Sequence Transduction with Recurrent Neural Networks

Many machine learning tasks can be expressed as the transformation—or \emph{transduction}—of input sequences into output sequences: speech recognition, machine translation, protein secondary structure prediction and text-to-speech to name but a few. One of the key challenges in sequence transduction is learning to represent both the input and output sequences in a way that is invariant to sequential distortions such as shrinking, stretching and translating. Recurrent neural networks (RNNs) are a powerful sequence learning architecture that has proven capable of learning such representations. However RNNs traditionally require a pre-defined alignment between the input and output sequences to perform transduction. This is a severe limitation since \emph{finding} the alignment is the most difficult aspect of many sequence transduction problems. Indeed, even determining the length of the output sequence is often challenging. This paper introduces an end-to-end, probabilistic sequence transduction system, based entirely on RNNs, that is in principle able to transform any input sequence into any finite, discrete output sequence. Experimental results for phoneme recognition are provided on the TIMIT speech corpus.

💡 Research Summary

The paper “Sequence Transduction with Recurrent Neural Networks” addresses a fundamental obstacle in many sequential learning tasks: the need for a predefined alignment between input and output sequences. Traditional recurrent neural network (RNN) approaches either assume a one‑to‑one correspondence or rely on external alignment procedures such as hidden Markov models (HMMs) or dynamic time warping. Both strategies become problematic when the output length is unknown or when the alignment itself is the most difficult part of the problem, as in speech recognition, machine translation, or protein secondary‑structure prediction.

To overcome this limitation, the authors introduce Connectionist Temporal Classification (CTC), a probabilistic loss function that enables an RNN to be trained end‑to‑end without any explicit alignment. CTC augments the target alphabet with a special “blank” symbol and defines the probability of an output label sequence as the sum over all possible alignments (paths) that collapse to that label sequence when blanks and repeated symbols are removed. The forward‑backward algorithm efficiently computes this sum: forward variables α(t, s) accumulate the probability of reaching label index s at time t, while backward variables β(t, s) accumulate the probability of completing the sequence from time t onward. The product α·β, normalized by the total probability Z, yields the posterior probability of each label at each time step, which in turn provides the gradient of the CTC loss with respect to the network outputs.

The network architecture consists of multiple layers of bidirectional Long Short‑Term Memory (LSTM) units followed by a soft‑max layer that outputs a distribution over |𝔏|+1 symbols (the original label set plus blank) at every time step. The bidirectional design allows each output to be conditioned on both past and future context, a crucial advantage for tasks where temporal dependencies are long‑range. Training proceeds by minimizing the negative log‑likelihood of the correct label sequence under the CTC loss, using standard stochastic gradient descent or its variants. Because the loss is defined over whole sequences, mini‑batch training on GPUs is straightforward.

The authors evaluate the method on the TIMIT speech corpus, converting raw acoustic frames (e.g., 39‑dimensional MFCCs sampled every 10 ms) into phoneme sequences. They compare three systems: a conventional HMM‑GMM baseline, an RNN‑HMM hybrid, and the proposed CTC‑RNN model. The CTC‑RNN achieves a phone error rate (PER) of 17.7 %, outperforming the HMM‑GMM baseline (≈20 %) and matching or surpassing the hybrid system, despite not requiring any forced alignment or explicit length modeling. Moreover, the model automatically determines the output length during inference, eliminating the need for a separate length predictor.

The paper also discusses limitations of CTC. Since the loss treats each time step independently given the network outputs, it does not explicitly model long‑range label dependencies, which can be important for language modeling. The insertion of blank symbols can sometimes lead to over‑segmentation, and the assumption that all alignments are equally likely may not hold for highly structured outputs. Subsequent work has extended CTC with additional components such as the RNN‑Transducer, attention mechanisms, and encoder‑decoder architectures to address these issues.

In summary, this work presents a pioneering end‑to‑end framework that couples recurrent neural networks with a novel alignment‑free loss, enabling direct transformation from arbitrary input sequences to discrete output sequences. By eliminating the need for pre‑aligned training data, CTC opened the door to a wide range of sequence‑to‑sequence applications and has become a foundational technique in modern speech recognition, handwriting recognition, and bio‑sequence analysis.