Soft Merging of Experts with Adaptive Routing

Sparsely activated neural networks with conditional computation learn to route their inputs through different "expert" subnetworks, providing a form of modularity that densely activated models lack. Despite their possible benefits, models with learned routing often underperform their parameter-matched densely activated counterparts as well as models that use non-learned heuristic routing strategies. In this paper, we hypothesize that these shortcomings stem from the gradient estimation techniques used to train sparsely activated models that use non-differentiable discrete routing decisions. To address this issue, we introduce Soft Merging of Experts with Adaptive Routing (SMEAR), which avoids discrete routing by using a single "merged" expert constructed via a weighted average of all of the experts' parameters. By routing activations through a single merged expert, SMEAR does not incur a significant increase in computational costs and enables standard gradient-based training. We empirically validate that models using SMEAR outperform models that route based on metadata or learn sparse routing through gradient estimation. Furthermore, we provide qualitative analysis demonstrating that the experts learned via SMEAR exhibit a significant amount of specialization. All of the code used in our experiments is publicly available

Learning-Based Methods for Comparing Sequences, with Applications to Audio-to-MIDI Alignment and Matching

Sequences of feature vectors are a natural way of representing temporal data. Given a database of sequences, a fundamental task is to find the database entry which is the most similar to a query. In this thesis, we present learning-based methods for efficiently and accurately comparing sequences in order to facilitate large-scale sequence search. Throughout, we will focus on the problem of matching MIDI files (a digital score format) to a large collection of audio recordings of music. The combination of our proposed approaches enables us to create the largest corpus of paired MIDI files and audio recordings ever assembled. Dynamic time warping (DTW) has proven to be an extremely effective method for both aligning and matching sequences. However, its performance is heavily affected by factors such as the feature representation used and its adjustable parameters. We therefore investigate automatically optimizing DTW-based alignment and matching of MIDI and audio data. Our approach uses Bayesian optimization to tune system design and parameters over a synthetically-created dataset of audio and MIDI pairs. We then perform an exhaustive search over DTW score normalization techniques to find the optimal method for reporting a reliable alignment confidence score, as required in matching tasks. This results in a DTW-based system which is conceptually simple and highly accurate at both alignment and matching. We also verify that this system achieves high performance in a large-scale qualitative evaluation of real-world alignments. Unfortunately, DTW can be far too inefficient for large-scale search when sequences are very long and consist of high-dimensional feature vectors. We therefore propose a method for mapping sequences of continuously-valued feature vectors to downsampled sequences of binary vectors. Our approach involves training a pair of convolutional networks to map paired groups of subsequent feature vectors to a Hamming space where similarity is preserved. Evaluated on the task of matching MIDI files to a large database of audio recordings, we show that this technique enables 99.99\% of the database to be discarded with a modest false reject rate while only requiring 0.2\% of the time to compute. Even when sped-up with a more efficient representation, the quadratic complexity of DTW greatly hinders its feasibility for very large-scale search. This cost can be avoided by mapping entire sequences to fixed-length vectors in an embedded space where sequence similarity is approximated by Euclidean distance. To achieve this embedding, we propose a feed-forward attention-based neural network model which can integrate arbitrarily long sequences. We show that this approach can extremely efficiently prune 90\% of our audio recording database with high confidence. After developing these approaches, we applied them together to the practical task of matching 178,561 unique MIDI files to the Million Song Dataset. The resulting ``Lakh MIDI Dataset'' provides a potential bounty of ground truth information for audio content-based music information retrieval. This can include transcription, meter, lyrics, and high-level musicological features. The reliability of the resulting annotations depends both on the quality of the transcription and the accuracy of the score-to-audio alignment. We therefore establish a baseline of reliability for score-derived information for different content-based MIR tasks. Finally, we discuss potential future uses of our dataset and the learning-based sequence comparison methods we developed

Learning Hard Alignments with Variational Inference

There has recently been significant interest in hard attention models for tasks such as object recognition, visual captioning and speech recognition. Hard attention can offer benefits over soft attention such as decreased computational cost, but training hard attention models can be difficult because of the discrete latent variables they introduce. Previous work used REINFORCE and Q-learning to approach these issues, but those methods can provide high-variance gradient estimates and be slow to train. In this paper, we tackle the problem of learning hard attention for a sequential task using variational inference methods, specifically the recently introduced VIMCO and NVIL. Furthermore, we propose a novel baseline that adapts VIMCO to this setting. We demonstrate our method on a phoneme recognition task in clean and noisy environments and show that our method outperforms REINFORCE, with the difference being greater for a more complicated task