**Variational Bi-LSTM**

Recurrent neural networks like long short-term memory (LSTM) are important architectures for sequential prediction tasks. LSTMs (and RNNs in general) model sequences along the forward time direction. Bidirectional LSTMs (Bi-LSTMs) on the other hand model sequences along both forward and backward directions and are generally known to perform better at such tasks because they capture a richer representation of the data. In the training of Bi-LSTMs, the forward and backward paths are learned independently. We propose a variant of the Bi-LSTM architecture, which we call Variational Bi-LSTM, that creates a channel between the two paths (during training, but which may be omitted during inference); thus optimizing the two paths jointly. We arrive at this joint objective for our model by minimizing a variational lower bound of the joint likelihood of the data sequence. Our model acts as a regularizer and encourages the two networks to inform each other in making their respective predictions using distinct information. We perform ablation studies to better understand the different components of our model and evaluate the method on various benchmarks, showing state-of-the-art performance. … **Deductive Reasoning**

Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion. Deductive reasoning goes in the same direction as that of the conditionals, and links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true. Deductive reasoning (‘top-down logic’) contrasts with inductive reasoning (‘bottom-up logic’) in the following way; in deductive reasoning, a conclusion is reached reductively by applying general rules which hold over the entirety of a closed domain of discourse, narrowing the range under consideration until only the conclusion(s) is left. In inductive reasoning, the conclusion is reached by generalizing or extrapolating from specific cases to general rules, i.e., there is epistemic uncertainty. However, the inductive reasoning mentioned here is not the same as induction used in mathematical proofs – mathematical induction is actually a form of deductive reasoning. Deductive reasoning differs from abductive reasoning by the direction of the reasoning relative to the conditionals. Deductive reasoning goes in the same direction as that of the conditionals, whereas abductive reasoning goes in the opposite direction to that of the conditionals. … **Ridge Polynomial Neural Network with Error-Output Feedback (RPNN-EOF)**

Time series forecasting gets much attention due to its impact on many practical applications. Higher-order neural network with recurrent feedback is a powerful technique which used successfully for forecasting. It maintains fast learning and the ability to learn the dynamics of the series over time. For that, in this paper, we propose a novel model which is called Ridge Polynomial Neural Network with Error-Output Feedbacks (RPNN-EOFs) that combines the properties of higher order and error-output feedbacks. The well-known Mackey-Glass time series is used to test the forecasting capability of RPNN-EOFS. Simulation results showed that the proposed RPNN-EOFs provides better understanding for the Mackey-Glass time series with root mean square error equal to 0.00416. This result is smaller than other models in the literature. Therefore, we can conclude that the RPNN-EOFs can be applied successfully for time series forecasting. … **BERTScore**

We propose BERTScore, an automatic evaluation metric for text generation. Analogous to common metrics, \method computes a similarity score for each token in the candidate sentence with each token in the reference. However, instead of looking for exact matches, we compute similarity using contextualized BERT embeddings. We evaluate on several machine translation and image captioning benchmarks, and show that BERTScore correlates better with human judgments than existing metrics, often significantly outperforming even task-specific supervised metrics. …

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