477 research outputs found
Apperceptive patterning: Artefaction, extensional beliefs and cognitive scaffolding
In “Psychopower and Ordinary Madness” my ambition, as it relates to Bernard Stiegler’s recent literature, was twofold: 1) critiquing Stiegler’s work on exosomatization and artefactual posthumanism—or, more specifically, nonhumanism—to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly’s conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This paper continues this project but first directs a critical analytic lens at the Derridean practice of the ontologization of grammatization from which Stiegler emerges while also distinguishing how metalanguages operate in relation to object-oriented environmental interaction by way of inferentialism. Stalking continental (Kapp, Simondon, Leroi-Gourhan, etc.) and analytic traditions (e.g., Carnap, Chalmers, Clark, Sutton, Novaes, etc.), we move from artefacts to AI and Predictive Processing so as to link theories related to technicity with philosophy of mind. Simultaneously drawing forth Robert Brandom’s conceptualization of the roles that commitments play in retrospectively reconstructing the social experiences that lead to our endorsement(s) of norms, we compliment this account with Reza Negarestani’s deprivatized account of intelligence while analyzing the equipollent role between language and media (both digital and analog)
Formal verification of higher-order probabilistic programs
Probabilistic programming provides a convenient lingua franca for writing
succinct and rigorous descriptions of probabilistic models and inference tasks.
Several probabilistic programming languages, including Anglican, Church or
Hakaru, derive their expressiveness from a powerful combination of continuous
distributions, conditioning, and higher-order functions. Although very
important for practical applications, these combined features raise fundamental
challenges for program semantics and verification. Several recent works offer
promising answers to these challenges, but their primary focus is on semantical
issues.
In this paper, we take a step further and we develop a set of program logics,
named PPV, for proving properties of programs written in an expressive
probabilistic higher-order language with continuous distributions and operators
for conditioning distributions by real-valued functions. Pleasingly, our
program logics retain the comfortable reasoning style of informal proofs thanks
to carefully selected axiomatizations of key results from probability theory.
The versatility of our logics is illustrated through the formal verification of
several intricate examples from statistics, probabilistic inference, and
machine learning. We further show the expressiveness of our logics by giving
sound embeddings of existing logics. In particular, we do this in a parametric
way by showing how the semantics idea of (unary and relational) TT-lifting can
be internalized in our logics. The soundness of PPV follows by interpreting
programs and assertions in quasi-Borel spaces (QBS), a recently proposed
variant of Borel spaces with a good structure for interpreting higher order
probabilistic programs
Editors' Introduction to [Algorithmic Learning Theory: 21st International Conference, ALT 2010, Canberra, Australia, October 6-8, 2010. Proceedings]
Learning theory is an active research area that incorporates ideas,
problems, and techniques from a wide range of disciplines including
statistics, artificial intelligence, information theory, pattern
recognition, and theoretical computer science. The research reported
at the 21st International Conference on Algorithmic Learning Theory
(ALT 2010) ranges over areas such as query models, online learning,
inductive inference, boosting, kernel methods, complexity and
learning, reinforcement learning, unsupervised learning, grammatical
inference, and algorithmic forecasting. In this introduction we give
an overview of the five invited talks and the regular contributions
of ALT 2010
A Theory of Sampling for Continuous-time Metric Temporal Logic
This paper revisits the classical notion of sampling in the setting of
real-time temporal logics for the modeling and analysis of systems. The
relationship between the satisfiability of Metric Temporal Logic (MTL) formulas
over continuous-time models and over discrete-time models is studied. It is
shown to what extent discrete-time sequences obtained by sampling
continuous-time signals capture the semantics of MTL formulas over the two time
domains. The main results apply to "flat" formulas that do not nest temporal
operators and can be applied to the problem of reducing the verification
problem for MTL over continuous-time models to the same problem over
discrete-time, resulting in an automated partial practically-efficient
discretization technique.Comment: Revised version, 43 pages
Bounded Expectations: Resource Analysis for Probabilistic Programs
This paper presents a new static analysis for deriving upper bounds on the
expected resource consumption of probabilistic programs. The analysis is fully
automatic and derives symbolic bounds that are multivariate polynomials of the
inputs. The new technique combines manual state-of-the-art reasoning techniques
for probabilistic programs with an effective method for automatic
resource-bound analysis of deterministic programs. It can be seen as both, an
extension of automatic amortized resource analysis (AARA) to probabilistic
programs and an automation of manual reasoning for probabilistic programs that
is based on weakest preconditions. As a result, bound inference can be reduced
to off-the-shelf LP solving in many cases and automatically-derived bounds can
be interactively extended with standard program logics if the automation fails.
Building on existing work, the soundness of the analysis is proved with respect
to an operational semantics that is based on Markov decision processes. The
effectiveness of the technique is demonstrated with a prototype implementation
that is used to automatically analyze 39 challenging probabilistic programs and
randomized algorithms. Experimental results indicate that the derived constant
factors in the bounds are very precise and even optimal for many programs
Probabilistic Couplings For Probabilistic Reasoning
This thesis explores proofs by coupling from the perspective of formal verification. Long employed in probability theory and theoretical computer science, these proofs construct couplings between the output distributions of two probabilistic processes. Couplings can imply various probabilistic relational properties, guarantees that compare two runs of a probabilistic computation.
To give a formal account of this clean proof technique, we first show that proofs in the program logic pRHL (probabilistic Relational Hoare Logic) describe couplings. We formalize couplings that establish various probabilistic properties, including distribution equivalence, convergence, and stochastic domination. Then we deepen the connection between couplings and pRHL by giving a proofs-as-programs interpretation: a coupling proof encodes a probabilistic product program, whose properties imply relational properties of the original two programs. We design the logic xpRHL (product pRHL) to build the product program, with extensions to model more advanced constructions including shift coupling and path coupling.
We then develop an approximate version of probabilistic coupling, based on approximate liftings. It is known that the existence of an approximate lifting implies differential privacy, a relational notion of statistical privacy. We propose a corresponding proof technique---proof by approximate coupling---inspired by the logic apRHL, a version of pRHL for building approximate liftings. Drawing on ideas from existing privacy proofs, we extend apRHL with novel proof rules for constructing new approximate couplings. We give approximate coupling proofs of privacy for the Report-noisy-max and Sparse Vector mechanisms, well-known algorithms from the privacy literature with notoriously subtle privacy proofs, and produce the first formalized proof of privacy for these algorithms in apRHL.
Finally, we enrich the theory of approximate couplings with several more sophisticated constructions: a principle for showing accuracy-dependent privacy, a generalization of the advanced composition theorem from differential privacy, and an optimal approximate coupling relating two subsets of samples. We also show equivalences between approximate couplings and other existing definitions. These ingredients support the first formalized proof of privacy for the Between Thresholds mechanism, an extension of the Sparse Vector mechanism
Branches of a Tree: Taking Derivatives of Programs with Discrete and Branching Randomness in High Energy Physics
We propose to apply several gradient estimation techniques to enable the
differentiation of programs with discrete randomness in High Energy Physics.
Such programs are common in High Energy Physics due to the presence of
branching processes and clustering-based analysis. Thus differentiating such
programs can open the way for gradient based optimization in the context of
detector design optimization, simulator tuning, or data analysis and
reconstruction optimization. We discuss several possible gradient estimation
strategies, including the recent Stochastic AD method, and compare them in
simplified detector design experiments. In doing so we develop, to the best of
our knowledge, the first fully differentiable branching program.Comment: 8 page
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