This blog post, written by Eric Jiang from Google Brain, presents a comprehensive framework for evaluating machine learning research through three key aspects: Expressivity, Trainability, and Generalization. The article is considered one of the most insightful summaries of recent advancements in machine learning techniques, offering valuable insights for researchers and practitioners alike.
When I read a paper on machine learning, I often ask myself whether its contribution falls under one or more of these categories: Expressivity, Trainability, or Generalization. This classification was introduced to me by my colleague Jascha Sohl-Dickstein and has since become a useful lens for understanding how different research areas connect within the broader field of AI.
In this post, I explore how these concepts intersect with current research in supervised learning, unsupervised learning, and reinforcement learning as of November 2017. I also distinguish between two types of generalization: "weak" and "strong," which I will discuss separately. Below is a summary of my perspective:
[Image: Google engineers machine learning dry goods: from the three aspects of expressiveness, trainability and generalization]
I would like to thank Jascha Sohl-Dickstein and Ben Poole for their feedback and editing, and Marcin Moczulski for his helpful discussions on RNN trainability. This article reflects my personal views and opinions, and any factual errors are solely my responsibility.
Expressivity refers to what a model can compute. It captures the complexity of functions that can be represented by parametric models such as neural networks. Deep neural networks have shown an exponential increase in expressiveness with depth, suggesting that many modern problems in supervised, unsupervised, and reinforcement learning can be addressed with medium-scale networks. One piece of evidence is the ability of deep networks to memorize large datasets.
Neural networks are capable of representing a wide range of data types—continuous, complex, discrete, and even random variables. With advances in generative modeling and Bayesian deep learning, they have been used to build probabilistic neural networks that achieve impressive results in generating realistic data.
Recent breakthroughs in generative modeling, such as those achieved by GANs, highlight the expressive power of neural networks. They can generate highly complex data manifolds (like images and audio) that are almost indistinguishable from real data. For instance, NVIDIA's GAN architecture produces outputs that are visually compelling, despite some imperfections.
Unsupervised learning is not limited to generative tasks. Some researchers, like Yann LeCun, refer to it as "predictive learning," aiming to infer past, present, or future states. However, many unsupervised methods focus on predicting complex joint distributions, making generative modeling a strong benchmark for evaluating performance.
Neural networks are also sufficient for reinforcement learning. A small network can solve tasks like Atari and Mujoco control, although training remains challenging. While expressivity is relatively easy to enhance (by adding more layers), measuring it effectively remains a mystery. We don't yet know what kind of problems require significantly larger networks, or why certain tasks demand such computational power. Do we need models as powerful as the human brain to achieve human-like intelligence? Does solving generalization require ultra-powerful models?
Trainability addresses the question of whether we can find a good model given a fully expressive model space. Machine learning involves searching for better models from a potentially vast space, typically framed as an optimization problem. Various optimization techniques are used, including minimizing cross-entropy loss in classification tasks.
However, defining the optimization goal can be challenging, especially in scenarios where perceptual loss is difficult to quantify. Techniques like co-adaptation and competitive self-play have emerged as effective strategies. These approaches avoid explicitly defining perceptual loss and instead rely on implicit optimization goals.
Evolutionary strategies offer another approach, simulating populations of models and updating them based on dynamic rules. While promising, these methods are still evolving.
Supervised learning has made significant progress in terms of trainability, thanks to techniques like batch normalization, residual networks, and good initialization. However, RNNs remain challenging, though recent work has improved their trainability.
Unsupervised learning faces additional challenges due to the complexity of the data it processes. GANs have seen notable improvements in trainability, with techniques like Wasserstein distance helping to stabilize training.
Reinforcement learning, however, continues to struggle with trainability and generalization. Issues like sparse rewards and non-stationary environments make it particularly difficult. Despite these challenges, progress is being made, and new methods like imitation learning and learning-to-learn are showing promise.
Generalization is the core of machine learning itself. It refers to how well a model performs on unseen data after being trained on a dataset. There are two main scenarios: weak generalization, where the test and training data come from the same distribution, and strong generalization, where they come from different distributions.
Weak generalization involves assessing how well a model handles small perturbations in the data distribution. Techniques like regularization help prevent overfitting, but they are often crude and may sacrifice trainability.
Strong generalization requires a model to understand the underlying structure of the data, beyond just fitting the training set. This is crucial for real-world applications, where the test data may differ significantly from the training data.
To improve generalization, we need to develop models that capture the basic laws of the world and learn abstract representations. This involves moving beyond static models and creating systems that can think, remember, and learn in real time.
In conclusion, while supervised learning has made great strides in trainability, unsupervised learning remains challenging, and reinforcement learning still faces significant hurdles. Solving generalization is key to advancing the field, and ongoing research into causal reasoning, representation learning, and adaptive systems offers promising directions.
[1] Some research areas, like interpretability, do not fit neatly into the framework of expressivity, trainability, and generalization. Understanding why a model makes certain decisions is crucial in high-risk fields like medicine. Similarly, differential privacy imposes constraints on ML models, but these topics are beyond the scope of this article.
[2] A simple explanation: a fully connected layer of size N followed by a ReLU nonlinearity can divide a vector space into N piecewise linear regions. Adding more layers increases the number of regions exponentially.
[3] Multi-level optimization problems involve both external and internal loops, where adaptation occurs simultaneously. Examples include asynchronous parallel processes and co-evolving species in ecosystems.
[4] Seq2seq with attention may excel due to trainability rather than expressivity or generalization. Proper initialization could yield similar results without attention mechanisms.
[5] To combat adversarial attacks, one approach is to use randomized models during inference. Each call selects a random model from a set of trained models, making it difficult to calculate gradients. Additionally, using multimodal data can enhance robustness against interference.
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