<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def predict(self, peptides, allele_encoding=None, batch_size=4096):
 """ Predict affinities. If peptides are specified as EncodableSequences, then the predictions will be cached for this predictor as long as the EncodableSequences object remains in memory. The cache is keyed in the object identity of the EncodableSequences, not the sequences themselves. Parameters peptides : EncodableSequences or list of string allele_encoding : AlleleEncoding, optional Only required when this model is a pan-allele model batch_size : int batch_size passed to Keras Returns ------- numpy.array of nM affinity predictions """

        assert self.prediction_cache is not None
        use_cache = (
            allele_encoding is None and
            isinstance(peptides, EncodableSequences))
        if use_cache and peptides in self.prediction_cache:
            return self.prediction_cache[peptides].copy()

        x_dict = {
            'peptide': self.peptides_to_network_input(peptides)
        }
        if allele_encoding is not None:
            allele_input = self.allele_encoding_to_network_input(allele_encoding)
            x_dict['allele'] = allele_input

        network = self.network(borrow=True)
        raw_predictions = network.predict(x_dict, batch_size=batch_size)
        predictions = numpy.array(raw_predictions, dtype = "float64")[:,0]
        result = to_ic50(predictions)
        if use_cache:
            self.prediction_cache[peptides] = result
        return result