Project: s41467-024-46976-4 | Function: detect (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Implements the dynamic neuron growth mechanism with exponentially decaying threshold based on Dirichlet prior, determining when to add new neurons during online continual learning

**KEY TERMS:** {
  "alpha": "Dirichlet prior hyperparameter α",
  "age": "current training iteration t",
  "thresh": "growth threshold ε computed from Dirichlet prior",
  "detect_type": "detection method selector",
  "avgmxlk": "average maximum likelihood for threshold computation",
  "gamma": "decay factor for moving average"
}

**CONTEXT CODE:**             return wts


    # Batch update for case where number of batch images equals num hidden layer neurons
    def load_wts(self, data):
        with torch.no_grad():
            self.wts.weight *= 0.0
            self.wts.weight.data += data.t()


    # Batch update for case where number of batch images is greater than num hidden layer neurons
    def load_wts2(self, data):
        with torch.no_grad():
            self.wts.weight *= 0.0
            self.wts.weight.data += data[0:self.layer_szs[1], :].t()
            self.counts += 1
            for x in range(self.layer_szs[1], data.size(0)):
                lk = self.infer_step(data[x].view(1,-1))
                z = F.one_hot(torch.argmax(lk, dim=1), num_classes=self.layer_szs[1]).float()
                self.update_wts(lk, z, data[x].view(1,-1))



    def update_wts(self, lk, z, input):
        # MASKED: Local Hebbian-like MAP learning rule implementation
        raise NotImplementedError("This function is masked for testing purposes.")



    def wt_update(self, targ, z, N):
        with torch.no_grad():
            # Update weights
            p = self.wts(z)
            err_pred = targ - p
            dw = err_pred.t().matmul(z)

            #Avg
            if self.wtUp == 0 or self.wtUp == 2:
                self.wts.weight += dw / self.counts[N]

            #Overwrite
            elif self.wtUp == 1:
                self.wts.weight += dw

            #Constant lr
            else:
                self.wts.weight += dw * self.l_rate



    def detect(self, mxlk, mxC):
        # MASKED: Dynamic neuron growth mechanism with exponentially decaying threshold implementation
        raise NotImplementedError("This function is masked for testing purposes.")



    def rules(self, lk, z, targ):
        with torch.no_grad():
            mxlk = torch.max(lk)
            mxC = torch.argmax(lk)
            new_detect = self.detect(mxlk, mxC)

            # If new cluster detected
            if new_detect and self.wtUp != 2:

                z *= 0
                N = torch.argmin(self.counts)
                z[0, N] = 1
                self.counts[N] = 1
                self.prior[N] = 1
                self.wt_update(targ, z, N)

            elif self.wtUp != 1:
                self.counts[mxC] += 1
                self.update_prior(mxlk, mxC)
                self.wt_update(targ, z, mxC)

            self.age += 1



    def rule2(self, z, targ):
        # Update cluster with max likelihood of data with a gradient step
        with torch.no_grad():
            N = torch.argmax(z)
            self.wt_update(targ, z, N)
            self.age += 1




    def update_prior(self, mxlk, mxC):
        '''new_angle = torch.arccos(self.prior[mxC]) + (torch.arccos(mxlk) - torch.arccos(self.prior[mxC])) / (self.counts[mxC] + 1)
        self.prior[mxC] = torch.cos(new_angle)'''
        self.prior[mxC] = self.prior[mxC] + (mxlk - self.prior[mxC]) / (self.counts[mxC] + 1)



    def infer_step(self, input):
        # MASKED: Core MAP inference using mean-shifted cosine similarity implementation
        raise NotImplementedError("This function is masked for testing purposes.")




    def predict(self, z):
        return self.wts(z)


    def recall(self, targ):
        with torch.no_grad():
            t = targ.clone().view(targ.size(0), -1)
            a = self.infer_step(t)
            if self.actFunc == 0:
                z = F.one_hot(torch.argmax(a, dim=1), num_classes=self.layer_szs[1]).float().to('cpu')
            else:
                z = softmax(a * self.beta)

            return self.predict(z)



    def recognize(self, targ):
        with torch.no_grad():
            t = targ.clone().view(targ.size(0), -1)
            a = self.infer_step(t)
            mxlk = torch.max(a, dim=1)[0]
            mxC = torch.argmax(a, dim=1)
            return mxlk >= (self.prior[mxC] * self.gamma)



    def recognize2(self, targ):
        with torch.no_grad():
            t = targ.clone().view(targ.size(0), -1)
            p = self.recall(t)
            err = torch.mean(torch.square(t - p), dim=1)
            return err <= (self.err_avg * self.gamma)

Complete the function implementation replacing "raise NotImplementedError".