Related papers: The layer complexity of Arthur-Merlin-like communi…
We show several results related to interactive proof modes of communication complexity. First we show lower bounds for the QMA-communication complexity of the functions Inner Product and Disjointness. We describe a general method to prove…
We introduce and study a new model of interactive proofs: AM(k), or Arthur-Merlin with k non-communicating Merlins. Unlike with the better-known MIP, here the assumption is that each Merlin receives an independent random challenge from…
Despite the significant improvements achieved by large language models (LLMs) in English reasoning tasks, these models continue to struggle with multilingual reasoning. Recent studies leverage a full-parameter and two-stage training…
We develop a new lower bound method for analysing the complexity of the Equality function (EQ) in the Simultaneous Message Passing (SMP) model of communication complexity. The new technique gives tight lower bounds of $\Omega(\sqrt n)$ for…
The quantum version of communication complexity allows the two communicating parties to exchange qubits and/or to make use of prior entanglement (shared EPR-pairs). Some lower bound techniques are available for qubit communication…
The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…
The Ambient Logic (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. In this paper, we study the expressiveness of AL. We…
Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent…
We investigate the power of the most important lower bound technique in randomized communication complexity, which is based on an evaluation of the maximal size of approximately monochromatic rectangles, minimized over all distributions on…
In this thesis, we study the place of regular languages within the communication complexity setting. In particular, we are interested in the non-deterministic communication complexity of regular languages. We show that a regular language…
Language model families exhibit striking disparity in their capacity to benefit from reinforcement learning: under identical training, models like Qwen achieve substantial gains, while others like Llama yield limited improvements.…
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared…
We propose an interactive multi-agent classifier that provides provable interpretability guarantees even for complex agents such as neural networks. These guarantees consist of lower bounds on the mutual information between selected…
Curvature regularization techniques like Sharpness Aware Minimization (SAM) have shown great promise in improving generalization on vision tasks. However, we find that SAM performs poorly in domains like natural language processing (NLP),…
Computer simulations offer a robust toolset for exploring complex systems across various disciplines. A particularly impactful approach within this realm is Agent-Based Modeling (ABM), which harnesses the interactions of individual agents…
The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the…
Traditional SLAM algorithms are typically based on artificial features, which lack high-level information. By introducing semantic information, SLAM can own higher stability and robustness rather than purely hand-crafted features. However,…
Proving lower bounds remains the most difficult of tasks in computational complexity theory. In this paper, we show that whereas most natural NP-complete problems belong to NLIN (linear time on nondeterministic RAMs), some of them,…
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…
The study of system complexity primarily has two objectives: to explore underlying patterns and to develop theoretical explanations. Pattern exploration seeks to clarify the mechanisms behind the emergence of system complexity, while…