Related papers: On the Computational Complexity of MapReduce
This work introduces a formulation of model predictive control (MPC) which adaptively reasons about the complexity of the model based on the task while maintaining feasibility and stability guarantees. Existing MPC implementations often…
Linearity and ramification constraints have been widely used to weaken higher-order (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions. We show that fine-tuning these two…
The problem of checking whether a recursive query can be rewritten as query without recursion is a fundamental reasoning task, known as the boundedness problem. Here we study the boundedness problem for Unions of Conjunctive Regular Path…
Strictly positive logics recently attracted attention both in the description logic and in the provability logic communities for their combination of efficiency and sufficient expressivity. The language of Reflection Calculus RC consists of…
Transformers have been established as the de-facto backbones for most recent advances in sequence modeling, mainly due to their growing memory capacity that scales with the context length. While plausible for retrieval tasks, it causes…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
MapReduce is a popular programming model for data parallel computation. In MapReduce, the reducer produces an output from a list of inputs. Due to the scheduling policy of the platform, the inputs may arrive at the reducers in different…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
Solving the explicit Model Predictive Control (MPC) problem requires enumerating all critical regions and their associated feedback laws, a task that scales exponentially with the system dimension and the prediction horizon, as well. When…
The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are…
Given any task $\Pi$, Brandt's speedup theorem (PODC 2019) provides a mechanical way to design another task~$\Pi'$ on the same input-set as $\Pi$ such that, for any $t\geq 1$, $\Pi$ is solvable in $t$ rounds if and only if $\Pi'$ is…
Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…
Current large language models (LLMs) primarily rely on linear sequence generation and massive parameter counts, yet they severely struggle with complex algorithmic reasoning. While recent reasoning architectures, such as the Hierarchical…
Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…
Achieving the no-regret property for Reinforcement Learning (RL) problems in continuous state and action-space environments is one of the major open problems in the field. Existing solutions either work under very specific assumptions or…
The main results of this paper are (I) a simulation algorithm which, under quite general constraints, transforms algorithms running on the Congested Clique into algorithms running in the MapReduce model, and (II) a distributed…
Robust reinforcement learning is essential for deploying reinforcement learning algorithms in real-world scenarios where environmental uncertainty predominates. Traditional robust reinforcement learning often depends on rectangularity…
Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (regularity), a key property of…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the…