We consider the problem of automatic parallelism in high-performance, tensor-based systems. Our focus is on intra-operator parallelism for inference tasks on a single GPU server or CPU cluster, where each operator is automatically broken op so that it runs on multiple devices. We assert that tensor-based systems should offer a programming abstraction based on an extended Einstein summation notation , which is a fully declarative, mathematical specification for tensor computations. We show that any computation specified in the Einstein summation notation can be re-written into an equivalent tensor-relational computation that facilitates intra-operator parallelism, and this re-write generalizes existing notations of tensor parallelism such as "data parallel" and "model parallel." We consider the algorithmic problem of optimally computing a tensor-relational decomposition of a graph of operations specified in our extended Einstein summation notation.

Large Language Models (LLMs) have a natural role in answering complex queries about data streams, but the high computational cost of LLM inference makes them infeasible in many such tasks. We propose *online cascade learning*, the first approach to address this challenge. The objective here is to learn a ``cascade'' of models, starting with lower-capacity models (such as logistic regression) and ending with a powerful LLM, along with a *deferral policy* that determines the model to be used on a given input. We formulate the task of learning cascades online as an imitation-learning problem, where smaller models are updated over time imitating the collected LLM demonstrations, and give a no-regret algorithm for the problem. Experimental results across four benchmarks show that our method parallels LLMs in accuracy while cutting down inference costs by as much as 90% with strong robustness against input distribution shifts, underscoring its efficacy and adaptability in stream processing. Our source code is available at https://github.com/flitternie/online_cascade_learning.

The relational data model was designed to facilitate large-scale data management and analytics. We consider the problem of how to differentiate computations expressed relationally. We show experimentally that a relational engine running an auto-differentiated relational algorithm can easily scale to very large datasets, and is competitive with state-of-the-art, special-purpose systems for large-scale distributed machine learning.

We study the realistic problem of range-based localization for mobile Internet of Things (IoT) without using GPS. This problem arises from the real-world applications and is characterized by the following three challenges: 1) inaccurate devices, such as the low cost motion sensors and moving parts in the mobile IoT nodes, make it infeasible to localize the nodes using their speed and direction; 2) when a team of IoT nodes keep moving, some nodes may get lost and be disconnected from the network due to the large accumulated errors in the distances; and 3) although the theory of global rigidity ensures the position uniqueness of nodes, there are still nonlocalizable nodes in a globally rigid graph. To address these challenges, we propose a distributed localization protocol, called GROLO. GROLO is able to perform efficient distributed localization through an adaptive global rigidity formation maintenance mechanism especially designed for the resource limited IoT nodes. GROLO is able to localize all of the nodes periodically in a mobile IoT by short distance adjustment. Furthermore, GROLO requires only necessary additional neighbor distance measurements. We evaluated GROLO and other localization protocols using both simulated nodes and ten real mobile nodes in an IoT. The results show that GROLO is promising for the localization and formation control with inaccurate mobile IoT in realistic environments.