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Learning Factored Representations in a Deep Mixture of Experts (1312.4314v3)

Published 16 Dec 2013 in cs.LG

Abstract: Mixtures of Experts combine the outputs of several "expert" networks, each of which specializes in a different part of the input space. This is achieved by training a "gating" network that maps each input to a distribution over the experts. Such models show promise for building larger networks that are still cheap to compute at test time, and more parallelizable at training time. In this this work, we extend the Mixture of Experts to a stacked model, the Deep Mixture of Experts, with multiple sets of gating and experts. This exponentially increases the number of effective experts by associating each input with a combination of experts at each layer, yet maintains a modest model size. On a randomly translated version of the MNIST dataset, we find that the Deep Mixture of Experts automatically learns to develop location-dependent ("where") experts at the first layer, and class-specific ("what") experts at the second layer. In addition, we see that the different combinations are in use when the model is applied to a dataset of speech monophones. These demonstrate effective use of all expert combinations.

Insights on Learning Factored Representations in a Deep Mixture of Experts

The explored article presents a compelling enhancement to the Mixture of Experts (MoE) framework by implementing a Deep Mixture of Experts (DMoE) model. This approach integrates multiple sets of gating and expert networks across different layers, promising efficient high-dimensional computation and scalability in deep learning architectures.

Objective and Methodology

The core contribution of this paper lies in the expansion of the traditional Mixture of Experts model to incorporate deep, stacked layers, thereby exponentially increasing the combination of effective experts while maintaining modest overall model size. The architecture utilizes distinct gating networks at each layer, thus dynamically assigning specialized subsets of the entire model to process individual inputs. The authors argue that this facilitates large-scale but computation-efficient deep networks.

The gating mechanism proposed is pivotal to the DMoE framework. Unlike the traditional MoE, which considers a single gating network, the DMoE strategically utilizes different gating networks across multiple layers, enabling an exponential number of effective expert paths through the combinations of experts at each layer. This organization allows the model to tailor its computation resources actively, based on the input features, leading to sparse activation in practice.

Experimental Analysis and Results

The paper proposes two experimental validations using a translated MNIST dataset and a dataset of speech monophones:

  1. Jittered MNIST Dataset: The DMoE exhibits impressive factorial representation, specializing the first layer in location (where) and the second layer in class (what). The experimental comparison against baseline models demonstrates the DMoE's ability to factor input characteristics efficiently, showing performance on par with fully-connected networks with a similar parameter count.
  2. Monophone Speech Dataset: The results from this experiment also follow the expectations laid out by the authors. Adding complexity with additional layers is shown to be effective, with the DMoE displaying competitive test error rates when compared with both single-expert models and combined-concatenation methods.

The primary insight gained from these experiments is the model's ability to exploit its layered architecture and gating strategy to deliver efficient computation and improved representation learning. The distinct assignment patterns due to translations and speech phonetics further affirm the model’s dynamic adaptability.

Implications and Future Prospects

The proposed DMoE model advances the existing MoE framework by offering a method to build efficient and scalable architectures. Practically, this could facilitate the construction of models with a higher parameter count without a proportional increase in computational expense. Theoretically, it hints at a potential paradigm shift towards architectures where conditional computations are a norm, motivating future exploration into other contexts such as natural language processing, large-scale simulations, and complex decision systems.

Future developments could focus on addressing the challenges related to learning optimal gating mechanisms that fully exploit sparsity in deeper architectures. The paper also points to potential advancements using stochastic selection mechanisms that could further reduce computational requirements, aligning with goals for larger-scale, yet intuitive deep learning networks.

By providing strong empirical support, this research lays foundational work capable of stimulating further explorations into conditional computation and complex model dynamics in neural networks.

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Authors (3)
  1. David Eigen (14 papers)
  2. Marc'Aurelio Ranzato (53 papers)
  3. Ilya Sutskever (58 papers)
Citations (334)
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