Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement (1903.06059v2)

Abstract: The well-known Gumbel-Max trick for sampling from a categorical distribution can be extended to sample $k$ elements without replacement. We show how to implicitly apply this 'Gumbel-Top-$k$' trick on a factorized distribution over sequences, allowing to draw exact samples without replacement using a Stochastic Beam Search. Even for exponentially large domains, the number of model evaluations grows only linear in $k$ and the maximum sampled sequence length. The algorithm creates a theoretical connection between sampling and (deterministic) beam search and can be used as a principled intermediate alternative. In a translation task, the proposed method compares favourably against alternatives to obtain diverse yet good quality translations. We show that sequences sampled without replacement can be used to construct low-variance estimators for expected sentence-level BLEU score and model entropy.

Stochastic Beam Search: An Advanced Approach to Sequence Sampling

The paper "Stochastic Beams and Where to Find Them: The Gumbel-Top-$k$ Trick for Sampling Sequences Without Replacement" presents an innovative approach in the field of sequence modeling and machine learning. It introduces a novel sampling method called Stochastic Beam Search (SBS), which applies the Gumbel-Top-$k$ trick to sample sequences from a probability distribution without replacement. This approach advances the capabilities of sequence models, commonly applied in domains such as neural machine translation and image captioning.

Key Contributions

The primary contribution of the paper is the development of the Gumbel-Top-$k$ trick, extending the well-known Gumbel-Max trick to sample $k$ elements without replacement efficiently. This method is significant for tasks where redundancy in sampled sequences is undesirable, such as when seeking diverse outputs in translation or captioning tasks. The paper elucidates the mechanism of sampling sequences over factorized distributions without needing to instantiate all possible sequences explicitly. Notably, the algorithm's computational complexity only scales linearly with the number of samples, $k$, and the maximum sequence length.

Stochastic Beam Search serves as an intermediary between traditional beam search and random sampling, synthesized through a theoretical connection between sampling and deterministic beam search methods. In empirical evaluations, such as a translation task, SBS demonstrated superior performance by producing diverse, high-quality translations compared to alternative sampling techniques.

Theoretical Framework and Numerical Results

The authors present a comprehensive theoretical framework detailing how the Gumbel-Top-$k$ trick can be implicitly woven into sequence models. The application of Gumbel-Top-$k$ allows for a top-down sampling strategy that efficiently computes the exact samples from an exponentially large domain using the Stochastic Beam Search algorithm. This efficiency is a paramount advantage when dealing with large datasets where computational resources are a limiting factor.

In experimental settings involving neural machine translation, the algorithm achieved encouraging results. It facilitated the generation of diverse translations, surpassing methods like Diverse Beam Search and sampling with replacement. The paper further highlights SBS's effectiveness in constructing low-variance estimators for metrics such as BLEU score and model entropy, underscoring the practical implications of the model for quality assessment in language tasks.

Implications and Future Directions

The Stochastic Beam Search methodology significantly impacts both the theoretical and applied aspects of sequence modeling. Practically, it offers an efficient, probabilistically grounded alternative to existing sequence generation techniques, thus enhancing the toolkit available for developing applications in machine translation, speech recognition, and other structured prediction tasks.

Theoretically, this work opens avenues for new research directions in sequence modeling, particularly in developing sampling techniques that intertwine the randomness and deterministic structure. The probabilistic interpretation of beam search offered by Stochastic Beam Search could also lead to advancements in training models on sequence level objectives, where both accuracy and diversity are valued.

The paper lays the groundwork for extending the principles of SBS into more complex models and encourages further explorations into hybrid algorithms that blend sampling and traditional search methods for efficient sequence predictions. Future work may also consider scalability in varied real-world applications, enhancing our understanding of sampling without replacement in diverse contexts.

In summary, the introduction of Stochastic Beam Search represents a substantial improvement in the field of machine learning and sequence modeling, providing a reliable, scalable, and innovative approach to tackling the challenges associated with sequence sampling without replacement.