Can the Brain Use Waves to Solve Planning Problems?

A variety of behaviors like spatial navigation or bodily motion can be formulated as graph traversal problems through cognitive maps. We present a neural network model which can solve such tasks and is compatible with a broad range of empirical findings about the mammalian neocortex and hippocampus. The neurons and synaptic connections in the model represent structures that can result from self-organization into a cognitive map via Hebbian learning, i.e. into a graph in which each neuron represents a point of some abstract task-relevant manifold and the recurrent connections encode a distance metric on the manifold. Graph traversal problems are solved by wave-like activation patterns which travel through the recurrent network and guide a localized peak of activity onto a path from some starting position to a target state.

You Only Traverse Twice: A YOTT Placement, Routing, and Timing Approach for CGRAs

Coarse-grained reconfigurable architecture (CGRA) mapping involves three main steps: placement, routing, and timing. The mapping is an NP-complete problem, and a common strategy is to decouple this process into its independent steps. This work focuses on the placement step, and its aim is to propose a technique that is both reasonably fast and leads to high-performance solutions. Furthermore, a near-optimal placement simplifies the following routing and timing steps. Exact solutions cannot find placements in a reasonable execution time as input designs increase in size. Heuristic solutions include meta-heuristics, such as Simulated Annealing (SA) and fast and straightforward greedy heuristics based on graph traversal. However, as these approaches are probabilistic and have a large design space, it is not easy to provide both run-time efficiency and good solution quality. We propose a graph traversal heuristic that provides the best of both: high-quality placements similar to SA and the execution time of graph traversal approaches. Our placement introduces novel ideas based on “you only traverse twice” (YOTT) approach that performs a two-step graph traversal. The first traversal generates annotated data to guide the second step, which greedily performs the placement, node per node, aided by the annotated data and target architecture constraints. We introduce three new concepts to implement this technique: I/O and reconvergence annotation, degree matching, and look-ahead placement. Our analysis of this approach explores the placement execution time/quality trade-offs. We point out insights on how to analyze graph properties during dataflow mapping. Our results show that YOTT is 60.6 , 9.7 , and 2.3 faster than a high-quality SA, bounding box SA VPR, and multi-single traversal placements, respectively. Furthermore, YOTT reduces the average wire length and the maximal FIFO size (additional timing requirement on CGRAs) to avoid delay mismatches in fully pipelined architectures.

Exploring graph traversal algorithms in graph-based molecular generation

Here we explore the impact of different graph traversal algorithms on molecular graph generation. We do this by training a graph-based deep molecular generative model to build structures using a node order determined via either a breadth- or depth-first search algorithm. What we observe is that using a breadth-first traversal leads to better coverage of training data features compared to a depth-first traversal. We have quantified these differences using a variety of metrics on a dataset of natural products. These metrics include: percent validity, molecular coverage, and molecular shape. We also observe that using either a breadth- or depth-first traversal it is possible to over-train the generative models, at which point the results with the graph traversal algorithm are identical

Hierarchical Graph Traversal for Aggregate k Nearest Neighbors Search in Road Networks (Extended Abstract)

A k nearest neighbors (kNN) query finds k closest points-of-interest (POIs) from an agent's location. In this paper, we study a natural extension of the kNN query for multiple agents, namely, the Aggregate k Nearest Neighbors (AkNN) query. An AkNN query retrieves k POIs with the smallest aggregate distances where the aggregate distance of a POI is obtained by aggregating its distances from the multiple agents (e.g., sum of its distances from each agent). We propose a novel data structure COLT (Compacted Object-Landmark Tree) which enables efficient hierarchical graph traversal and utilize it to efficiently answer AkNN queries. Our experiments on real-world and synthetic data sets show that our techniques outperform existing approaches by more than an order of magnitude in almost all settings.

Sanskrit Parsing Following Indian Theories of Verbal Cognition

Pāṇini’s grammar is an important milestone in the Indian grammatical tradition. Unlike grammars of other languages, it is almost exhaustive and together with the theories of śābdabodha (verbal cognition), this grammar provides a system for language analysis as well as generation. The theories of śābdabodha describe three conditions necessary for verbal cognition. They are ākāṅkṣā (expectancy), yogyatā (meaning congruity), and sannidhi (proximity). We examine them from a computational viewpoint and provide appropriate computational models for their representation. Next, we describe the design of a parser following the theories of śābdabodha and present three algorithms for solving the constraints imposed by the theories of śābdabodha . The first algorithm is modeled as a constraint satisfaction problem, the second one as a vertex-centric graph traversal, and the third one as an edge-centric binary join, each one being an improvement over the previous one.