Shannon Limits on Certified Perception
Dr. Samuel Kline
LeMay Publishing
ACADEMIC
Shannon Limits on Certified Perception
Monographs6,666 words55 chapters
Published by LeMay Publishing. 6,666 words across 55 chapters.
About This Publication
A monograph on the information-theoretic limits of deterministic perception certification, investigating what a machine can reliably perceive and what it can be certified to perceive at the intersection of information theory and computer science.
Published by LeMay Publishing, a division of LeMay. Massachusetts.
ISBN: 979-8-0000-7097-0
Chapters
1SHANNON LIMITS ON CERTIFIED PERCEPTION
2A Monograph on the Information-Theoretic Limits of Deterministic Perception Certification
3TABLE OF CONTENTS
4PREFACE
5CHAPTER 1
6INTRODUCTION AND MOTIVATION
71.1 The Certification Problem in Perception
81.2 Why Information Theory?
91.3 Summary of Contributions
101.4 Relation to Prior Work
11CHAPTER 2
12FORMAL PRELIMINARIES — CHANNELS, PERCEPTION, AND CERTIFICATION
132.1 The Input Space and Perturbation Model
142.2 Classifiers and Deterministic Certification
152.3 The Adversarial Channel
162.4 Zero-Error Capacity
172.5 Packing Numbers
18CHAPTER 3
19THE FUNDAMENTAL BOUND — SHANNON CAPACITY AS A CEILING ON CERTIFIED PERCEPTION
203.1 Statement of the Main Theorem
213.2 The Bound in Euclidean Space
223.3 The Bound in Hamming Space
233.4 Asymptotic Capacity
24CHAPTER 4
25DETERMINISTIC CERTIFICATION AND THE IMPOSSIBILITY REGIME
264.1 The Impossibility Threshold
274.2 Dimension-Dependent Collapse
284.3 Impossibility Beyond Metric Balls
29CHAPTER 5
30PERTURBATION SEMANTICS AND ADVERSARIAL CHANNELS
315.1 From Geometric to Semantic Perturbations
325.2 Product Channels and the Shannon Capacity
335.3 Non-Product Channels
34CHAPTER 6
35RATE–ROBUSTNESS TRADEOFFS IN CLASSIFIER CERTIFICATION
366.1 The Tradeoff Curve
376.2 Explicit Tradeoff Curves
386.3 Converse and Achievability
39CHAPTER 7
40EXTENSIONS TO CONTINUOUS AND HIGH-DIMENSIONAL DOMAINS
417.1 The Continuous Input Space
427.2 Data Manifold Hypothesis
437.3 Metric Entropy and Covering Numbers
44CHAPTER 8
45IMPLICATIONS FOR AUTONOMOUS SYSTEMS AND SAFETY-CRITICAL DEPLOYMENT
468.1 The Certification Imperative
478.2 Class Granularity vs. Robustness
488.3 The Role of Dimensionality Reduction
498.4 Probabilistic Relaxation
50CHAPTER 9
51CONCLUSION AND OPEN PROBLEMS
529.1 Summary
539.2 Open Problems
549.3 Closing Remarks
55BIBLIOGRAPHY