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Perturbation Theory for the Information Bottleneck.

ABSTRACT: Extracting relevant information from data is crucial for all forms of learning. The information bottleneck (IB) method formalizes this, offering a mathematically precise and conceptually appealing framework for understanding learning phenomena. However the nonlinearity of the IB problem makes it computationally expensive and analytically intractable in general. Here we derive a perturbation theory for the IB method and report the first complete characterization of the learning onset-the limit of maximum relevant information per bit extracted from data. We test our results on synthetic probability distributions, finding good agreement with the exact numerical solution near the onset of learning. We explore the difference and subtleties in our derivation and previous attempts at deriving a perturbation theory for the learning onset and attribute the discrepancy to a flawed assumption. Our work also provides a fresh perspective on the intimate relationship between the IB method and the strong data processing inequality.

SUBMITTER: Ngampruetikorn V

PROVIDER: S-EPMC9806839 | biostudies-literature | 2021 Dec

REPOSITORIES: biostudies-literature

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Perturbation Theory for the Information Bottleneck.

Ngampruetikorn Vudtiwat V Schwab David J DJ

Advances in neural information processing systems 20211201

Extracting relevant information from data is crucial for all forms of learning. The information bottleneck (IB) method formalizes this, offering a mathematically precise and conceptually appealing framework for understanding learning phenomena. However the nonlinearity of the IB problem makes it computationally expensive and analytically intractable in general. Here we derive a perturbation theory for the IB method and report the first complete characterization of the learning onset-the limit of ...[more]

PMID: 36597463

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Project description:Markov state models (MSMs) have proven valuable in studying the dynamics of protein conformational changes via statistical analysis of molecular dynamics simulations. In MSMs, the complex configuration space is coarse-grained into conformational states, with dynamics modeled by a series of Markovian transitions among these states at discrete lag times. Constructing the Markovian model at a specific lag time necessitates defining states that circumvent significant internal energy barriers, enabling internal dynamics relaxation within the lag time. This process effectively coarse-grains time and space, integrating out rapid motions within metastable states. Thus, MSMs possess a multiresolution nature, where the granularity of states can be adjusted according to the time-resolution, offering flexibility in capturing system dynamics. This work introduces a continuous embedding approach for molecular conformations using the state predictive information bottleneck (SPIB), a framework that unifies dimensionality reduction and state space partitioning via a continuous, machine learned basis set. Without explicit optimization of the VAMP-based scores, SPIB demonstrates state-of-the-art performance in identifying slow dynamical processes and constructing predictive multiresolution Markovian models. Through applications to well-validated mini-proteins, SPIB showcases unique advantages compared to competing methods. It autonomously and self-consistently adjusts the number of metastable states based on a specified minimal time resolution, eliminating the need for manual tuning. While maintaining efficacy in dynamical properties, SPIB excels in accurately distinguishing metastable states and capturing numerous well-populated macrostates. This contrasts with existing VAMP-based methods, which often emphasize slow dynamics at the expense of incorporating numerous sparsely populated states. Furthermore, SPIB's ability to learn a low-dimensional continuous embedding of the underlying MSMs enhances the interpretation of dynamic pathways. With these benefits, we propose SPIB as an easy-to-implement methodology for end-to-end MSM construction.

Project description:Background:In the classical psychological refractory period (PRP) paradigm, two stimuli are presented in brief succession, and participants are asked to make separate speeded responses to both stimuli. Due to a central cognitive bottleneck, responses to the second stimulus are delayed, especially at short stimulus-onset asynchrony (SOA) between the two stimuli. Although the mechanisms of dual-task interference in the classical PRP paradigm have been extensively investigated, specific mechanisms underlying the cross-modal PRP paradigm are not well understood. In particular, it remains unknown whether the dominance of vision over audition manifests in the cross-modal PRP tasks. The present study aimed to investigate whether the visual dominance effect manifests in the cross-modal PRP paradigm. Methods:We adapted the classical PRP paradigm by manipulating the order of a visual and an auditory task: the visual task could either precede the auditory task or vice versa, at either short or long SOAs. Twenty-five healthy participants took part in Experiment 1, and thirty-three new participants took part in Experiment 2. Reaction time and accuracy data were calculated and further analyzed by repeated-measures analysis of variance. Results:The results showed that visual precedence in the Visual-Auditory condition caused larger impairments to the subsequent auditory processing than vice versa in the Auditory-Visual condition: a larger delay of second response was revealed in the Visual-Auditory condition (135 ± 10 ms) than the Auditory-Visual condition (88 ± 9 ms). This effect was found only at the short SOAs under the existence of the central bottleneck, but not at the long SOAs. Moreover, this effect occurred both when the single visual and the single auditory task were of equal difficulty in Experiment 1 and when the single auditory task was more difficult than the single visual task in Experiment 2. Conclusion:Results of the two experiments suggested that the visual dominance effect occurred under the central bottleneck of cognitive processing.

Dataset Information

Perturbation Theory for the Information Bottleneck.

Publications

Perturbation Theory for the Information Bottleneck.

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