reviews: 
Comments: This work introduces two different information-theory-based modules for multimodal (histology and genomics) survival prediction problem. Based on information bottleneck theory, these modules aim to remove redundant information, which are prevalent in WSIs, within each modality and across different modalities. In the process, the concept of prototypes are introduced to guide the learning of the multimodal prognosis framework, while only retaining necessary information.
Strengths: - While the use of information bottleneck theory is not new in computational pathology, the use of it for 1) survival prediction setting and 2) reduction of intra-modal redundant information is quite novel.
- The authors conduct extensive baseline comparisons to demonstrate that PIBD framework indeed is better/highly-competitive compared to even the most recent baselines (MOTCat and SurvPath). This is to be appreciated by any fellow researchers looking to get understanding of the available survival prediction methods in CPath.
- Probabilistic modeling of the bag of patch features (although it leads to several variational approximations), opens up new avenues for probabilistic approaches for CPath, which have been under-explored thus far.
Weaknesses: Clarity
- The explanation around PIB and PID need to be much more straightforward for the work to be appreciated. In its current form, it is really hard to understand and Section 3 lacks clarity. The authors should understand that typical readership of this article will either be pathologist or ML practitioner who would be less-versed in probabilistic and variational language. This, in my opinion, significantly reduces the impact of the paper as any other researcher hoping to reuse the framework for their own experiments. Authors should try to inject more  pathology-related intuition throughout the work.

Discriminative assumption
-  I am not sure if "discriminative" approach (despite its good performance as shown in the paper) is the right approach for survival. Different from diagnosis problems where subtype/grades are indeed decided with discriminative instances (patches), survival prediction problems are not as clear-cut. Certain morphological characteristics will overlap between different risk groups (or bands), which the current approach, centered around sampling positive/negative prototypes for maximum discrimination, is not well suited for.
- Related to the comment above, this approach seems only applicable to NLL loss, which treats the problem as a classification problem and thus have "different" bins (i.e., discretized timeline). What if more common loss functions, such as Cox PH or rank losses, were to be used that do not rely on such discriminative hypothesis?

Kaplan-Meier analysis
- In Kaplan-Meier analysis section, authors state that "our approach demonstrates significantly improved discrimination.... as indicated by lower p-values". While it is tempting to compare between p-values as a metric for separation of the risk groups, it is statistically not correct. Once these are below significance threshold, it shouldn't be over-interpreted. Maybe, use median survival days for each risk group?

Sampling operation
- Since both PID and PIB rely on sampling from distribution, it does seem that the performance will indeed by affected by which samples are chosen or how many of them are sampled. The discussion around this point needs to be made explicit.

Inference
- While there are detailed information about training procedure, not much is written about the actual inference step. For instance, how many samples for each prototype are required for reliable performance?
Recommendation: 6: marginally above the acceptance threshold
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 3 good
Clarity: 3 good