Neural Information Processing Systems http://nips.cc/

We study the task of smoothing a circuit, i.e., ensuring that all children of a

Finally, we illustrate how our framework can be used for exploratory data analysis.

Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be efficiently transformed, or compiled, into d-DNNF. Our main contribution is the fixed-parameter tractable (FPT) compilation of conjunctions of specific constraints parameterized by incidence treewidth. This subsumes the known result for CNF. The constraints in question are all functions representable by constant-width ordered binary decision diagrams (OBDDs) for all variable orderings. For instance, this includes parity constraints and cardinality constraints with constant threshold. The running time of the FPT compilation is singly exponential in the incidence treewidth but hides large constants in the exponent. To balance that, we give a more efficient FPT algorithm for model counting that applies to a sub-family of the constraints and does not require compilation.

Probabilistic circuits (PCs) is a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits. Existing multiplication algorithms require that the circuits respect the same structure, i.e. variable scopes decomposes according to the same vtree. In this work, we propose and study the task of restructuring structured(-decomposable) PCs, that is, transforming a structured PC such that it conforms to a target vtree. We propose a generic approach for this problem and show that it leads to novel polynomial-time algorithms for multiplying circuits respecting different vtrees, as well as a practical depth-reduction algorithm that preserves structured decomposibility. Our work opens up new avenues for tractable PC inference, suggesting the possibility of training with less restrictive PC structures while enabling efficient inference by changing their structures at inference time.

--A recently proposed canonical form of Boolean functions, namely tagged sentential decision diagrams (TSDDs), exploits both the standard and zero-suppressed trimming rules. The standard ones minimize the size of sentential decision diagrams (SDDs) while the zero-suppressed trimming rules have the same objective as the standard ones but for zero-suppressed sentential decision diagrams (ZSDDs). The original TSDDs, which we call zero-suppressed TSDDs (ZTSDDs), firstly fully utilize the zero-suppressed trimming rules, and then the standard ones. In this paper, we present a variant of TSDDs which we call standard TSDDs (STSDDs) by reversing the order of trimming rules. We then prove the canonicity of STSDDs and present the algorithms for binary operations on TSDDs. In addition, we offer two kinds of implementations of STSDDs and ZTSDDs and acquire three variations of the original TSDDs. Experimental evaluations demonstrate that the four versions of TSDDs have the size advantage over SDDs and ZSDDs. Knowledge compilation aims to transform a Boolean function into a tractable representation. Binary decision diagrams (BDDs) [1] is one of the most notable representations that is widely employed for numerous fields of computer science including computer-aided design [2], [3], cryptography [4], [5], formal method [6], [7]. Interestingly, BDDs are a canonical form under the two restrictions: ordering and reduction, that means, any Boolean function has a unique BDD representation. This property reduces the storage space of BDDs and enables an O (1) time equality-test on BDDs. Following the success of BDDs, a variant zero-suppressed BDDs (ZDDs) was proposed in [8]. ZDDs enjoy the same properties: canonicity and supporting polytime Boolean operations as BDDs.

Probabilistic circuits (PCs) are a class of tractable probabilistic models, which admit efficient inference routines depending on their structural properties. In this paper, we introduce md-vtrees, a novel structural formulation of (marginal) determinism in structured decomposable PCs, which generalizes previously proposed classes such as probabilistic sentential decision diagrams. Crucially, we show how mdvtrees can be used to derive tractability conditions and efficient algorithms for advanced inference queries expressed as arbitrary compositions of basic probabilistic operations, such as marginalization, multiplication and reciprocals, in a sound and generalizable manner. In particular, we derive the first polytime algorithms for causal inference queries such as backdoor adjustment on PCs. As a practical instantiation of the framework, we propose MDNets, a novel PC architecture using md-vtrees, and empirically demonstrate their application to causal inference.

Belief revision is the task of modifying a knowledge base when new information becomes available, while also respecting a number of desirable properties. Classical belief revision schemes have been already specialised to \emph{binary decision diagrams} (BDDs), the classical formalism to compactly represent propositional knowledge. These results also apply to \emph{ordered} BDDs (OBDDs), a special class of BDDs, designed to guarantee canonicity. Yet, those revisions cannot be applied to \emph{sentential decision diagrams} (SDDs), a typically more compact but still canonical class of Boolean circuits, which generalizes OBDDs, while not being a subclass of BDDs. Here we fill this gap by deriving a general revision algorithm for SDDs based on a syntactic characterisation of Dalal revision. A specialised procedure for DNFs is also presented. Preliminary experiments performed with randomly generated knowledge bases show the advantages of directly perform revision within SDD formalism.

Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we propose a new scheme based on a partial closed-world assumption: data implicitly provide the logical base of the circuit. Sum nodes are thus learned by recursively clustering batches in the initial data base, while the partitioning of the variables obeys a given input vtree. Preliminary experiments show that the proposed approach might properly fit training data, and generalize well to test data, provided that these remain consistent with the underlying logical base, that is a relaxation of the training data base.

Solving multiagent problems can be an uphill task due to uncertainty in the environment, partial observability, and scalability of the problem at hand. Especially in an urban setting, there are more challenges since we also need to maintain safety for all users while minimizing congestion of the agents as well as their travel times. To this end, we tackle the problem of multiagent pathfinding under uncertainty and partial observability where the agents are tasked to move from their starting points to ending points while also satisfying some constraints, e.g., low congestion, and model it as a multiagent reinforcement learning problem. We compile the domain constraints using propositional logic and integrate them with the RL algorithms to enable fast simulation for RL.