matlab - 为什么MatConvNet说数据和导数没有匹配的格式？

Question

问题陈述

我使用 MatConvNet 使用示例库附带的函数 cnn_train 构建一个非常简单的一维示例和小型网络。按照他们的示例，我构建了一个小型 CNN 示例，如下所示:

    clc;clear;clc;clear;
%% prepare Data
M = 32; %batch size
X_train = zeros(1,1,1,M); % (1 1 1 2) = (1 1 1 M)
for m=1:M,
    X_train(:,:,:,m) = m; %training example value
end
Y_test = 10*X_train;
split = ones(1,M);
split(floor(M*0.75):end) = 2;
% load image dadabase (imgdb)
imdb.images.data = X_train;
imdb.images.label = Y_test;
imdb.images.set = split;
%% prepare parameters
L1=3;
w1 = randn(1,1,1,L1); %1st layer weights
w2 = randn(1,1,1,L1); %2nd layer weights
b1 = randn(1,1,1,L1); %1st layer biases
b2 = randn(1,1,1,L1); %2nd layer biases
G1 = ones(1,1,1,L1); % (1 1 1 3) = (1 1 1 L1) BN scale, one per  dimension
B1 = zeros(1,1,1,L1); % (1 1 1 3) = (1 1 1 L1) BN shift, one per  dimension
EPS = 1e-4;
%% make CNN layers: conv, BN, relu, conv, pdist, l2-loss
net.layers = {} ;
net.layers{end+1} = struct('type', 'conv', ...
                           'name', 'conv1', ...
                           'weights', {{w1, b1}}, ...
                           'pad', 0) ;
net.layers{end+1} = struct('type', 'bnorm', ...
                           'weights', {{G1, B1}}, ...
                           'EPSILON', EPS, ...
                           'learningRate', [1 1 0.05], ...
                           'weightDecay', [0 0]) ;                       
net.layers{end+1} = struct('type', 'relu', ...
                           'name', 'relu1' ) ;
net.layers{end+1} = struct('type', 'conv', ...
                           'name', 'conv2', ...
                           'weights', {{w2, b2}}, ...
                           'pad', 0) ;
net.layers{end+1} = struct('type', 'pdist', ...
                           'name', 'averageing1', ...
                           'class', 0, ...
                           'p', 1) ;
%% add L2-loss                   
fwfun = @l2LossForward;
bwfun = @l2LossBackward;
net = addCustomLossLayer(net, fwfun, bwfun) ;
net.layers{end}.class = Y_test; % its the test set
net = vl_simplenn_tidy(net) ;
res = vl_simplenn(net, X_train);
%% prepare train options
trainOpts.expDir = 'results/' ; %save results/trained cnn
trainOpts.gpus = [] ;
trainOpts.batchSize = 2 ;
trainOpts.learningRate = 0.02 ;
trainOpts.plotDiagnostics = false ;
%trainOpts.plotDiagnostics = true ; % Uncomment to plot diagnostics
trainOpts.numEpochs = 20 ; % number of training epochs
trainOpts.errorFunction = 'none' ;
%% CNN TRAIN
vl_simplenn_display(net) ;
net = cnn_train(net, imdb, @getBatch, trainOpts) ;

我根据 the example they provided 创建了这个，每当我运行该示例时，我都会收到错误:

Error using vl_nnconv
DATA and DEROUTPUT do not have compatible formats.

Error in vl_simplenn (line 397)
          [res(i).dzdx, dzdw{1}, dzdw{2}] = vl_nnconv(res(i).x, l.weights{1},
          l.weights{2}, res(i+1).dzdx)

Error in cnn_train>process_epoch (line 323)
    res = vl_simplenn(net, im, dzdy, res, ...

Error in cnn_train (line 139)
    [net,stats.train,prof] = process_epoch(opts, getBatch, epoch, train, learningRate,
    imdb, net) ;

Error in main_1D_1layer_hard_coded_example (line 64)
net = cnn_train(net, imdb, @getBatch, trainOpts) ;

有人知道发生了什么事吗？这个例子实际上应该很简单，所以它让我困惑什么可能是错误的。

<小时/>

我尝试解决此问题的补充部分。

有关我尝试解决此问题的更多详细信息，请提前阅读。

我转到文件中导致错误的那一行，并将输入打印到该函数，以确保我给出的参数有意义，并且在这方面似乎一切都很好:

  case 'conv'
      size(res(i).x)
      size(res(i+1).dzdx)
      size(l.weights{1})
      size(l.weights{2})
      [res(i).dzdx, dzdw{1}, dzdw{2}] = vl_nnconv(res(i).x, l.weights{1}, l.weights{2}, res(i+1).dzdx)
    [res(i).dzdx, dzdw{1}, dzdw{2}] = ...
      vl_nnconv(res(i).x, l.weights{1}, l.weights{2}, res(i+1).dzdx, ...
      'pad', l.pad, ...
      'stride', l.stride, ...
      l.opts{:}, ...
      cudnn{:}) ;

打印:

ans =

     1     1     3    16


ans =

     1     1     3    16


ans =

     1     1     1     3


ans =

     1     1     1     3

我所期望的。

我什至手动硬编码了网络应该计算的衍生品链，并且该文件似乎工作正常:

clc;clear;clc;clear;
%% prepare Data
M = 3;
x = zeros(1,1,1,M); % (1 1 1 2) = (1 1 1 M)
for m=1:M,
    x(:,:,:,m) = m;
end
Y = 5;
r=Y;
%% parameters
L1 = 3;
w1 = randn(1,1,1,L1); % (1 1 1 L1) = (1 1 1 3)
b1 = ones(1,L1);
w2 = randn(1,1,1,L1); % (1 1 1 L1) = (1 1 1 3)
b2 = ones(1,L1);
G1 = ones(1,1,1,L1); % (1 1 1 3) = (1 1 1 L1) BN scale, one per  dimension
B1 = zeros(1,1,1,L1); % (1 1 1 3) = (1 1 1 L1) BN shift, one per  dimension
EPS = 1e-4;
%% Forward Pass
z1 = vl_nnconv(x,w1,b1); % (1 1 3 2) = (1 1 L1 M)
%bn1 = z1;
bn1 = vl_nnbnorm(z1,G1,B1,'EPSILON',EPS); % (1 1 3 2) = (1 1 L1 M)
a1 = vl_nnrelu(bn1); % (1 1 3 2) = (1 1 L1 M) 
z2 = vl_nnconv(a1,w2,b2);
y1 = vl_nnpdist(z2, 0, 1);
loss_forward = l2LossForward(y1,Y);
%%
net.layers = {} ;
net.layers{end+1} = struct('type', 'conv', ...
                           'name', 'conv1', ...
                           'weights', {{w1, b1}}, ...
                           'pad', 0) ;
net.layers{end+1} = struct('type', 'bnorm', ...
                           'weights', {{G1, B1}}, ...
                           'EPSILON', EPS, ...
                           'learningRate', [1 1 0.05], ...
                           'weightDecay', [0 0]) ;                       
net.layers{end+1} = struct('type', 'relu', ...
                           'name', 'relu1' ) ;
net.layers{end+1} = struct('type', 'conv', ...
                           'name', 'conv2', ...
                           'weights', {{w2, b2}}, ...
                           'pad', 0) ;
net.layers{end+1} = struct('type', 'pdist', ...
                           'name', 'averageing1', ...
                           'class', 0, ...
                           'p', 1) ;
fwfun = @l2LossForward;
bwfun = @l2LossBackward;
net = addCustomLossLayer(net, fwfun, bwfun) ;
net.layers{end}.class = Y;
net = vl_simplenn_tidy(net) ;
res = vl_simplenn(net, x);
%%
loss_forward = squeeze( loss_forward ) % (1 1)
loss_res = squeeze( res(end).x ) % (1 1)
%% Backward Pass
p = 1;
dldx = l2LossBackward(y1,r,p);
dy1dx = vl_nnpdist(z2, 0, 1, dldx);
[dz2dx, dz2dw2] = vl_nnconv(a1, w2, b2, dy1dx);
da1dx = vl_nnrelu(bn1, dz2dx);
[dbn1dx,dbn1dG1,dbn1dB1] = vl_nnbnorm(z1,G1,B1,da1dx);
[dz1dx, dz1dw1] = vl_nnconv(x, w1, b1, dbn1dx);
%%
dzdy = 1;
res = vl_simplenn(net, x, dzdy, res);
%%
% func = @(x) proj(p, forward(x, x0)) ;
% err = checkDerivativeNumerically(f, x, dx)
% %%
dz1dx = squeeze(dz1dx)
dz1dx_vl_simplenn = squeeze(res(1).dzdx)

导数似乎是数学式的，所以我假设该文件中的所有内容都有效。它不会抛出错误，所以它甚至没有运行这一事实让我非常困惑。有人知道这是怎么回事吗？

<小时/>

我加载 CNN 的方式基于 the example file他们提供了该教程。我将粘贴该文件的重要方面的摘要(可以与 cnn_train 函数一起正常运行，而我的则不能)。

setup() ;
% setup('useGpu', true); % Uncomment to initialise with a GPU support
%% Part 3.1: Prepare the data
% Load a database of blurred images to train from
imdb = load('data/text_imdb.mat') ;

%% Part 3.2: Create a network architecture

net = initializeSmallCNN() ;
%net = initializeLargeCNN() ;
% Display network
vl_simplenn_display(net) ;

%% Part 3.3: learn the model
% Add a loss (using a custom layer)
net = addCustomLossLayer(net, @l2LossForward, @l2LossBackward) ;

% Train
trainOpts.expDir = 'data/text-small' ;
trainOpts.gpus = [] ;
% Uncomment for GPU training:
%trainOpts.expDir = 'data/text-small-gpu' ;
%trainOpts.gpus = [1] ;
trainOpts.batchSize = 16 ;
trainOpts.learningRate = 0.02 ;
trainOpts.plotDiagnostics = false ;
%trainOpts.plotDiagnostics = true ; % Uncomment to plot diagnostics
trainOpts.numEpochs = 20 ;
trainOpts.errorFunction = 'none' ;

net = cnn_train(net, imdb, @getBatch, trainOpts) ;

Answer 1

w2 的尺寸应为 1x1x3x3。

通常偏差会被指定为 1x3，因为它们只有一个维度(或者权重为 1x1x3xN，相应偏差为 1xN，其中 N 是滤波器的数量)，B1 和 G1 也是如此(这里是1xM，其中M是前一层的滤波器数量)。但无论哪种方式都可能有效。

在您的示例中，第一次卷积后 x 的尺寸为 1x1x3x16。这意味着一个批处理中有 16 个元素，其中每个元素的宽度和高度为 1，深度为 3。深度为 3，因为第一个卷积是使用 3 个滤波器完成的(w1 的尺寸为 1x1x1x3)。

示例中的 w2 的尺寸为 1x1x1x3，表示 3 个宽度、高度和深度为 1 的过滤器。因此过滤器的深度与输入的深度不匹配。