SearcharxivSearch

arXiv subjects

Rodrigo De Castro

Publications and source records attributed to Rodrigo De Castro.

4 recordsLinked to original sources

HCCL: Collective Communication for Meta Training and Inference Accelerators

We present HCCL, a collective communication library co-designed with Meta's MTIA 300 accelerator, the first Meta chip to integrate backend networking directly on chip package. MTIA 300 includes dedicated message engines (MEs) with near-memory compute (NMC) that fully offload collective execution from the compute grid, enabling large overlap between computation and communication. HCCL uses a compiled communication model in which the host generates a complete description of each collective including dependencies. We describe the control and data path architecture, topology-aware algorithm selection across MTIA 300's asymmetric scale-up and scale-out network, and optimizations for both training and inference workloads. For training, HCCL achieves up to 940 GB/s on intra-rack collectives while introducing less than 0.5% degradation to concurrent compute throughput. For inference, we leverage one-sided communication primitives that bypass the scheduling path to minimize collective latency and describe collective designs that improve compute-communication pipelining for latency-sensitive workloads.

cs.NI

Binomial coefficients and multifactorial numbers through generative grammars

In this paper, the formal derivative operator defined with respect to context-free grammars is used to prove some properties about binomial coefficients and multifactorial numbers. In addition, we extend the formal derivative operator to matrix grammars and show that multifactorial numbers can also be generated.

math.CO

Enumeration of $k$-Fibonacci Paths using Infinite Weighted Automata

In this paper, we introduce a new family of generalized colored Motzkin paths, where horizontal steps are colored by means of $F_{k,l}$ colors, where $F_{k,l}$ is the $l$th $k$-Fibonacci number. We study the enumeration of this family according to the length. For this, we use infinite weighted automata.

math.CO

Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs

In this paper we studied infinite weighted automata and a general methodology to solve a wide variety of classical lattice path counting problems in an uniform way. This counting problems are related to Dyck paths, Motzkin paths and some generalizations. These methodology uses weighted automata, equations of ordinary generating functions and continued fractions. It is a variation of the one proposed by J. Rutten.

cs.DM