On the Information Bottleneck Theory of Deep Learning
The practical successes of deep neural networks have not been matched by theoretical progress that satisfyingly explains their behavior. In this work, we study the information bottleneck (IB) theory of deep learning, which makes three specific claims: first, that deep networks undergo two distinct phases consisting of an initial fitting phase and a subsequent compression phase; second, that the compression phase is causally related to the excellent generalization performance of deep networks; and third, that the compression phase occurs due to the diffusion-like behavior of stochastic gradient descent. Here we show that none of these claims hold true in the general case. Through a combination of analytical results and simulation, we demonstrate that the information plane trajectory is predominantly a function of the neural nonlinearity employed: double-sided saturating nonlinearities like tanh yield a compression phase as neural activations enter the saturation regime, but linear activation functions and single-sided saturating nonlinearities like the widely used ReLU in fact do not. Moreover, we find that there is no evident causal connection between compression and generalization: networks that do not compress are still capable of generalization, and vice versa. Next, we show that the compression phase, when it exists, does not arise from stochasticity in training by demonstrating that we can replicate the IB findings using full batch gradient descent rather than stochastic gradient descent. Finally, we show that when an input domain consists of a subset of task-relevant and task-irrelevant information, hidden representations do compress the task-irrelevant information, although the overall information about the input may monotonically increase with training time, and that this compression happens concurrently with the fitting process rather than during a subsequent compression period.
 A thorough investigation on Info Bottleneck and deep learning, nice to read with interesting experiments and references. Even though not all of the approach is uncontroversial (as the discussion shows), the paper contributes to much needed theory of deep learning rather than just another architecture. Estimating the mutual information could have been handled in a more sophisticated way (eg using a Kraskov estimator rather than simple binning), and given that no noise is usually added the discussion about noise and generalisation doesn*t seem to make too much sense to me. It would have been good to see a discussion whether another measurement that would be useful for single-sided saturating nonlinearities that do show a compression (eg information from a combination of layers), from learnt representations that are different to representations learnt using double-sided nonlinearities. Regarding the finite representation of units (as in the discussion) it might be helpful to also consider an implementation of a network with arbitrary precision arithmetic as an additional experiment. Overall I think it would be nice to see the paper accepted at the very least to continue the discussion.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
On the Information Bottleneck Theory of Deep Learning
The practical successes of deep neural networks have not been matched by theoretical progress that satisfyingly explains their behavior. In this work, we study the information bottleneck (IB) theory of deep learning, which makes three specific claims: first, that deep networks undergo two distinct phases consisting of an initial fitting phase and a subsequent compression phase; second, that the compression phase is causally related to the excellent generalization performance of deep networks; and third, that the compression phase occurs due to the diffusion-like behavior of stochastic gradient descent. Here we show that none of these claims hold true in the general case. Through a combination of analytical results and simulation, we demonstrate that the information plane trajectory is predominantly a function of the neural nonlinearity employed: double-sided saturating nonlinearities like tanh yield a compression phase as neural activations enter the saturation regime, but linear activation functions and single-sided saturating nonlinearities like the widely used ReLU in fact do not. Moreover, we find that there is no evident causal connection between compression and generalization: networks that do not compress are still capable of generalization, and vice versa. Next, we show that the compression phase, when it exists, does not arise from stochasticity in training by demonstrating that we can replicate the IB findings using full batch gradient descent rather than stochastic gradient descent. Finally, we show that when an input domain consists of a subset of task-relevant and task-irrelevant information, hidden representations do compress the task-irrelevant information, although the overall information about the input may monotonically increase with training time, and that this compression happens concurrently with the fitting process rather than during a subsequent compression period.
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>



 A thorough investigation on Info Bottleneck and deep learning, nice to read with interesting experiments and references. Even though not all of the approach is uncontroversial (as the discussion shows), the paper contributes to much needed theory of deep learning rather than just another architecture. Estimating the mutual information could have been handled in a more sophisticated way (eg using a Kraskov estimator rather than simple binning), and given that no noise is usually added the discussion about noise and generalisation doesn*t seem to make too much sense to me. It would have been good to see a discussion whether another measurement that would be useful for single-sided saturating nonlinearities that do show a compression (eg information from a combination of layers), from learnt representations that are different to representations learnt using double-sided nonlinearities. Regarding the finite representation of units (as in the discussion) it might be helpful to also consider an implementation of a network with arbitrary precision arithmetic as an additional experiment. Overall I think it would be nice to see the paper accepted at the very least to continue the discussion.
assistant
 A thorough investigation on Info Bottleneck and deep learning, nice to read with interesting experiments and references. Even though not all of the approach is uncontroversial (as the discussion shows), the paper contributes to much needed theory of deep learning rather than just another architecture. Estimating the mutual information could have been handled in a more sophisticated way (eg using a Kraskov estimator rather than simple binning), and given that no noise is usually added the discussion about noise and generalisation doesn*t seem to make too much sense to me. It would have been good to see a discussion whether another measurement that would be useful for single-sided saturating nonlinearities that do show a compression (eg information from a combination of layers), from learnt representations that are different to representations learnt using double-sided nonlinearities. Regarding the finite representation of units (as in the discussion) it might be helpful to also consider an implementation of a network with arbitrary precision arithmetic as an additional experiment. Overall I think it would be nice to see the paper accepted at the very least to continue the discussion.