Guralnik, Dan P
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ORCID
Disciplines
Artificial Intelligence and Robotics
Geometry and Topology
Other Applied Mathematics
Geometry and Topology
Other Applied Mathematics
Research Projects
Organizational Units
Position
Post-doctoral researcher
Introduction
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Now showing 1 - 3 of 3
Publication Universal Memory Architectures for Autonomous Machines(2016-01-01) Guralnik, Dan P; Koditschek, Daniel EWe propose a self-organizing memory architecture (UMA) for perceptual experience provably capable of supporting autonomous learning and goal-directed problem solving in the absence of any prior information about the agent’s environment. The architecture is simple enough to ensure (1) a quadratic bound (in the number of available sensors) on space requirements, and (2) a quadratic bound on the time-complexity of the update-execute cycle. At the same time, it is sufficiently complex to provide the agent with an internal representation which is (3) minimal among all representations which account for every sensory equivalence class consistent with the agent’s belief state; (4) capable, in principle, of recovering a topological model of the problem space; and (5) learnable with arbitrary precision through a random application of the available actions. These provable properties — both the trainability and the operational efficacy of an effectively trained memory structure — exploit a duality between weak poc sets — a symbolic (discrete) representation of subset nesting relations — and non-positively curved cubical complexes, whose rich convexity theory underlies the planning cycle of the proposed architecture.Publication Detecting Poisoning Attacks on Hierarchical Malware Classification Systems(2017-03-25) Guralnik, Dan P; Moran, Bill; Pezeshki, Ali; Arslan, OmurAnti-virus software based on unsupervised hierarchical clustering (HC) of malware samples has been shown to be vulnerable to poisoning attacks. In this kind of attack, a malicious player degrades anti-virus performance by submitting to the database samples specifically designed to collapse the classification hierarchy utilized by the anti-virus (and constructed through HC) or otherwise deform it in a way that would render it useless. Though each poisoning attack needs to be tailored to the particular HC scheme deployed, existing research seems to indicate that no particular HC method by itself is immune. We present results on applying a new notion of entropy for combinatorial dendrograms to the problem of controlling the influx of samples into the data base and deflecting poisoning attacks. In a nutshell, effective and tractable measures of change in hierarchy complexity are derived from the above, enabling on-the-fly flagging and rejection of potentially damaging samples. The information-theoretic underpinnings of these measures ensure their indifference to which particular poisoning algorithm is being used by the attacker, rendering them particularly attractive in this setting.Publication Iterated Belief Revision Under Resource Constraints: Logic as Geometry(2018-12-18) Guralnik, Dan P; Koditschek, Daniel EWe propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots. The proposed memory architecture---called the universal memory architecture (UMA)---maintains an epistemic state in the form of a system of default rules similar to those studied by Pearl and by Goldszmidt and Pearl (systems Z and Z+). A duality between the category of UMA representations and the category of the corresponding model spaces, extending the Sageev-Roller duality between discrete poc sets and discrete median algebras provides a two-way dictionary from inference to geometry, leading to immense savings in computation, at a cost in the quality of representation that can be quantified in terms of topological invariants. Moreover, the same framework naturally enables comparisons between different model spaces, making it possible to analyze the deficiencies of one model space in comparison to others. This paper develops the formalism underlying UMA, analyzes the complexity of maintenance and inference operations in UMA, and presents some learning guarantees for different UMA-based learners. Finally, we present simulation results to illustrate the viability of the approach, and close with a discussion of the strengths, weaknesses, and potential development of UMA-based learners.