14 research outputs found
Quasipolynomial simulation of DNNF by a non-determinstic read-once branching program
We prove that dnnfs can be simulated by Non-deterministic Read-Once Branching Programs (nrobps) of quasi-polynomial size. As a result, all the exponential lower bounds for nrobps immediately apply for dnnfs
Efficient Computation of Shap Explanation Scores for Neural Network Classifiers via Knowledge Compilation
The use of Shap scores has become widespread in Explainable AI. However,
their computation is in general intractable, in particular when done with a
black-box classifier, such as neural network. Recent research has unveiled
classes of open-box Boolean Circuit classifiers for which Shap can be computed
efficiently. We show how to transform binary neural networks into those
circuits for efficient Shap computation. We use logic-based knowledge
compilation techniques. The performance gain is huge, as we show in the light
of our experiments.Comment: Conference submission. It replaces the previously uploaded paper
"Opening Up the Neural Network Classifier for Shap Score Computation", by the
same authors. This version considerably revised the previous on
Symbolic Exact Inference for Discrete Probabilistic Programs
The computational burden of probabilistic inference remains a hurdle for
applying probabilistic programming languages to practical problems of interest.
In this work, we provide a semantic and algorithmic foundation for efficient
exact inference on discrete-valued finite-domain imperative probabilistic
programs. We leverage and generalize efficient inference procedures for
Bayesian networks, which exploit the structure of the network to decompose the
inference task, thereby avoiding full path enumeration. To do this, we first
compile probabilistic programs to a symbolic representation. Then we adapt
techniques from the probabilistic logic programming and artificial intelligence
communities in order to perform inference on the symbolic representation. We
formalize our approach, prove it sound, and experimentally validate it against
existing exact and approximate inference techniques. We show that our inference
approach is competitive with inference procedures specialized for Bayesian
networks, thereby expanding the class of probabilistic programs that can be
practically analyzed
Regular resolution for CNF of bounded incidence treewidth with few long clauses
We demonstrate that Regular Resolution is FPT for two restricted families of
CNFs of bounded incidence treewidth. The first includes CNFs having at most
clauses whose removal results in a CNF of primal treewidth at most . The
parameters we use in this case are and . The second class includes CNFs
of bounded one-sided (incidence) treewdth, a new parameter generalizing both
primal treewidth and incidence pathwidth. The parameter we use in this case is
the one-sided treewidth
On the read-once property of branching programs and CNFs of bounded treewidth
for non-deterministic (syntactic) read-once branching programs (nrobps) on functions expressible as cnfs with treewidth at most k of their primal graphs. This lower bound rules out the possibility of fixed-parameter space complexity of nrobps parameterized by k. We use lower bound for nrobps to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the existing upper bound introduced by Beame et al. (Proceedings of the twenty-ninth conference on uncertainty in artificial intelligence, Bellevue, 2013) and thus proving the tightness of the latter
Certified Knowledge Compilation with Application to Verified Model Counting
Computing many useful properties of Boolean formulas, such as their weighted or unweighted model count, is intractable on general representations. It can become tractable when formulas are expressed in a special form, such as the decision-decomposable, negation normal form (dec-DNNF) . Knowledge compilation is the process of converting a formula into such a form. Unfortunately existing knowledge compilers provide no guarantee that their output correctly represents the original formula, and therefore they cannot validate a model count, or any other computed value.
We present Partitioned-Operation Graphs (POGs), a form that can encode all of the representations used by existing knowledge compilers. We have designed CPOG, a framework that can express proofs of equivalence between a POG and a Boolean formula in conjunctive normal form (CNF).
We have developed a program that generates POG representations from dec-DNNF graphs produced by the state-of-the-art knowledge compiler D4, as well as checkable CPOG proofs certifying that the output POGs are equivalent to the input CNF formulas. Our toolchain for generating and verifying POGs scales to all but the largest graphs produced by D4 for formulas from a recent model counting competition. Additionally, we have developed a formally verified CPOG checker and model counter for POGs in the Lean 4 proof assistant. In doing so, we proved the soundness of our proof framework. These programs comprise the first formally verified toolchain for weighted and unweighted model counting