基于自动微分的全连接神经网络 - DNN

Posted on Edited on In , Views: Word count in article: 202 Reading time ≈ 1 mins.

是拿来实现 XOR 的拟合的，有时候可能是参数初始化的问题，导致无法收敛 （我感觉我梯度计算没问题）

原理

大致上是将网络映射到一张计算图上，基于计算图的自动微分，由拓扑排序确定求导和计算顺序。

实现

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#include <bits/stdc++.h>
using namespace std;
using ld = long double;
using ll = long long;

class Function {
 public:
  virtual ld exec(vector<ld> &inputs) = 0;
  virtual vector<ld> grad(vector<ld> &inputs) = 0;
  virtual ~Function() = default;
  virtual void bp(ld grad) {};
  virtual void initializeWeights(size_t outputLength) = 0;
};

class ComputeNode {
 public:
  size_t inputLength = 0;
  ld value = 0;
  vector<ld> pfpx;
  vector<ComputeNode *> nextNodes;
  vector<ComputeNode *> operands;
  Function *fp = nullptr;
  size_t id = 999;
  ld grad = 0;
  ComputeNode(size_t _inputLength, Function *_fp, size_t _id)
      : inputLength(_inputLength), fp(_fp), id(_id) {}
  ComputeNode(ld val, size_t _id) : value(val), id(_id) {};
  virtual ~ComputeNode() {
    if (fp != nullptr) delete fp;
  };
  virtual ld compute();
};

ld ComputeNode::compute() {
  if (inputLength == 0) return value;
  vector<ld> inputs;
  for (size_t i = 0; i < inputLength; i++) {
    inputs.push_back(operands[i]->value);
  }
  value = fp->exec(inputs);
  pfpx = fp->grad(inputs);
  return value;
}

class ComputationalGraph {
 public:
  vector<ComputeNode *> Nodes;
  vector<ComputeNode *> outNodes;
  vector<ComputeNode *> inNodes;
  vector<ComputeNode *> topo_forward;
  vector<ComputeNode *> topo_backward;
  ComputationalGraph() = default;
  ComputeNode *addNode(size_t inputLength, Function *fp);
  ComputeNode *addNode(ld value);
  void bindNode(vector<ComputeNode *> ops, ComputeNode *ComputeNodePtr);
  vector<ld> compute();
  vector<ld> grad();
  vector<ld> grad(vector<ld> &outputGrad);
  void clearGrad() {
    for (auto nd : Nodes) nd->grad = 0;
  }
  virtual ~ComputationalGraph() {
    for (auto &it : Nodes) delete it;
  }
};

ComputeNode *ComputationalGraph::addNode(size_t inputLength, Function *fp) {
  ComputeNode *nd = new ComputeNode(inputLength, fp, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

ComputeNode *ComputationalGraph::addNode(ld value) {
  ComputeNode *nd = new ComputeNode(value, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

void ComputationalGraph::bindNode(vector<ComputeNode *> ops,
                                  ComputeNode *ComputeNodePtr) {
  for (auto nd : ops) {
    ComputeNodePtr->operands.push_back(nd);
    nd->nextNodes.push_back(ComputeNodePtr);
  }
}

vector<ld> ComputationalGraph::compute() {
  if (!topo_forward.size()) {
    map<ComputeNode *, ll> indegree;
    bool flag = false;
    for (auto nd : Nodes) {
      for (auto nnd : nd->nextNodes) {
        indegree[nnd]++;
      }
    }
    if (outNodes.size() != 0) flag = true;
    queue<ComputeNode *> q;
    if (inNodes.size() == 0) {
      for (auto nd : Nodes)
        if (indegree[nd] == 0) inNodes.push_back(nd);
      sort(inNodes.begin(), inNodes.end(),
           [&](auto a, auto b) { return a->id < b->id; });
    }
    for (auto nd : inNodes) q.push(nd);
    while (!q.empty()) {
      auto nd = q.front();
      q.pop();
      topo_forward.push_back(nd);
      for (auto nnd : nd->nextNodes) {
        --indegree[nnd];
        if (indegree[nnd] == 0) q.push(nnd);
      }
      if (nd->nextNodes.size() == 0 && !flag) {
        outNodes.push_back(nd);
      }
    }
    if (!flag) {
      sort(outNodes.begin(), outNodes.end(),
           [&](auto a, auto b) { return a->id < b->id; });
    }
    topo_backward = topo_forward;
    reverse(topo_backward.begin(), topo_backward.end());
  }
  for (auto nd : topo_forward) {
    nd->compute();
  }
  vector<ld> res;
  for (auto nd : outNodes) {
    res.push_back(nd->value);
  }
  return res;
}

vector<ld> ComputationalGraph::grad(vector<ld> &outputGrad) {
  clearGrad();
  for (size_t i = 0; i < outNodes.size(); i++)
    outNodes[i]->grad = outputGrad[i];
  for (auto nd : topo_backward)
    for (size_t i = 0; i < nd->inputLength; i++)
      nd->operands[i]->grad += nd->grad * nd->pfpx[i];
  vector<ld> res;
  for (auto nd : inNodes) {
    res.push_back(nd->grad);
  }
  return res;
}

vector<ld> ComputationalGraph::grad() {
  clearGrad();
  for (auto nd : outNodes) nd->grad = 1;
  for (auto nd : topo_backward)
    for (size_t i = 0; i < nd->inputLength; i++)
      nd->operands[i]->grad += nd->grad * nd->pfpx[i];
  vector<ld> res;
  for (auto nd : inNodes) {
    res.push_back(nd->grad);
  }
  return res;
}

class Liner : public Function {
 public:
  vector<ld> W;
  vector<ld> _inputs;
  Liner(size_t inputLength) {
    for (size_t i = 0; i <= inputLength; i++) {
      W.push_back(ld(rand()) / RAND_MAX);
    }
  }
  void initializeWeights(size_t outputLength) {
    for (auto &it : W) {
      double limit = std::sqrt(6.0 / (W.size() + outputLength));
      it = (ld(rand()) / RAND_MAX) * 2 * limit - limit;
    }
    W[W.size() - 1] = 0.0;
  }
  ld exec(vector<ld> &inputs) {
    _inputs = inputs;
    _inputs.push_back(1);  // for bias, extra input unit 1
    ld res = 0;
    for (size_t i = 0; i < W.size(); i++) {
      res += _inputs[i] * W[i];
    }
    return res;
  }
  vector<ld> grad(vector<ld> &inputs) {
    vector<ld> d;
    for (size_t i = 0; i < inputs.size(); i++) {
      d.push_back(W[i]);
    }
    return d;
  }
  void bp(ld grad) {
    for (size_t i = 0; i < W.size(); i++) {
      W[i] -= grad * _inputs[i];
    }
  }
};

class Activation : Function {
 public:
  ld input;
  Activation() = default;
  void bp(ld grad) {}
  void initializeWeights(size_t outputLength) {}
  virtual Activation *newInstance() = 0;
};

class Sigmoid : public Activation {
 public:
  Sigmoid() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return 1.0 / (1 + exp(-input));
  }
  vector<ld> grad(vector<ld> &inputs) {
    return {exec(inputs) * (1 - exec(inputs))};
  }
  Sigmoid *newInstance() { return new Sigmoid(); }
};

class Neuron : public ComputeNode {
 public:
  Neuron(size_t inputLength, size_t id)
      : ComputeNode(inputLength, new Liner(inputLength), id) {};
  Neuron(size_t inputLength, Function *fp, size_t id)
      : ComputeNode(inputLength, fp, id) {};
  Neuron(size_t id) : ComputeNode(0, id) {}
  void input(ld v) {  // for input node only
    value = v;
  }
  void bp(ld lr);
};

void Neuron::bp(ld lr) {
  if (fp != nullptr) fp->bp(grad * lr);
}

class DNN : public ComputationalGraph {
 public:
  DNN() = default;
  vector<vector<Neuron *>> Layers;
  void addLayer(size_t outputLength);
  Neuron *addNeuron(size_t inputLength);
  Neuron *addNeuron();
  Neuron *addNeuron(Activation *fp);
  void bp(ld lr, vector<ld> &labels);
  vector<ld> eval(vector<ld> &inputs);
  void training(ld lr, size_t epoch, vector<vector<ld>> &inputs,
                vector<vector<ld>> &labels);
  void addLayer(Activation *fp);  // activation layer
};

Neuron *DNN::addNeuron() {
  Neuron *nd = new Neuron(Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

Neuron *DNN::addNeuron(Activation *fp) {
  Neuron *nd = new Neuron(1, (Function *)fp, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

Neuron *DNN::addNeuron(size_t inputLength) {
  Neuron *nd = new Neuron(inputLength, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

void DNN::addLayer(size_t outputLength) {
  size_t inputLength = Layers.size() > 0 ? Layers[Layers.size() - 1].size() : 0;
  vector<Neuron *> Layer;
  vector<ComputeNode *> lastLayer;
  if (inputLength)
    lastLayer = vector<ComputeNode *>(Layers[Layers.size() - 1].begin(),
                                      Layers[Layers.size() - 1].end());
  for (size_t i = 0; i < outputLength; i++) {
    Neuron *nd = inputLength != 0 ? addNeuron(inputLength) : addNeuron();
    if (nd->fp != nullptr) nd->fp->initializeWeights(outputLength);
    Layer.push_back(nd);
    if (inputLength) bindNode(lastLayer, nd);
  }
  Layers.push_back(Layer);
}

void DNN::addLayer(Activation *fp) {
  vector<Neuron *> Layer;
  vector<ComputeNode *> lastLayer = vector<ComputeNode *>(
      Layers[Layers.size() - 1].begin(), Layers[Layers.size() - 1].end());
  for (size_t i = 0; i < lastLayer.size(); i++) {
    Neuron *nd = addNeuron(fp->newInstance());
    Layer.push_back(nd);
    bindNode({lastLayer[i]}, nd);
  }
  Layers.push_back(Layer);
}

void DNN::bp(ld lr, vector<ld> &outputGrad) {
  grad(outputGrad);
  Neuron *n;
  for (auto nd : Nodes) {
    n = (Neuron *)nd;
    n->bp(lr);
  }
}

vector<ld> DNN::eval(vector<ld> &inputs) {
  for (size_t i = 0; i < inputs.size(); i++) {
    Layers[0][i]->input(inputs[i]);
  }
  return compute();
}

void DNN::training(ld lr, size_t epoch, vector<vector<ld>> &inputs,
                   vector<vector<ld>> &labels) {
  for (size_t i = 0; i < epoch; i++) {
    vector<ld> grad(outNodes.size(), 0);
    for (size_t t = 0; t < inputs.size(); t++) {
      vector<ld> res = eval(inputs[t]);
      for (size_t j = 0; j < labels[t].size(); j++) {
        grad[j] = 2 * (res[j] - labels[t][j]);
        // grad[j] += 2 * (res[j] - labels[t][j]) / inputs.size();
      }
      bp(lr, grad);
    }
    // ld sum = 0;
    // for (auto it : grad) sum += it;
    // sum /= grad.size();
    // cout << i + 1 << " " << sum << endl;
    // bp(lr, grad);
  }
}

int main() {
  srand(time(nullptr));
  DNN net;
  Sigmoid *sig = new Sigmoid;
  net.addLayer(2);
  net.addLayer(2);
  net.addLayer(sig);
  net.addLayer(1);
  vector<vector<ld>> inputs = {{0, 0}, {0, 1}, {1, 0}, {1, 1}};
  vector<vector<ld>> labels = {{0}, {1}, {1}, {0}};
  cout << "[before training] --------------------" << endl;
  for (size_t i = 0; i < inputs.size(); i++) {
    vector<ld> res = net.eval(inputs[i]);
    cout << "output: " << res[0] << " target: " << labels[i][0] << endl;
  }
  net.training(0.1, 10000, inputs, labels);
  cout << "[after  training] --------------------" << endl;
  for (size_t i = 0; i < inputs.size(); i++) {
    vector<ld> res = net.eval(inputs[i]);
    cout << "output: " << res[0] << " target: " << labels[i][0] << endl;
  }
  delete sig;
  return 0;
}

UPD

找AI要了份手写的梯度下降代码，对这个俩层网络验证了一下，根据结果来看，梯度算的倒是没毛病，看来真是参数初始化的问题了

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#include <bits/stdc++.h>
using namespace std;
using ld = long double;
using ll = long long;

class Function {
 public:
  virtual ld exec(vector<ld> &inputs) = 0;
  virtual vector<ld> grad(vector<ld> &inputs) = 0;
  virtual ~Function() = default;
  virtual void bp(ld grad) {};
  virtual void initializeWeights(size_t outputLength) = 0;
};

class ComputeNode {
 public:
  size_t inputLength = 0;
  ld value = 0;
  vector<ld> pfpx;
  vector<ComputeNode *> nextNodes;
  vector<ComputeNode *> operands;
  Function *fp = nullptr;
  size_t id = 999;
  ld grad = 0;
  ComputeNode(size_t _inputLength, Function *_fp, size_t _id)
      : inputLength(_inputLength), fp(_fp), id(_id) {}
  ComputeNode(ld val, size_t _id) : value(val), id(_id) {};
  virtual ~ComputeNode() {
    if (fp != nullptr) delete fp;
  };
  virtual ld compute();
};

ld ComputeNode::compute() {
  if (inputLength == 0) return value;
  vector<ld> inputs;
  for (size_t i = 0; i < inputLength; i++) {
    inputs.push_back(operands[i]->value);
  }
  value = fp->exec(inputs);
  pfpx = fp->grad(inputs);
  return value;
}

class ComputationalGraph {
 public:
  vector<ComputeNode *> Nodes;
  vector<ComputeNode *> outNodes;
  vector<ComputeNode *> inNodes;
  vector<ComputeNode *> topo_forward;
  vector<ComputeNode *> topo_backward;
  ComputationalGraph() = default;
  ComputeNode *addNode(size_t inputLength, Function *fp);
  ComputeNode *addNode(ld value);
  void bindNode(vector<ComputeNode *> ops, ComputeNode *ComputeNodePtr);
  vector<ld> compute();
  vector<ld> grad();
  vector<ld> grad(vector<ld> &outputGrad);
  void clearGrad() {
    for (auto nd : Nodes) nd->grad = 0;
  }
  virtual ~ComputationalGraph() {
    for (auto &it : Nodes) delete it;
  }
};

ComputeNode *ComputationalGraph::addNode(size_t inputLength, Function *fp) {
  ComputeNode *nd = new ComputeNode(inputLength, fp, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

ComputeNode *ComputationalGraph::addNode(ld value) {
  ComputeNode *nd = new ComputeNode(value, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

void ComputationalGraph::bindNode(vector<ComputeNode *> ops,
                                  ComputeNode *ComputeNodePtr) {
  for (auto nd : ops) {
    ComputeNodePtr->operands.push_back(nd);
    nd->nextNodes.push_back(ComputeNodePtr);
  }
}

vector<ld> ComputationalGraph::compute() {
  if (!topo_forward.size()) {
    map<ComputeNode *, ll> indegree;
    bool flag = false;
    for (auto nd : Nodes) {
      for (auto nnd : nd->nextNodes) {
        indegree[nnd]++;
      }
    }
    if (outNodes.size() != 0) flag = true;
    queue<ComputeNode *> q;
    if (inNodes.size() == 0) {
      for (auto nd : Nodes)
        if (indegree[nd] == 0) inNodes.push_back(nd);
      sort(inNodes.begin(), inNodes.end(),
           [&](auto a, auto b) { return a->id < b->id; });
    }
    for (auto nd : inNodes) q.push(nd);
    while (!q.empty()) {
      auto nd = q.front();
      q.pop();
      topo_forward.push_back(nd);
      for (auto nnd : nd->nextNodes) {
        --indegree[nnd];
        if (indegree[nnd] == 0) q.push(nnd);
      }
      if (nd->nextNodes.size() == 0 && !flag) {
        outNodes.push_back(nd);
      }
    }
    if (!flag) {
      sort(outNodes.begin(), outNodes.end(),
           [&](auto a, auto b) { return a->id < b->id; });
    }
    topo_backward = topo_forward;
    reverse(topo_backward.begin(), topo_backward.end());
  }
  for (auto nd : topo_forward) {
    nd->compute();
  }
  vector<ld> res;
  for (auto nd : outNodes) {
    res.push_back(nd->value);
  }
  return res;
}

vector<ld> ComputationalGraph::grad(vector<ld> &outputGrad) {
  clearGrad();
  for (size_t i = 0; i < outNodes.size(); i++)
    outNodes[i]->grad = outputGrad[i];
  for (auto nd : topo_backward)
    for (size_t i = 0; i < nd->inputLength; i++)
      nd->operands[i]->grad += nd->grad * nd->pfpx[i];
  vector<ld> res;
  for (auto nd : inNodes) {
    res.push_back(nd->grad);
  }
  return res;
}

vector<ld> ComputationalGraph::grad() {
  clearGrad();
  for (auto nd : outNodes) nd->grad = 1;
  for (auto nd : topo_backward)
    for (size_t i = 0; i < nd->inputLength; i++)
      nd->operands[i]->grad += nd->grad * nd->pfpx[i];
  vector<ld> res;
  for (auto nd : inNodes) {
    res.push_back(nd->grad);
  }
  return res;
}

class Liner : public Function {
 public:
  vector<ld> W;
  vector<ld> _inputs;
  Liner(size_t inputLength) {
    for (size_t i = 0; i <= inputLength; i++) {
      // W.push_back(ld(rand()) / RAND_MAX);
      W.push_back(1+i);
    }
  }
  void initializeWeights(size_t outputLength) {
    // for (auto &it : W) {
    //   double limit = std::sqrt(6.0 / (W.size() - 1 + outputLength));
    //   it = (ld(rand()) / RAND_MAX) * 2 * limit - limit;
    // }
    W[W.size() - 1] = 0.0;
  }
  ld exec(vector<ld> &inputs) {
    _inputs = inputs;
    _inputs.push_back(1);  // for bias, extra input unit 1
    ld res = 0;
    for (size_t i = 0; i < W.size(); i++) {
      res += _inputs[i] * W[i];
    }
    return res;
  }
  vector<ld> grad(vector<ld> &inputs) {
    vector<ld> d;
    for (size_t i = 0; i < inputs.size(); i++) {
      d.push_back(W[i]);
    }
    return d;
  }
  void bp(ld grad) {
    for (size_t i = 0; i < W.size(); i++) {
      W[i] -= grad * _inputs[i];
    }
  }
};

class Activation : Function {
 public:
  ld input;
  Activation() = default;
  void bp(ld grad) {}
  void initializeWeights(size_t outputLength) {}
  virtual Activation *newInstance() = 0;
};

class Sigmoid : public Activation {
 public:
  Sigmoid() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return 1.0 / (1 + exp(-input));
  }
  vector<ld> grad(vector<ld> &inputs) {
    return {exec(inputs) * (1 - exec(inputs))};
  }
  Sigmoid *newInstance() { return new Sigmoid; }
};

class Sgn : public Activation {
 public:
  Sgn() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return 2.0 / (1 + exp(-input)) - 1;
  }
  vector<ld> grad(vector<ld> &inputs) {
    return {2 * exp(-inputs[0]) /
            (2 * exp(-inputs[0]) + (exp(-inputs[0]) * exp(-inputs[0])) + 1)};
  }
  Sgn *newInstance() { return new Sgn; }
};

class ReLU : public Activation {
 public:
  ReLU() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return input > 0 ? input : 0;
  }
  vector<ld> grad(vector<ld> &inputs) { return {ld(inputs[0] >= 0 ? 1 : 0)}; }
  ReLU *newInstance() { return new ReLU; }
};

class Neuron : public ComputeNode {
 public:
  Neuron(size_t inputLength, size_t id)
      : ComputeNode(inputLength, new Liner(inputLength), id) {};
  Neuron(size_t inputLength, Function *fp, size_t id)
      : ComputeNode(inputLength, fp, id) {};
  Neuron(size_t id) : ComputeNode(0, id) {}
  void input(ld v) {  // for input node only
    value = v;
  }
  void bp(ld lr);
};

void Neuron::bp(ld lr) {
  if (fp != nullptr) fp->bp(grad * lr);
}

class DNN : public ComputationalGraph {
 public:
  DNN() = default;
  vector<vector<Neuron *>> Layers;
  void addLayer(size_t outputLength);
  Neuron *addNeuron(size_t inputLength);
  Neuron *addNeuron();
  Neuron *addNeuron(Activation *fp);
  void bp(ld lr, vector<ld> &labels);
  vector<ld> eval(vector<ld> &inputs);
  void training(ld lr, size_t epoch, vector<vector<ld>> &inputs,
                vector<vector<ld>> &labels);
  void addLayer(Activation *fp);  // activation layer
};

Neuron *DNN::addNeuron() {
  Neuron *nd = new Neuron(Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

Neuron *DNN::addNeuron(Activation *fp) {
  Neuron *nd = new Neuron(1, (Function *)fp, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

Neuron *DNN::addNeuron(size_t inputLength) {
  Neuron *nd = new Neuron(inputLength, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

void DNN::addLayer(size_t outputLength) {
  size_t inputLength = Layers.size() > 0 ? Layers[Layers.size() - 1].size() : 0;
  vector<Neuron *> Layer;
  vector<ComputeNode *> lastLayer;
  if (inputLength)
    lastLayer = vector<ComputeNode *>(Layers[Layers.size() - 1].begin(),
                                      Layers[Layers.size() - 1].end());
  for (size_t i = 0; i < outputLength; i++) {
    Neuron *nd = inputLength != 0 ? addNeuron(inputLength) : addNeuron();
    if (nd->fp != nullptr) nd->fp->initializeWeights(outputLength);
    Layer.push_back(nd);
    if (inputLength) bindNode(lastLayer, nd);
  }
  Layers.push_back(Layer);
}

void DNN::addLayer(Activation *fp) {
  vector<Neuron *> Layer;
  vector<ComputeNode *> lastLayer = vector<ComputeNode *>(
      Layers[Layers.size() - 1].begin(), Layers[Layers.size() - 1].end());
  for (size_t i = 0; i < lastLayer.size(); i++) {
    Neuron *nd = addNeuron(fp->newInstance());
    Layer.push_back(nd);
    bindNode({lastLayer[i]}, nd);
  }
  Layers.push_back(Layer);
}

void DNN::bp(ld lr, vector<ld> &outputGrad) {
  grad(outputGrad);
  Neuron *n;
  for (auto nd : Nodes) {
    n = (Neuron *)nd;
    n->bp(lr);
  }
}

vector<ld> DNN::eval(vector<ld> &inputs) {
  for (size_t i = 0; i < inputs.size(); i++) {
    Layers[0][i]->input(inputs[i]);
  }
  return compute();
}

void DNN::training(ld lr, size_t epoch, vector<vector<ld>> &inputs,
                   vector<vector<ld>> &labels) {
  for (size_t i = 0; i < epoch; i++) {
    vector<ld> grad(outNodes.size(), 0);
    for (size_t t = 0; t < inputs.size(); t++) {
      vector<ld> res = eval(inputs[t]);
      for (size_t j = 0; j < labels[t].size(); j++) {
        grad[j] = 2 * (res[j] - labels[t][j]);
        // cout << j << " " << 2 * (res[j] - labels[t][j]) << endl;
        // grad[j] += 2 * (res[j] - labels[t][j]) / inputs.size();
      }
      bp(lr, grad);
    }
    // ld sum = 0;
    // for (auto it : grad) sum += it;
    // sum /= grad.size();
    // cout << i + 1 << " " << grad[0] << endl;
    // bp(lr, grad);
  }
}

int main() {
  // srand(time(nullptr));
  // srand(42);
  DNN net;
  // Sgn *sgn = new Sgn;
  Sigmoid *sig = new Sigmoid;
  net.addLayer(2);
  net.addLayer(2);
  // net.addLayer(sgn);
  net.addLayer(sig);
  net.addLayer(1);
  // net.addLayer(sgn);
  net.addLayer(sig);

  vector<vector<ld>> inputs = {{0, 0}, {0, 1}, {1, 0}, {1, 1}};
  vector<vector<ld>> labels = {{0}, {1}, {1}, {0}};
  cout << "[before training] --------------------" << endl;
  for (size_t i = 0; i < inputs.size(); i++) {
    vector<ld> res = net.eval(inputs[i]);
    cout << "output: " << res[0] << " target: " << labels[i][0] << endl;
  }
  vector<vector<vector<ld>>> W;
  for (size_t i = 0; i < net.Layers.size(); i++) {
    vector<vector<ld>> w;
    if (i == 0 || i == 2 || i == 4) continue;
    // if(i == 0) continue;
    for (auto &node : net.Layers[i]) {
      if (node->fp != nullptr) {
        Liner *f = (Liner *)node->fp;
        w.push_back(f->W);
      }
    }
    W.push_back(w);
  }
  cout << "-----------------------------" << endl;
  for (int i = 0; i < (int)W.size(); i++) {
    for (int j = 0; j < (int)W[i].size(); j++) {
      for (auto it : W[i][j]) {
        cout << it << " ";
      }
      cout << endl;
    }
    cout << "-----------------------------" << endl;
  }
  net.training(0.1, 10000, inputs, labels);
  cout << "[after  training] --------------------" << endl;
  for (size_t i = 0; i < inputs.size(); i++) {
    vector<ld> res = net.eval(inputs[i]);
    cout << "output: " << res[0] << " target: " << labels[i][0] << endl;
  }
  // vector<vector<vector<ld>>>W1;
  W.clear();
  for (size_t i = 0; i < net.Layers.size(); i++) {
    vector<vector<ld>> w;
    if (i == 0 || i == 2 || i == 4) continue;
    // if(i == 0) continue;
    for (auto &node : net.Layers[i]) {
      if (node->fp != nullptr) {
        Liner *f = (Liner *)node->fp;
        w.push_back(f->W);
      }
    }
    W.push_back(w);
  }
  cout << "-----------------------------" << endl;
  for (int i = 0; i < (int)W.size(); i++) {
    for (int j = 0; j < (int)W[i].size(); j++) {
      for (auto it : W[i][j]) {
        cout << it << " ";
      }
      cout << endl;
    }
    cout << "-----------------------------" << endl;
  }
  // delete sgn;
  delete sig;
  return 0;
}
output-cpp
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[before training] --------------------
output: 0.817574 target: 0
output: 0.93354 target: 1
output: 0.899635 target: 1
output: 0.945716 target: 0
-----------------------------
1 2 0 
1 2 0 
-----------------------------
1 2 0 
-----------------------------
[after  training] --------------------
output: 0.0321611 target: 0
output: 0.971427 target: 1
output: 0.971321 target: 1
output: 0.030212 target: 0
-----------------------------
4.24897 4.25892 -6.51776 
6.22279 6.27278 -2.70055 
-----------------------------
-9.20646 8.56062 -3.92954 
-----------------------------
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import math

# 定义 sigmoid 激活函数
def sigmoid(x):
  return 1 / (1 + math.exp(-x))

# 定义 sigmoid 函数的导数
def sigmoid_derivative(x):
  return sigmoid(x) * (1 - sigmoid(x))

# 输入数据集
X = [[0, 0], [0, 1], [1, 0], [1, 1]]
# 输出数据集
y = [0, 1, 1, 0]

# 初始化权重为 1
syn0 = [[1, 1], [2, 2]]
syn1 = [1, 2]

# 初始化偏置为 0
b0 = [0, 0]
b1 = 0

# 学习率
learning_rate = 0.1

# 输出训练前的结果
for i in range(len(X)):
  l0 = X[i]
  l1_input = [0, 0]
  for j in range(2):
    l1_input[j] = l0[0] * syn0[0][j] + l0[1] * syn0[1][j] + b0[j]
  l1 = [sigmoid(x) for x in l1_input]

  l2_input = l1[0] * syn1[0] + l1[1] * syn1[1] + b1
  l2 = sigmoid(l2_input)
  print(f"输入: {l0}, 预测输出: {l2}")

print("-----")

print(syn0, b0)
print(syn1, b1)

print("-----")

# 训练次数
for iter in range(10000):
  for i in range(len(X)):
    # 前向传播
    l0 = X[i]
    # 计算第一层的加权和
    l1_input = [0, 0]
    for j in range(2):
      l1_input[j] = l0[0] * syn0[0][j] + l0[1] * syn0[1][j] + b0[j]
    l1 = [sigmoid(x) for x in l1_input]

    # 计算第二层的加权和
    l2_input = l1[0] * syn1[0] + l1[1] * syn1[1] + b1
    l2 = sigmoid(l2_input)

    # 计算误差
    l2_error = 2 * (l2 - y[i])

    # 反向传播
    l2_delta = l2_error * sigmoid_derivative(l2_input)
    l1_error = [l2_delta * syn1[k] for k in range(2)]
    l1_delta = [l1_error[k] * sigmoid_derivative(l1_input[k]) for k in range(2)]

    # 更新权重
    for k in range(2):
      syn1[k] -= learning_rate * l1[k] * l2_delta
      for j in range(2):
        syn0[j][k] -= learning_rate * l0[j] * l1_delta[k]

    # 更新偏置
    b1 -= learning_rate * l2_delta
    for k in range(2):
      b0[k] -= learning_rate * l1_delta[k]

# 输出训练后的结果
for i in range(len(X)):
  l0 = X[i]
  l1_input = [0, 0]
  for j in range(2):
    l1_input[j] = l0[0] * syn0[0][j] + l0[1] * syn0[1][j] + b0[j]
  l1 = [sigmoid(x) for x in l1_input]

  l2_input = l1[0] * syn1[0] + l1[1] * syn1[1] + b1
  l2 = sigmoid(l2_input)
  print(f"输入: {l0}, 预测输出: {l2}")

print("-----")

print(syn0, b0)
print(syn1, b1)

output-python
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输入: [0, 0], 预测输出: 0.8175744761936437
输入: [0, 1], 预测输出: 0.9335404768183254
输入: [1, 0], 预测输出: 0.899635013659718
输入: [1, 1], 预测输出: 0.9457164924311116
-----
[[1, 1], [2, 2]] [0, 0]
[1, 2] 0
-----
输入: [0, 0], 预测输出: 0.03216114545991441
输入: [0, 1], 预测输出: 0.9714274383937241
输入: [1, 0], 预测输出: 0.9713208449898518
输入: [1, 1], 预测输出: 0.03021196946428554
-----
[[4.248966453859427, 6.222789573694698], [4.258917152971988, 6.2727816735983035]] [-6.517757196383422, -2.700554991982005]
[-9.206458188124406, 8.560618703440802] -3.929539465326751

UPDD

还是两层Leaky ReLU吧（悲

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#include <bits/stdc++.h>
using namespace std;
using ld = long double;
using ll = long long;

class Function {
 public:
  virtual ld exec(vector<ld> &inputs) = 0;
  virtual vector<ld> grad(vector<ld> &inputs) = 0;
  virtual ~Function() = default;
  virtual void bp(ld grad) {};
  virtual void initializeWeights(size_t outputLength) = 0;
};

class ComputeNode {
 public:
  size_t inputLength = 0;
  ld value = 0;
  vector<ld> pfpx;
  vector<ComputeNode *> nextNodes;
  vector<ComputeNode *> operands;
  Function *fp = nullptr;
  size_t id = 999;
  ld grad = 0;
  ComputeNode(size_t _inputLength, Function *_fp, size_t _id)
      : inputLength(_inputLength), fp(_fp), id(_id) {}
  ComputeNode(ld val, size_t _id) : value(val), id(_id) {};
  virtual ~ComputeNode() {
    if (fp != nullptr) delete fp;
  };
  virtual ld compute();
};

ld ComputeNode::compute() {
  if (inputLength == 0) return value;
  vector<ld> inputs;
  for (size_t i = 0; i < inputLength; i++) {
    inputs.push_back(operands[i]->value);
  }
  value = fp->exec(inputs);
  pfpx = fp->grad(inputs);
  return value;
}

class ComputationalGraph {
 public:
  vector<ComputeNode *> Nodes;
  vector<ComputeNode *> outNodes;
  vector<ComputeNode *> inNodes;
  vector<ComputeNode *> topo_forward;
  vector<ComputeNode *> topo_backward;
  ComputationalGraph() = default;
  ComputeNode *addNode(size_t inputLength, Function *fp);
  ComputeNode *addNode(ld value);
  void bindNode(vector<ComputeNode *> ops, ComputeNode *ComputeNodePtr);
  vector<ld> compute();
  vector<ld> grad();
  vector<ld> grad(vector<ld> &outputGrad);
  void clearGrad() {
    for (auto nd : Nodes) nd->grad = 0;
  }
  virtual ~ComputationalGraph() {
    for (auto &it : Nodes) delete it;
  }
};

ComputeNode *ComputationalGraph::addNode(size_t inputLength, Function *fp) {
  ComputeNode *nd = new ComputeNode(inputLength, fp, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

ComputeNode *ComputationalGraph::addNode(ld value) {
  ComputeNode *nd = new ComputeNode(value, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

void ComputationalGraph::bindNode(vector<ComputeNode *> ops,
                                  ComputeNode *ComputeNodePtr) {
  for (auto nd : ops) {
    ComputeNodePtr->operands.push_back(nd);
    nd->nextNodes.push_back(ComputeNodePtr);
  }
}

vector<ld> ComputationalGraph::compute() {
  if (!topo_forward.size()) {
    map<ComputeNode *, ll> indegree;
    bool flag = false;
    for (auto nd : Nodes) {
      for (auto nnd : nd->nextNodes) {
        indegree[nnd]++;
      }
    }
    if (outNodes.size() != 0) flag = true;
    queue<ComputeNode *> q;
    if (inNodes.size() == 0) {
      for (auto nd : Nodes)
        if (indegree[nd] == 0) inNodes.push_back(nd);
      sort(inNodes.begin(), inNodes.end(),
           [&](auto a, auto b) { return a->id < b->id; });
    }
    for (auto nd : inNodes) q.push(nd);
    while (!q.empty()) {
      auto nd = q.front();
      q.pop();
      topo_forward.push_back(nd);
      for (auto nnd : nd->nextNodes) {
        --indegree[nnd];
        if (indegree[nnd] == 0) q.push(nnd);
      }
      if (nd->nextNodes.size() == 0 && !flag) {
        outNodes.push_back(nd);
      }
    }
    if (!flag) {
      sort(outNodes.begin(), outNodes.end(),
           [&](auto a, auto b) { return a->id < b->id; });
    }
    topo_backward = topo_forward;
    reverse(topo_backward.begin(), topo_backward.end());
  }
  for (auto nd : topo_forward) {
    nd->compute();
  }
  vector<ld> res;
  for (auto nd : outNodes) {
    res.push_back(nd->value);
  }
  return res;
}

vector<ld> ComputationalGraph::grad(vector<ld> &outputGrad) {
  clearGrad();
  for (size_t i = 0; i < outNodes.size(); i++)
    outNodes[i]->grad = outputGrad[i];
  for (auto nd : topo_backward)
    for (size_t i = 0; i < nd->inputLength; i++)
      nd->operands[i]->grad += nd->grad * nd->pfpx[i];
  vector<ld> res;
  for (auto nd : inNodes) {
    res.push_back(nd->grad);
  }
  return res;
}

vector<ld> ComputationalGraph::grad() {
  clearGrad();
  for (auto nd : outNodes) nd->grad = 1;
  for (auto nd : topo_backward)
    for (size_t i = 0; i < nd->inputLength; i++)
      nd->operands[i]->grad += nd->grad * nd->pfpx[i];
  vector<ld> res;
  for (auto nd : inNodes) {
    res.push_back(nd->grad);
  }
  return res;
}

class Linear : public Function {
 public:
  vector<ld> W;
  vector<ld> _inputs;
  Linear(size_t inputLength) {
    for (size_t i = 0; i <= inputLength; i++) {
      // W.push_back(ld(rand()) / RAND_MAX);
      W.push_back(1 + i);
    }
  }
  void initializeWeights(size_t outputLength) {
    ld bound_weight = 1.0 / sqrt(W.size());
    for (auto &it : W) {
      ld rand_num = (ld)rand() / RAND_MAX * 2 * bound_weight - bound_weight;
      it = rand_num;
    }
    // W[W.size() - 1] = 0.0;  // zero for bias
  }
  ld exec(vector<ld> &inputs) {
    _inputs = inputs;
    _inputs.push_back(1);  // for bias, extra input unit 1
    ld res = 0;
    for (size_t i = 0; i < W.size(); i++) {
      res += _inputs[i] * W[i];
    }
    return res;
  }
  vector<ld> grad(vector<ld> &inputs) {
    vector<ld> d;
    for (size_t i = 0; i < inputs.size(); i++) {
      d.push_back(W[i]);
    }
    return d;
  }
  void bp(ld grad) {
    for (size_t i = 0; i < W.size(); i++) {
      W[i] -= grad * _inputs[i];
    }
  }
};

class Activation : Function {
 public:
  ld input;
  Activation() = default;
  void bp(ld grad) {}
  void initializeWeights(size_t outputLength) {}
  virtual Activation *newInstance() = 0;
};

class Sigmoid : public Activation {
 public:
  Sigmoid() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return 1.0 / (1 + exp(-input));
  }
  vector<ld> grad(vector<ld> &inputs) {
    return {exec(inputs) * (1 - exec(inputs))};
  }
  Sigmoid *newInstance() { return new Sigmoid; }
};

class Sgn : public Activation {
 public:
  Sgn() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return 2.0 / (1 + exp(-input)) - 1;
  }
  vector<ld> grad(vector<ld> &inputs) {
    return {2 * exp(-inputs[0]) /
            (2 * exp(-inputs[0]) + (exp(-inputs[0]) * exp(-inputs[0])) + 1)};
  }
  Sgn *newInstance() { return new Sgn; }
};

class LeakyReLU : public Activation {
 public:
  LeakyReLU() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return input > 0 ? input : -1 / 5.5 * input;
  }
  vector<ld> grad(vector<ld> &inputs) {
    return {ld(inputs[0] >= 0 ? 1 : -1 / 5.5)};
  }
  LeakyReLU *newInstance() { return new LeakyReLU; }
};

class ReLU : public Activation {
 public:
  ReLU() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return input > 0 ? input : 0;
  }
  vector<ld> grad(vector<ld> &inputs) { return {ld(inputs[0] >= 0 ? 1 : 0)}; }
  ReLU *newInstance() { return new ReLU; }
};

class Neuron : public ComputeNode {
 public:
  Neuron(size_t inputLength, size_t id)
      : ComputeNode(inputLength, new Linear(inputLength), id) {};
  Neuron(size_t inputLength, Function *fp, size_t id)
      : ComputeNode(inputLength, fp, id) {};
  Neuron(size_t id) : ComputeNode(0, id) {}
  void input(ld v) {  // for input node only
    value = v;
  }
  void bp(ld lr);
};

void Neuron::bp(ld lr) {
  if (fp != nullptr) fp->bp(grad * lr);
}

class DNN : public ComputationalGraph {
 public:
  DNN() = default;
  vector<vector<Neuron *>> Layers;
  void addLayer(size_t outputLength);
  Neuron *addNeuron(size_t inputLength);
  Neuron *addNeuron();
  Neuron *addNeuron(Activation *fp);
  void bp(ld lr, vector<ld> &labels);
  vector<ld> eval(vector<ld> &inputs);
  void training(ld lr, size_t epoch, vector<vector<ld>> &inputs,
                vector<vector<ld>> &labels);
  void addLayer(Activation *fp);  // activation layer
};

Neuron *DNN::addNeuron() {
  Neuron *nd = new Neuron(Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

Neuron *DNN::addNeuron(Activation *fp) {
  Neuron *nd = new Neuron(1, (Function *)fp, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

Neuron *DNN::addNeuron(size_t inputLength) {
  Neuron *nd = new Neuron(inputLength, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

void DNN::addLayer(size_t outputLength) {
  size_t inputLength = Layers.size() > 0 ? Layers[Layers.size() - 1].size() : 0;
  vector<Neuron *> Layer;
  vector<ComputeNode *> lastLayer;
  if (inputLength)
    lastLayer = vector<ComputeNode *>(Layers[Layers.size() - 1].begin(),
                                      Layers[Layers.size() - 1].end());
  for (size_t i = 0; i < outputLength; i++) {
    Neuron *nd = inputLength != 0 ? addNeuron(inputLength) : addNeuron();
    if (nd->fp != nullptr) nd->fp->initializeWeights(outputLength);
    Layer.push_back(nd);
    if (inputLength) bindNode(lastLayer, nd);
  }
  Layers.push_back(Layer);
}

void DNN::addLayer(Activation *fp) {
  vector<Neuron *> Layer;
  vector<ComputeNode *> lastLayer = vector<ComputeNode *>(
      Layers[Layers.size() - 1].begin(), Layers[Layers.size() - 1].end());
  for (size_t i = 0; i < lastLayer.size(); i++) {
    Neuron *nd = addNeuron(fp->newInstance());
    Layer.push_back(nd);
    bindNode({lastLayer[i]}, nd);
  }
  Layers.push_back(Layer);
}

void DNN::bp(ld lr, vector<ld> &outputGrad) {
  grad(outputGrad);
  Neuron *n;
  for (auto nd : Nodes) {
    n = (Neuron *)nd;
    n->bp(lr);
  }
}

vector<ld> DNN::eval(vector<ld> &inputs) {
  for (size_t i = 0; i < inputs.size(); i++) {
    Layers[0][i]->input(inputs[i]);
  }
  return compute();
}

void DNN::training(ld lr, size_t epoch, vector<vector<ld>> &inputs,
                   vector<vector<ld>> &labels) {
  for (size_t i = 0; i < epoch; i++) {
    vector<ld> grad(outNodes.size(), 0);
    for (size_t t = 0; t < inputs.size(); t++) {
      vector<ld> res = eval(inputs[t]);
      for (size_t j = 0; j < labels[t].size(); j++) {
        grad[j] = 2 * (res[j] - labels[t][j]);
      }
      // cout << grad[0] << endl;
      bp(lr, grad);
    }
  }
}

int main() {
  srand(time(nullptr));
  // srand(42);
  DNN net;
  LeakyReLU *relu = new LeakyReLU;
  Sgn *sgn = new Sgn;
  Sigmoid *sig = new Sigmoid;

  net.addLayer(2);
  net.addLayer(2);
  // net.addLayer(sgn);
  // net.addLayer(sig);
  net.addLayer(relu);
  net.addLayer(1);
  net.addLayer(relu);
  // net.addLayer(sgn);
  // net.addLayer(sig);

  vector<vector<ld>> inputs = {{0, 0}, {0, 1}, {1, 0}, {1, 1}};
  vector<vector<ld>> labels = {{0}, {1}, {1}, {0}};
  cout << "[before training] --------------------" << endl;
  for (size_t i = 0; i < inputs.size(); i++) {
    vector<ld> res = net.eval(inputs[i]);
    cout << "output: " << res[0] << " target: " << labels[i][0]
         << endl;
  }
  net.training(0.1, 10000, inputs, labels);
  cout << "[after  training] --------------------" << endl;
  for (size_t i = 0; i < inputs.size(); i++) {
    vector<ld> res = net.eval(inputs[i]);
    cout << "output: " << res[0] << " target: " << labels[i][0]
         << endl;
  }
  delete sgn;
  delete sig;
  delete relu;
  return 0;
}

UPDDD

总算算对了，找到问题了，是bp的时候用了最后一组的输入计算grad，实际上应该将每一组的grad进行累加，最后step再修改参数

success 
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#include <bits/stdc++.h>
using namespace std;
using ld = long double;
using ll = long long;
class Function {
 public:
  virtual ld exec(vector<ld> &inputs) = 0;
  virtual vector<ld> grad(vector<ld> &inputs) = 0;
  virtual ~Function() = default;
  virtual void bp(ld grad) {}
  virtual void step() {}
  virtual void initializeWeights(size_t outputLength) = 0;
  virtual vector<ld> getWeights() = 0;
  virtual void clearGrad() = 0;
};

class ComputeNode {
 public:
  size_t inputLength = 0;
  ld value = 0;
  vector<ld> pfpx;
  vector<ComputeNode *> nextNodes;
  vector<ComputeNode *> operands;
  Function *fp = nullptr;
  size_t id = 999;
  ld grad = 0;
  ComputeNode(size_t _inputLength, Function *_fp, size_t _id)
      : inputLength(_inputLength), fp(_fp), id(_id) {}
  ComputeNode(ld val, size_t _id) : value(val), id(_id) {};
  virtual ~ComputeNode() {
    if (fp != nullptr) delete fp;
  };
  virtual ld compute();
  virtual void clearGrad() {};
};

ld ComputeNode::compute() {
  if (inputLength == 0) return value;
  vector<ld> inputs;
  for (size_t i = 0; i < inputLength; i++) {
    inputs.push_back(operands[i]->value);
  }
  value = fp->exec(inputs);
  pfpx = fp->grad(inputs);
  return value;
}

class ComputationalGraph {
 public:
  vector<ComputeNode *> Nodes;
  vector<ComputeNode *> outNodes;
  vector<ComputeNode *> inNodes;
  vector<ComputeNode *> topo_forward;
  vector<ComputeNode *> topo_backward;
  ComputationalGraph() = default;
  ComputeNode *addNode(size_t inputLength, Function *fp);
  ComputeNode *addNode(ld value);
  void bindNode(vector<ComputeNode *> ops, ComputeNode *ComputeNodePtr);
  vector<ld> compute();
  vector<ld> grad();
  vector<ld> grad(vector<ld> &outputGrad);
  void clearGrad() {
    for (auto nd : Nodes) nd->clearGrad();
  }
  virtual ~ComputationalGraph() {
    for (auto &it : Nodes) delete it;
  }
};

ComputeNode *ComputationalGraph::addNode(size_t inputLength, Function *fp) {
  ComputeNode *nd = new ComputeNode(inputLength, fp, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

ComputeNode *ComputationalGraph::addNode(ld value) {
  ComputeNode *nd = new ComputeNode(value, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

void ComputationalGraph::bindNode(vector<ComputeNode *> ops,
                                  ComputeNode *ComputeNodePtr) {
  for (auto nd : ops) {
    ComputeNodePtr->operands.push_back(nd);
    nd->nextNodes.push_back(ComputeNodePtr);
  }
}

vector<ld> ComputationalGraph::compute() {
  if (!topo_forward.size()) {
    map<ComputeNode *, ll> indegree;
    bool flag = false;
    for (auto nd : Nodes) {
      for (auto nnd : nd->nextNodes) {
        indegree[nnd]++;
      }
    }
    if (outNodes.size() != 0) flag = true;
    queue<ComputeNode *> q;
    if (inNodes.size() == 0) {
      for (auto nd : Nodes)
        if (indegree[nd] == 0) inNodes.push_back(nd);
      sort(inNodes.begin(), inNodes.end(),
           [&](auto a, auto b) { return a->id < b->id; });
    }
    for (auto nd : inNodes) q.push(nd);
    while (!q.empty()) {
      auto nd = q.front();
      q.pop();
      topo_forward.push_back(nd);
      for (auto nnd : nd->nextNodes) {
        --indegree[nnd];
        if (indegree[nnd] == 0) q.push(nnd);
      }
      if (nd->nextNodes.size() == 0 && !flag) {
        outNodes.push_back(nd);
      }
    }
    if (!flag) {
      sort(outNodes.begin(), outNodes.end(),
           [&](auto a, auto b) { return a->id < b->id; });
    }
    topo_backward = topo_forward;
    reverse(topo_backward.begin(), topo_backward.end());
  }
  for (auto nd : topo_forward) {
    nd->compute();
  }
  vector<ld> res;
  for (auto nd : outNodes) {
    res.push_back(nd->value);
  }
  return res;
}

vector<ld> ComputationalGraph::grad(vector<ld> &outputGrad) {
  // clearGrad();
  for (size_t i = 0; i < outNodes.size(); i++)
    outNodes[i]->grad = outputGrad[i];
  for (auto nd : topo_backward)
    for (size_t i = 0; i < nd->inputLength; i++)
      nd->operands[i]->grad += nd->grad * nd->pfpx[i];
  vector<ld> res;
  for (auto nd : inNodes) {
    res.push_back(nd->grad);
  }
  return res;
}

vector<ld> ComputationalGraph::grad() {
  clearGrad();
  for (auto nd : outNodes) nd->grad = 1;
  for (auto nd : topo_backward)
    for (size_t i = 0; i < nd->inputLength; i++)
      nd->operands[i]->grad += nd->grad * nd->pfpx[i];
  vector<ld> res;
  for (auto nd : inNodes) {
    res.push_back(nd->grad);
  }
  return res;
}

class Linear : public Function {
 public:
  vector<ld> W;
  vector<ld> grads;
  vector<ld> _inputs;
  Linear(size_t inputLength) {
    for (size_t i = 0; i <= inputLength; i++) {
      // W.push_back(ld(rand()) / RAND_MAX);
      W.push_back(1 + i);
    }
  }
  void initializeWeights(size_t outputLength) {
    // ld bound_weight = 1.0 / sqrt(W.size());
    // for (auto &it : W) {
    //   ld rand_num = (ld)rand() / RAND_MAX * 2 * bound_weight - bound_weight;
    //   it = rand_num;
    // }
    // W[W.size() - 1] = 0.0;  // zero for bias
  }
  ld exec(vector<ld> &inputs) {
    _inputs = inputs;
    _inputs.push_back(1);  // for bias, extra input unit 1
    ld res = 0;
    for (size_t i = 0; i < W.size(); i++) {
      res += _inputs[i] * W[i];
    }
    return res;
  }
  vector<ld> grad(vector<ld> &inputs) {
    vector<ld> d;
    for (size_t i = 0; i < inputs.size(); i++) {
      d.push_back(W[i]);
    }
    return d;
  }
  void bp(ld grad) {
    if (!grads.size()) grads = vector<ld>(W.size(), 0);
    for (size_t i = 0; i < W.size(); i++) {
      grads[i] += grad * _inputs[i];
    }
  }
  void step() {
    for (size_t i = 0; i < W.size(); i++) {
      W[i] -= grads[i];
    }
  }
  vector<ld> getWeights() { return W; }
  void clearGrad() {
    for (auto &it : grads) it = 0;
  }
};

class Activation : Function {
 public:
  ld input;
  Activation() = default;
  void bp(ld grad) {}
  void initializeWeights(size_t outputLength) {}
  virtual Activation *newInstance() = 0;
  vector<ld> getWeights() { return vector<ld>(); }
  void clearGrad() {}
};

class Sigmoid : public Activation {
 public:
  Sigmoid() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return 1.0 / (1 + exp(-input));
  }
  vector<ld> grad(vector<ld> &inputs) {
    return {exec(inputs) * (1 - exec(inputs))};
  }
  Sigmoid *newInstance() { return new Sigmoid; }
};

class Sgn : public Activation {
 public:
  Sgn() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return 2.0 / (1 + exp(-input)) - 1;
  }
  vector<ld> grad(vector<ld> &inputs) {
    return {2 * exp(-inputs[0]) /
            (2 * exp(-inputs[0]) + (exp(-inputs[0]) * exp(-inputs[0])) + 1)};
  }
  Sgn *newInstance() { return new Sgn; }
};

class LeakyReLU : public Activation {
 public:
  LeakyReLU() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return input > 0 ? input : -1 / 5.5 * input;
  }
  vector<ld> grad(vector<ld> &inputs) {
    return {ld(inputs[0] >= 0 ? 1 : -1 / 5.5)};
  }
  LeakyReLU *newInstance() { return new LeakyReLU; }
};

class ReLU : public Activation {
 public:
  ReLU() = default;
  ld exec(vector<ld> &inputs) {
    input = inputs[0];
    return input > 0 ? input : 0;
  }
  vector<ld> grad(vector<ld> &inputs) { return {ld(inputs[0] >= 0 ? 1 : 0)}; }
  ReLU *newInstance() { return new ReLU; }
};

class Neuron : public ComputeNode {
 public:
  Neuron(size_t inputLength, size_t id)
      : ComputeNode(inputLength, new Linear(inputLength), id) {};
  Neuron(size_t inputLength, Function *fp, size_t id)
      : ComputeNode(inputLength, fp, id) {};
  Neuron(size_t id) : ComputeNode(0, id) {}
  void input(ld v) {  // for input node only
    value = v;
  }
  void bp(ld lr);
  void step();
  void clearGrad() {
    grad = 0;
    if (fp) fp->clearGrad();
  }
};

void Neuron::bp(ld lr) {
  if (fp != nullptr) fp->bp(grad * lr);
  grad = 0;
}

void Neuron::step() {
  if (fp) fp->step();
}

class DNN : public ComputationalGraph {
 public:
  DNN() = default;
  vector<vector<Neuron *>> Layers;
  void addLayer(size_t outputLength);
  Neuron *addNeuron(size_t inputLength);
  Neuron *addNeuron();
  Neuron *addNeuron(Activation *fp);
  void bp(ld lr, vector<ld> &labels);
  vector<ld> eval(vector<ld> &inputs);
  void training(ld lr, size_t epoch, vector<vector<ld>> &inputs,
                vector<vector<ld>> &labels);
  void addLayer(Activation *fp);  // activation layer
  void step();
  vector<vector<vector<ld>>> getWeights();
};

Neuron *DNN::addNeuron() {
  Neuron *nd = new Neuron(Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

Neuron *DNN::addNeuron(Activation *fp) {
  Neuron *nd = new Neuron(1, (Function *)fp, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

Neuron *DNN::addNeuron(size_t inputLength) {
  Neuron *nd = new Neuron(inputLength, Nodes.size());
  Nodes.push_back(nd);
  return nd;
}

void DNN::addLayer(size_t outputLength) {
  size_t inputLength = Layers.size() > 0 ? Layers[Layers.size() - 1].size() : 0;
  vector<Neuron *> Layer;
  vector<ComputeNode *> lastLayer;
  if (inputLength)
    lastLayer = vector<ComputeNode *>(Layers[Layers.size() - 1].begin(),
                                      Layers[Layers.size() - 1].end());
  for (size_t i = 0; i < outputLength; i++) {
    Neuron *nd = inputLength != 0 ? addNeuron(inputLength) : addNeuron();
    if (nd->fp != nullptr) nd->fp->initializeWeights(outputLength);
    Layer.push_back(nd);
    if (inputLength) bindNode(lastLayer, nd);
  }
  Layers.push_back(Layer);
}

void DNN::addLayer(Activation *fp) {
  vector<Neuron *> Layer;
  vector<ComputeNode *> lastLayer = vector<ComputeNode *>(
      Layers[Layers.size() - 1].begin(), Layers[Layers.size() - 1].end());
  for (size_t i = 0; i < lastLayer.size(); i++) {
    Neuron *nd = addNeuron(fp->newInstance());
    Layer.push_back(nd);
    bindNode({lastLayer[i]}, nd);
  }
  Layers.push_back(Layer);
}

void DNN::bp(ld lr, vector<ld> &outputGrad) {
  grad(outputGrad);
  Neuron *n;
  for (auto nd : Nodes) {
    n = (Neuron *)nd;
    n->bp(lr);
  }
}

void DNN::step() {
  // grad(outputGrad);
  Neuron *n;
  for (auto nd : Nodes) {
    n = (Neuron *)nd;
    n->step();
  }
}

vector<ld> DNN::eval(vector<ld> &inputs) {
  for (size_t i = 0; i < inputs.size(); i++) {
    Layers[0][i]->input(inputs[i]);
  }
  return compute();
}

void DNN::training(ld lr, size_t epoch, vector<vector<ld>> &inputs,
                   vector<vector<ld>> &labels) {
  for (size_t i = 0; i < epoch; i++) {
    clearGrad();
    vector<ld> grad(outNodes.size(), 0);
    for (size_t t = 0; t < inputs.size(); t++) {
      vector<ld> res = eval(inputs[t]);
      for (size_t j = 0; j < labels[t].size(); j++) {
        grad[j] = 2 * (res[j] - labels[t][j]) / inputs.size();
      }
      // cout << grad[0] << endl;
      bp(lr, grad);
    }
    step();
  }
}

vector<vector<vector<ld>>> DNN::getWeights() {
  vector<vector<vector<ld>>> W;
  for (auto &layer : Layers) {
    vector<vector<ld>> w;
    for (auto &node : layer) {
      if (!node->fp) continue;
      vector<ld> fw = node->fp->getWeights();
      if (fw.size()) w.push_back(fw);
    }
    W.push_back(w);
  }
  return W;
}

int main() {
  cout << fixed << setprecision(4);
  srand(time(nullptr));
  // srand(42);
  DNN net;
  LeakyReLU *relu = new LeakyReLU;
  Sgn *sgn = new Sgn;
  Sigmoid *sig = new Sigmoid;

  net.addLayer(2);
  net.addLayer(2);
  // net.addLayer(sgn);
  net.addLayer(sig);
  // net.addLayer(relu);
  net.addLayer(1);
  // net.addLayer(relu);
  // net.addLayer(sgn);
  net.addLayer(sig);

  vector<vector<ld>> inputs = {{1, 1}, {0, 0}, {0, 1}, {1, 0}};
  vector<vector<ld>> labels = {{0}, {0}, {1}, {1}};
  cout << "[before training] --------------------" << endl;
  for (size_t i = 0; i < inputs.size(); i++) {
    vector<ld> res = net.eval(inputs[i]);
    cout << "output: " << res[0] << " target: " << labels[i][0] << endl;
  }

  vector<vector<vector<ld>>> W = net.getWeights();
  for (auto &layer : W) {
    for (auto &node : layer) {
      for (auto &w : node) {
        cout << w << " ";
      }
      cout << endl;
    }
    cout << "---------------------" << endl;
  }

  net.training(0.1, 1000, inputs, labels);
  cout << "[after  training] --------------------" << endl;
  for (size_t i = 0; i < inputs.size(); i++) {
    vector<ld> res = net.eval(inputs[i]);
    cout << "output: " << res[0] << " target: " << labels[i][0] << endl;
  }
  W = net.getWeights();
  for (auto &layer : W) {
    for (auto &node : layer) {
      for (auto &w : node) {
        cout << w << " ";
      }
      cout << endl;
    }
    cout << "---------------------" << endl;
  }

  delete sgn;
  delete sig;
  delete relu;
  return 0;
}