | backspace(unit) | |
| 630 |
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1 | activation = read_activation(unit, iline) |
| 631 | case("KERNEL_INITIALISER", "KERNEL_INIT", "KERNEL_INITIALIZER") | ||
| 632 | ✗ | call assign_val(buffer, kernel_initialiser_name, itmp1) | |
| 633 | case("BIAS_INITIALISER", "BIAS_INIT", "BIAS_INITIALIZER") | ||
| 634 | ✗ | call assign_val(buffer, bias_initialiser_name, itmp1) | |
| 635 | case("WEIGHTS") | ||
| 636 | 1 | kernel_initialiser_name = 'zeros' | |
| 637 | 1 | bias_initialiser_name = 'zeros' | |
| 638 | 1 | param_line = iline | |
| 639 | case default | ||
| 640 |
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16 | if(scan(to_lower(trim(adjustl(buffer))),& |
| 641 | 'abcdfghijklmnopqrstuvwxyz').eq.0)then | ||
| 642 | 8 | cycle tag_loop | |
| 643 |
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1 | elseif(tag(:3).eq.'END')then |
| 644 | 8 | cycle tag_loop | |
| 645 | end if | ||
| 646 | write(err_msg,'("Unrecognised line in input file: ",A)') & | ||
| 647 | ✗ | trim(adjustl(buffer)) | |
| 648 | ✗ | call stop_program(err_msg) | |
| 649 |
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28 | return |
| 650 | end select | ||
| 651 | end do tag_loop | ||
| 652 |
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1 | kernel_initialiser = initialiser_setup(kernel_initialiser_name) |
| 653 |
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1 | bias_initialiser = initialiser_setup(bias_initialiser_name) |
| 654 | |||
| 655 | call this%set_hyperparams( & | ||
| 656 | num_outputs = num_outputs, & | ||
| 657 | num_basis = num_basis, & | ||
| 658 | use_bias = use_bias, & | ||
| 659 | activation = activation, & | ||
| 660 | kernel_initialiser = kernel_initialiser, & | ||
| 661 | bias_initialiser = bias_initialiser, & | ||
| 662 | verbose = verbose_ & | ||
| 663 | 1 | ) | |
| 664 |
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2 | call this%init(input_shape=[num_inputs]) |
| 665 | |||
| 666 |
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1 | if(param_line.eq.0)then |
| 667 | ✗ | write(0,*) "WARNING: WEIGHTS card in " // trim(this%name) // " not found" | |
| 668 | else | ||
| 669 | 1 | call move(unit, param_line - iline, iostat=stat) | |
| 670 | |||
| 671 | ! Read R (num_basis^2) | ||
| 672 | 1 | num_vals = num_basis * num_basis | |
| 673 |
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1 | allocate(data_list(num_vals), source=0._real32) |
| 674 | 1 | c = 1; k = 1 | |
| 675 |
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2 | do while(c.le.num_vals) |
| 676 | 1 | read(unit,'(A)',iostat=stat) buffer | |
| 677 |
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1 | if(stat.ne.0) exit |
| 678 | 1 | k = icount(buffer) | |
| 679 |
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5 | read(buffer,*,iostat=stat) (data_list(j),j=c,c+k-1) |
| 680 | 1 | c = c + k | |
| 681 | end do | ||
| 682 |
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5 | this%params(1)%val(:,1) = data_list |
| 683 |
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1 | deallocate(data_list) |
| 684 | |||
| 685 | ! Read B (num_inputs * num_basis) | ||
| 686 | 1 | num_vals = num_inputs * num_basis | |
| 687 |
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1 | allocate(data_list(num_vals), source=0._real32) |
| 688 | 1 | c = 1; k = 1 | |
| 689 |
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3 | do while(c.le.num_vals) |
| 690 | 2 | read(unit,'(A)',iostat=stat) buffer | |
| 691 |
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2 | if(stat.ne.0) exit |
| 692 | 2 | k = icount(buffer) | |
| 693 |
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12 | read(buffer,*,iostat=stat) (data_list(j),j=c,c+k-1) |
| 694 | 2 | c = c + k | |
| 695 | end do | ||
| 696 |
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11 | this%params(2)%val(:,1) = data_list |
| 697 |
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1 | deallocate(data_list) |
| 698 | |||
| 699 | ! Read W (num_outputs * num_inputs) | ||
| 700 | 1 | num_vals = num_outputs * num_inputs | |
| 701 |
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1 | allocate(data_list(num_vals), source=0._real32) |
| 702 | 1 | c = 1; k = 1 | |
| 703 |
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4 | do while(c.le.num_vals) |
| 704 | 3 | read(unit,'(A)',iostat=stat) buffer | |
| 705 |
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3 | if(stat.ne.0) exit |
| 706 | 3 | k = icount(buffer) | |
| 707 |
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18 | read(buffer,*,iostat=stat) (data_list(j),j=c,c+k-1) |
| 708 | 3 | c = c + k | |
| 709 | end do | ||
| 710 |
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16 | this%params(3)%val(:,1) = data_list |
| 711 |
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1 | deallocate(data_list) |
| 712 | |||
| 713 | ! Read b if use_bias | ||
| 714 |
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1 | if(use_bias)then |
| 715 |
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1 | allocate(data_list(num_outputs), source=0._real32) |
| 716 | 1 | c = 1; k = 1 | |
| 717 |
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2 | do while(c.le.num_outputs) |
| 718 | 1 | read(unit,'(A)',iostat=stat) buffer | |
| 719 |
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1 | if(stat.ne.0) exit |
| 720 | 1 | k = icount(buffer) | |
| 721 |
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4 | read(buffer,*,iostat=stat) (data_list(j),j=c,c+k-1) |
| 722 | 1 | c = c + k | |
| 723 | end do | ||
| 724 |
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4 | this%params(4)%val(:,1) = data_list(1:num_outputs) |
| 725 |
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1 | deallocate(data_list) |
| 726 | end if | ||
| 727 | |||
| 728 | 1 | read(unit,'(A)') buffer | |
| 729 |
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1 | if(trim(adjustl(buffer)).ne."END WEIGHTS")then |
| 730 | ✗ | call stop_program("END WEIGHTS not where expected") | |
| 731 | ✗ | return | |
| 732 | end if | ||
| 733 | end if | ||
| 734 | |||
| 735 | 1 | call move(unit, final_line - iline, iostat=stat) | |
| 736 | 1 | read(unit,'(A)') buffer | |
| 737 |
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2 | if(trim(adjustl(buffer)).ne."END "//to_upper(trim(this%name)))then |
| 738 | ✗ | write(err_msg,'("END ",A," not where expected")') to_upper(this%name) | |
| 739 | ✗ | call stop_program(err_msg) | |
| 740 | 1 | return | |
| 741 | end if | ||
| 742 | |||
| 743 |
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1 | end subroutine read_ono |
| 744 | !############################################################################### | ||
| 745 | |||
| 746 | |||
| 747 | !############################################################################### | ||
| 748 | 1 | function read_orthogonal_nop_block(unit, verbose) result(layer) | |
| 749 | !! Read an orthogonal neural operator block from file and return it | ||
| 750 | implicit none | ||
| 751 | |||
| 752 | ! Arguments | ||
| 753 | integer, intent(in) :: unit | ||
| 754 | !! Input unit number | ||
| 755 | integer, optional, intent(in) :: verbose | ||
| 756 | !! Verbosity level | ||
| 757 | class(base_layer_type), allocatable :: layer | ||
| 758 | !! Allocated base-layer instance containing the result | ||
| 759 | |||
| 760 | ! Local variables | ||
| 761 | integer :: verbose_ = 0 | ||
| 762 | !! Effective verbosity level | ||
| 763 | |||
| 764 |
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1 | if(present(verbose)) verbose_ = verbose |
| 765 | ✗ | allocate(layer, source=orthogonal_nop_block_type( & | |
| 766 |
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|
2 | num_outputs=0, num_basis=1)) |
| 767 | 1 | call layer%read(unit, verbose=verbose_) | |
| 768 | |||
| 769 | 2 | end function read_orthogonal_nop_block | |
| 770 | !############################################################################### | ||
| 771 | |||
| 772 | |||
| 773 | !############################################################################### | ||
| 774 |
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5 | subroutine forward_ono(this, input) |
| 775 | !! Forward propagation for the Orthogonal Neural Operator layer | ||
| 776 | !! | ||
| 777 | !! Computes: | ||
| 778 | !! encoded = Phi^T @ u [k, batch] | ||
| 779 | !! mixed = R @ encoded [k, batch] | ||
| 780 | !! decoded = Phi @ mixed [n_in, batch] | ||
| 781 | !! spectral= W @ decoded [n_out, batch] (reuse W for output proj) | ||
| 782 | !! | ||
| 783 | !! bypass = W @ u [n_out, batch] | ||
| 784 | !! | ||
| 785 | !! v = sigma( spectral + bypass + b ) | ||
| 786 | !! | ||
| 787 | !! Actually, we separate the spectral and bypass paths clearly: | ||
| 788 | !! spectral path uses the orthogonal basis + R mixing | ||
| 789 | !! bypass path uses W directly on input | ||
| 790 | !! Both project to [n_out] via W (shared) or separate matrices. | ||
| 791 | !! | ||
| 792 | !! Here we implement: | ||
| 793 | !! spectral = W @ Phi @ R @ Phi^T @ u | ||
| 794 | !! bypass = W @ u | ||
| 795 | !! v = sigma( spectral + bypass + b ) | ||
| 796 | !! | ||
| 797 | !! Note: W is params(3) [n_out x n_in], shared for both paths | ||
| 798 | !! This means: v = sigma( W @ (Phi @ R @ Phi^T @ u + u) + b ) | ||
| 799 | !! = sigma( W @ ((Phi @ R @ Phi^T + I) @ u) + b ) | ||
| 800 | implicit none | ||
| 801 | |||
| 802 | ! Arguments | ||
| 803 | class(orthogonal_nop_block_type), intent(inout) :: this | ||
| 804 | !! Layer instance to execute | ||
| 805 | class(array_type), dimension(:,:), intent(in) :: input | ||
| 806 | !! Input batch tensor collection | ||
| 807 | |||
| 808 | ! Local variables | ||
| 809 | type(array_type), pointer :: ptr, ptr_spec, ptr_bypass | ||
| 810 | !! Combined output, spectral-path output and bypass-path output | ||
| 811 | type(array_type), pointer :: ptr_encoded, ptr_mixed, ptr_decoded | ||
| 812 | !! Encoded spectrum, mixed spectrum and decoded tensor | ||
| 813 | |||
| 814 | |||
| 815 | ! Spectral pathway: Phi @ R @ Phi^T @ u | ||
| 816 | ! Uses autodiff-tracked ono_encode/ono_decode for basis gradients | ||
| 817 | !--------------------------------------------------------------------------- | ||
| 818 | |||
| 819 | ! Encode: Q(B)^T @ u -> [k, batch] | ||
| 820 | ✗ | ptr_encoded => ono_encode(input(1,1), this%params(2), & | |
| 821 |
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5 | this%num_inputs, this%num_basis) |
| 822 | |||
| 823 | ! Mix: R @ encoded -> [k, batch] | ||
| 824 |
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5 | ptr_mixed => matmul(this%params(1), ptr_encoded) |
| 825 | |||
| 826 | ! Decode: Q(B) @ mixed -> [n_in, batch] | ||
| 827 | 10 | ptr_decoded => ono_decode(ptr_mixed, this%params(2), & | |
| 828 |
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5 | this%num_inputs, this%num_basis) |
| 829 | |||
| 830 | ! Spectral projection: W @ decoded -> [n_out, batch] | ||
| 831 |
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5 | ptr_spec => matmul(this%params(3), ptr_decoded) |
| 832 | |||
| 833 | ! Bypass: W @ u -> [n_out, batch] | ||
| 834 |
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5 | ptr_bypass => matmul(this%params(3), input(1,1)) |
| 835 | |||
| 836 | ! Combine | ||
| 837 | 5 | ptr => ptr_spec + ptr_bypass | |
| 838 | |||
| 839 | ! Add bias | ||
| 840 |
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5 | if(this%use_bias)then |
| 841 |
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5 | ptr => ptr + this%params(4) |
| 842 | end if | ||
| 843 | |||
| 844 | ! Apply activation | ||
| 845 |
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5 | call this%output(1,1)%zero_grad() |
| 846 |
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5 | if(trim(this%activation%name) .eq. "none")then |
| 847 |
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2 | call this%output(1,1)%assign_and_deallocate_source(ptr) |
| 848 | else | ||
| 849 | 3 | call this%z(1)%zero_grad() | |
| 850 | 3 | call this%z(1)%assign_and_deallocate_source(ptr) | |
| 851 | 3 | this%z(1)%is_temporary = .false. | |
| 852 | 3 | ptr => this%activation%apply(this%z(1)) | |
| 853 |
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3 | call this%output(1,1)%assign_and_deallocate_source(ptr) |
| 854 | end if | ||
| 855 |
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5 | this%output(1,1)%is_temporary = .false. |
| 856 | |||
| 857 | 5 | end subroutine forward_ono | |
| 858 | !############################################################################### | ||
| 859 | |||
| 860 | |||
| 861 | !############################################################################### | ||
| 862 | 2 | function get_attributes_ono(this) result(attributes) | |
| 863 | !! Return list of ONO attributes for ONNX export | ||
| 864 | implicit none | ||
| 865 | |||
| 866 | ! Arguments | ||
| 867 | class(orthogonal_nop_block_type), intent(in) :: this | ||
| 868 | !! Instance of the ONO block | ||
| 869 | type(onnx_attribute_type), allocatable, dimension(:) :: attributes | ||
| 870 | !! List of attributes for ONNX export | ||
| 871 | |||
| 872 | ! Local variables | ||
| 873 | character(32) :: buffer | ||
| 874 | !! Buffer for formatting | ||
| 875 | |||
| 876 |
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12 | allocate(attributes(5)) |
| 877 | |||
| 878 | 2 | write(buffer, '(I0)') this%num_inputs | |
| 879 | ✗ | attributes(1) = onnx_attribute_type( & | |
| 880 |
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2 | name='num_inputs', type='int', val=trim(buffer)) |
| 881 | 2 | write(buffer, '(I0)') this%num_outputs | |
| 882 | ✗ | attributes(2) = onnx_attribute_type( & | |
| 883 |
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2 | name='num_outputs', type='int', val=trim(buffer)) |
| 884 | 2 | write(buffer, '(I0)') this%num_basis | |
| 885 | ✗ | attributes(3) = onnx_attribute_type( & | |
| 886 |
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2 | name='num_basis', type='int', val=trim(buffer)) |
| 887 |
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2 | if(this%use_bias)then |
| 888 | 2 | buffer = '1' | |
| 889 | else | ||
| 890 | ✗ | buffer = '0' | |
| 891 | end if | ||
| 892 | ✗ | attributes(4) = onnx_attribute_type( & | |
| 893 |
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2 | name='use_bias', type='int', val=trim(buffer)) |
| 894 | ✗ | attributes(5) = onnx_attribute_type( & | |
| 895 |
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2 | name='activation', type='string', val=trim(this%activation%name)) |
| 896 | |||
| 897 | 2 | end function get_attributes_ono | |
| 898 | !############################################################################### | ||
| 899 | |||
| 900 |
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338 | end module athena__orthogonal_nop_block |
| 901 |