With a view towards molecular communication systems and molecular multi-agent systems, we propose the Chemical Baum-Welch Algorithm, a novel reaction network scheme that learns parameters for Hidden Markov Models (HMMs). Each reaction in our scheme changes only one molecule of one species to one molecule of another. The reverse change is also accessible but via a different set of enzymes, in a design reminiscent of futile cycles in biochemical pathways. We show that every fixed point of the Baum-Welch algorithm for HMMs is a fixed point of our reaction network scheme, and every positive fixed point of our scheme is a fixed point of the Baum-Welch algorithm. We prove that the “Expectation” step and the “Maximization” step of our reaction network separately converge exponentially fast. We simulate mass-action kinetics for our network on an example sequence, and show that it learns the same parameters for the HMM as the Baum-Welch algorithm.
Recently @cite_3 have given a brilliant experimental demonstration of learning with DNA molecules. They have empirically demonstrated a DNA molecular system that can classify @math types of handwritten digits from the MNIST database. Their approach is based on the notion of winner-takes-all'' circuits due to Maass @cite_13 which was originally a proposal for how neural networks in the brain work. Winner-take-all might also be capable of approximating HMM learning, at least in theory @cite_7 , and it is worth understanding precisely how such schemes relate to the kind of scheme we have described here. It is conceivable that our scheme could be converted to winner-take-all by getting different species in the same flower to give negative feedback to each other. This might well lead to sampling the most likely path, performing a decoding task similar to the Viterbi algorithm.
@cite_13 @cite_7 @cite_3
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From bacteria following simple chemical gradients to the brain distinguishing complex odour information, the ability to recognize molecular patterns is essential for biological organisms. This type of information-processing function has been implemented using DNA-based neural networks, but has been limited to the recognition of a set of no more than four patterns, each composed of four distinct DNA molecules. Winner-take-all computation has been suggested as a potential strategy for enhancing the capability of DNA-based neural networks. Compared to the linear-threshold circuits and Hopfield networks used previously, winner-take-all circuits are computationally more powerful, allow simpler molecular implementation and are not constrained by the number of patterns and their complexity, so both a large number of simple patterns and a small number of complex patterns can be recognized. Here we report a systematic implementation of winner-take-all neural networks based on DNA-strand-displacement reactions. We use a previously developed seesaw DNA gate motif, extended to include a simple and robust component that facilitates the cooperative hybridization that is involved in the process of selecting a ‘winner’. We show that with this extended seesaw motif DNA-based neural networks can classify patterns into up to nine categories. Each of these patterns consists of 20 distinct DNA molecules chosen from the set of 100 that represents the 100 bits in 10 × 10 patterns, with the 20 DNA molecules selected tracing one of the handwritten digits ‘1’ to ‘9’. The network successfully classified test patterns with up to 30 of the 100 bits flipped relative to the digit patterns ‘remembered’ during training, suggesting that molecular circuits can robustly accomplish the sophisticated task of classifying highly complex and noisy information on the basis of similarity to a memory. This article initiates a rigorous theoretical analysis of the computational power of circuits that employ modules for computing winner-take-all. Computational models that involve competitive stages have so far been neglected in computational complexity theory, although they are widely used in computational brain models, artificial neural networks, and analog VLSI. Our theoretical analysis shows that winner-take-all is a surprisingly powerful computational module in comparison with threshold gates (also referred to as McCulloch-Pitts neurons) and sigmoidal gates. We prove an optimal quadratic lower bound for computing winner-take-all in any feedforward circuit consisting of threshold gates. In addition we show that arbitrary continuous functions can be approximated by circuits employing a single soft winner-take-all gate as their only nonlinear operation. Our theoretical analysis also provides answers to two basic questions raised by neurophysiologists in view of the well-known asymmetry between excitatory and inhibitory connections in cortical circuits: how much computational power of neural networks is lost if only positive weights are employed in weighted sums and how much adaptive capability is lost if only the positive weights are subject to plasticity. Most previous work on trainable language generation has focused on two paradigms: (a) using a generation decisions of an existing generator. Both approaches rely on the existence of a handcrafted generation component, which is likely to limit their scalability to new domains. The first contribution of this article is to present Bagel, a fully data-driven generation method that treats the language generation task as a search for the most likely sequence of semantic concepts and realization phrases, according to Factored Language Models (FLMs). As domain utterances are not readily available for most natural language generation tasks, a large creative effort is required to produce the data necessary to represent human linguistic variation for nontrivial domains. This article is based on the assumption that learning to produce paraphrases can be facilitated by collecting data from a large sample of untrained annotators using crowdsourcing—rather than a few domain experts—by relying on a coarse meaning representation. A second contribution of this article is to use crowdsourced data to show how dialogue naturalness can be improved by learning to vary the output utterances generated for a given semantic input. Two data-driven methods for generating paraphrases in dialogue are presented: (a) by sampling from the n-best list of realizations produced by Bagel's FLM reranker; and (b) by learning a structured perceptron predicting whether candidate realizations are valid paraphrases. We train Bagel on a set of 1,956 utterances produced by 137 annotators, which covers 10 types of dialogue acts and 128 semantic concepts in a tourist information system for Cambridge. An automated evaluation shows that Bagel outperforms utterance class LM baselines on this domain. A human evaluation of 600 resynthesized dialogue extracts shows that Bagel's FLM output produces utterances comparable to a handcrafted baseline, whereas the perceptron classifier performs worse. Interestingly, human judges find the system sampling from the n-best list to be more natural than a system always returning the first-best utterance. The judges are also more willing to interact with the n-best system in the future. These results suggest that capturing the large variation found in human language using data-driven methods is beneficial for dialogue interaction. We propose introspective convolutional networks (ICN) that emphasize the importance of having convolutional neural networks empowered with generative capabilities. We employ a reclassification-by-synthesis algorithm to perform training using a formulation stemmed from the Bayes theory. Our ICN tries to iteratively: (1) synthesize pseudo-negative samples; and (2) enhance itself by improving the classification. The single CNN classifier learned is at the same time generative --- being able to directly synthesize new samples within its own discriminative model. We conduct experiments on benchmark datasets including MNIST, CIFAR-10, and SVHN using state-of-the-art CNN architectures, and observe improved classification results.