Phase Transitions for the Information Bottleneck in Representation Learning
In the Information Bottleneck (IB) (Tishby et al., 2000), when tuning the relative strength between compression and prediction terms, how do the two terms behave, and what’s their relationship with the dataset and the learned representation? In this paper, we set out to answer this question by studying multiple phase transitions in the IB objective: IB?[p(z|x)] = I(X;Z) ? ?I(Y ;Z), where sudden jumps of dI(Y ;Z)/d? and prediction accuracy are observed with increasing ?. We introduce a definition for IB phase transitions as a qualitative change of the IB loss landscape, and show that the transitions correspond to the onset of learning new classes. Using second-order calculus of variations, we derive a formula that provides the condition for IB phase transitions, and draw its connection with the Fisher information matrix for parameterized models. We provide two perspectives to understand the formula, revealing that each IB phase transition is finding a component of maximum (nonlinear) correlation between X and Y orthogonal to the learned representation, in close analogy with canonical-correlation analysis (CCA) in linear settings. Based on the theory, we present an algorithm for discovering phase transition points. Finally, we verify that our theory and algorithm accurately predict phase transitions in categorical datasets, predict the onset of learning new classes and class difficulty in MNIST, and predict prominent phase transitions in CIFAR10 experiments.
This paper studies the phase transition problem in the information bottleneck (IB) objective and derives a formula for IB phase transitions. Based on the theory developed in the paper, an algorithm is developed to find phase transition points. The interesting observation is phase transition can correspond to learning new class and this paper conjectures in IB for classification, the number of phase transitions is at most C-1, C the number of classes. This observation deserves to be further explored and may be a key to a deeper understanding of neural networks. The theory developed connects the IB objective, dataset and the representation, and thorough proofs are given. The experiments matches the theoretical findings.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Phase Transitions for the Information Bottleneck in Representation Learning
In the Information Bottleneck (IB) (Tishby et al., 2000), when tuning the relative strength between compression and prediction terms, how do the two terms behave, and what’s their relationship with the dataset and the learned representation? In this paper, we set out to answer this question by studying multiple phase transitions in the IB objective: IB?[p(z|x)] = I(X;Z) ? ?I(Y ;Z), where sudden jumps of dI(Y ;Z)/d? and prediction accuracy are observed with increasing ?. We introduce a definition for IB phase transitions as a qualitative change of the IB loss landscape, and show that the transitions correspond to the onset of learning new classes. Using second-order calculus of variations, we derive a formula that provides the condition for IB phase transitions, and draw its connection with the Fisher information matrix for parameterized models. We provide two perspectives to understand the formula, revealing that each IB phase transition is finding a component of maximum (nonlinear) correlation between X and Y orthogonal to the learned representation, in close analogy with canonical-correlation analysis (CCA) in linear settings. Based on the theory, we present an algorithm for discovering phase transition points. Finally, we verify that our theory and algorithm accurately predict phase transitions in categorical datasets, predict the onset of learning new classes and class difficulty in MNIST, and predict prominent phase transitions in CIFAR10 experiments.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper studies the phase transition problem in the information bottleneck (IB) objective and derives a formula for IB phase transitions. Based on the theory developed in the paper, an algorithm is developed to find phase transition points. The interesting observation is phase transition can correspond to learning new class and this paper conjectures in IB for classification, the number of phase transitions is at most C-1, C the number of classes. This observation deserves to be further explored and may be a key to a deeper understanding of neural networks. The theory developed connects the IB objective, dataset and the representation, and thorough proofs are given. The experiments matches the theoretical findings.
assistant
This paper studies the phase transition problem in the information bottleneck (IB) objective and derives a formula for IB phase transitions. Based on the theory developed in the paper, an algorithm is developed to find phase transition points. The interesting observation is phase transition can correspond to learning new class and this paper conjectures in IB for classification, the number of phase transitions is at most C-1, C the number of classes. This observation deserves to be further explored and may be a key to a deeper understanding of neural networks. The theory developed connects the IB objective, dataset and the representation, and thorough proofs are given. The experiments matches the theoretical findings.