In this paper, we propose TauRieL and target Traveling Salesman Problem (TSP) since it has broad applicability in theoretical and applied sciences. TauRieL utilizes an actor-critic inspired architecture that adopts ordinary feedforward nets to obtain a policy update vector @math . Then, we use @math to improve the state transition matrix from which we generate the policy. Also, the state transition matrix allows the solver to initialize from precomputed solutions such as nearest neighbors. In an online learning setting, TauRieL unifies the training and the search where it can generate near-optimal results in seconds. The input to the neural nets in the actor-critic architecture are raw 2-D inputs, and the design idea behind this decision is to keep neural nets relatively smaller than the architectures with wide embeddings with the tradeoff of omitting any distributed representations of the embeddings. Consequently, TauRieL generates TSP solutions two orders of magnitude faster per TSP instance as compared to state-of-the-art offline techniques with a performance impact of 6.1 in the worst case.
Deudon el at. @cite_4 proposes a TSP solver framework based on the attention architecture @cite_13 . The attention mechanism consists of the input encoder and output decoder. The input encoder uses multi-head attention mechanism to compute the embeddings of the input nodes. Given an input set, the output decoder calculates a probability distribution over the input nodes using attention. The decoder uses the chain rule to factorize the probability of a tour as the mean of all the node embeddings that are generated at each hidden attention layer. The critic net computes a glimpse vector, a weighted sum of the action vectors. The authors also improve the best tour results by using 2-opt heuristic.
@cite_13 @cite_4
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We propose a novel extension of the encoder-decoder framework, called a review network. The review network is generic and can enhance any existing encoder- decoder model: in this paper, we consider RNN decoders with both CNN and RNN encoders. The review network performs a number of review steps with attention mechanism on the encoder hidden states, and outputs a thought vector after each review step; the thought vectors are used as the input of the attention mechanism in the decoder. We show that conventional encoder-decoders are a special case of our framework. Empirically, we show that our framework improves over state-of- the-art encoder-decoder systems on the tasks of image captioning and source code captioning. Celebrated and its fruitful variants are powerful models to achieve excellent performance on the tasks that map sequences to sequences. However, these are many machine learning tasks with inputs naturally represented in a form of graphs, which imposes significant challenges to existing Seq2Seq models for lossless conversion from its graph form to the sequence. In this work, we present a general end-to-end approach to map the input graph to a sequence of vectors, and then another attention-based LSTM to decode the target sequence from these vectors. Specifically, to address inevitable information loss for data conversion, we introduce a novel graph-to-sequence neural network model that follows the encoder-decoder architecture. Our method first uses an improved graph-based neural network to generate the node and graph embeddings by a novel aggregation strategy to incorporate the edge direction information into the node embeddings. We also propose an attention based mechanism that aligns node embeddings and decoding sequence to better cope with large graphs. Experimental results on bAbI task, Shortest Path Task, and Natural Language Generation Task demonstrate that our model achieves the state-of-the-art performance and significantly outperforms other baselines. We also show that with the proposed aggregation strategy, our proposed model is able to quickly converge to good performance. We replace the Hidden Markov Model (HMM) which is traditionally used in in continuous speech recognition with a bi-directional recurrent neural network encoder coupled to a recurrent neural network decoder that directly emits a stream of phonemes. The alignment between the input and output sequences is established using an attention mechanism: the decoder emits each symbol based on a context created with a subset of input symbols elected by the attention mechanism. We report initial results demonstrating that this new approach achieves phoneme error rates that are comparable to the state-of-the-art HMM-based decoders, on the TIMIT dataset. We propose a framework for solving combinatorial optimization problems of which the output can be represented as a sequence of input elements. As an alternative to the Pointer Network, we parameterize a policy by a model based entirely on (graph) attention layers, and train it efficiently using REINFORCE with a simple and robust baseline based on a deterministic (greedy) rollout of the best policy found during training. We significantly improve over state-of-the-art results for learning algorithms for the 2D Euclidean TSP, reducing the optimality gap for a single tour construction by more than 75 (to 0.33 ) and 50 (to 2.28 ) for instances with 20 and 50 nodes respectively.