Mohsen Dehghankar

Mohsen Dehghankar, Abolfazl Asudeh, Raghav Mittal et al.

We extend Random Access, a fundamental operation that enables efficient search and exploration algorithms, to the modern interactive data systems based on Ranked Retrieval and Similarity Search, where orderings are dynamically defined over a high-dimensional feature space. This extension enables efficient solutions for a wide range of applications, from data analytics tools and database systems to recommendation systems and machine learning. We formalize the Random-Access Ranked Retrieval (RAR) problem, and extend it to Similarity Search. Our algorithmic innovations include the development of a theoretically efficient algorithm based on geometric arrangements, achieving logarithmic query time. However, this method suffers from exponential space complexity in high dimensions. Therefore, we develop a second class of algorithms based on $\varepsilon$-sampling, which consume a linear space. Since exactly locating the tuple at a specific rank is challenging due to its connection to the range counting problem, we introduce a relaxed variant called $κ$-Random-Access Ranked Retrieval, which returns a small subset of size $κ$ guaranteed to contain the target tuple. To solve this problem efficiently, we define an intermediate problem, Stripe Range Retrieval (SRR), and design a hierarchical sampling data structure tailored for narrow stripe range queries. Our method achieves practical scalability in both data size and dimensionality. We prove near-optimal bounds on the efficiency of our algorithms and validate their performance through extensive experiments on real and synthetic datasets, demonstrating scalability to millions of tuples and hundreds of dimensions.

Rishi Advani, Abolfazl Asudeh, Mohsen Dehghankar et al.

The necklace splitting problem is a classic problem in fair division with many applications, including data-informed fair hash maps. We extend necklace splitting to a dynamic setting, allowing for relocation, insertion, and deletion of beads. We present linear-time, optimal algorithms for the two-color case that support all dynamic updates. For more than two colors, we give linear-time, optimal algorithms for relocation subject to a restriction on the number of agents. Finally, we propose a randomized algorithm for the two-color case that handles all dynamic updates, guarantees approximate fairness with high probability, and runs in polylogarithmic time when the number of agents is small.

Sana Ebrahimi, Mohsen Dehghankar, Abolfazl Asudeh

While multi-agent LLM systems show strong capabilities in various domains, they are highly vulnerable to adversarial and low-performing agents. To resolve this issue, in this paper, we introduce a general and adversary-resistant multi-agent LLM framework based on credibility scoring. We model the collaborative query-answering process as an iterative game, where the agents communicate and contribute to a final system output. Our system associates a credibility score that is used when aggregating the team outputs. The credibility scores are learned gradually based on the past contributions of each agent in query answering. Our experiments across multiple tasks and settings demonstrate our system's effectiveness in mitigating adversarial influence and enhancing the resilience of multi-agent cooperation, even in the adversary-majority settings.

Mohsen Dehghankar, Abolfazl Asudeh

Large language models (LLMs) have quickly emerged as practical and versatile tools that provide new solutions for a wide range of domains. In this paper, we consider the application of LLMs on symmetric tasks where a query is asked on an (unordered) bag of elements. Examples of such tasks include answering aggregate queries on a database table. In general, when the bag contains a large number of elements, LLMs tend to overlook some elements, leading to challenges in generating accurate responses to the query. LLMs receive their inputs as ordered sequences. However, in this problem, we leverage the fact that the symmetric input is not ordered, and reordering should not affect the LLM's response. Observing that LLMs are less likely to miss elements at certain positions of the input, we introduce the problem of LLM input reranking: to find a ranking of the input that maximizes the LLM's accuracy for the given query without making explicit assumptions about the query. Finding the optimal ranking requires identifying (i) the relevance of each input element for answering the query and (ii) the importance of each rank position for the LLM's attention. We develop algorithms for estimating these values efficiently utilizing a helper LLM. We conduct comprehensive experiments on different synthetic and real datasets to validate our proposal and to evaluate the effectiveness of our proposed algorithms. Our experiments confirm that our reranking approach improves the accuracy of the LLMs on symmetric tasks by up to $99\%$ proximity to the optimum upper bound.

Mohsen Dehghankar, Abolfazl Asudeh

Due to a variety of reasons, such as privacy, data in the wild often misses the grouping information required for identifying minorities. On the other hand, it is known that machine learning models are only as good as the data they are trained on and, hence, may underperform for the under-represented minority groups. The missing grouping information presents a dilemma for responsible data scientists who find themselves in an unknown-unknown situation, where not only do they not have access to the grouping attributes but do not also know what groups to consider. This paper is an attempt to address this dilemma. Specifically, we propose a minority mining problem, where we find vectors in the attribute space that reveal potential groups that are under-represented and under-performing. Technically speaking, we propose a geometric transformation of data into a dual space and use notions such as the arrangement of hyperplanes to design an efficient algorithm for the problem in lower dimensions. Generalizing our solution to the higher dimensions is cursed by dimensionality. Therefore, we propose a solution based on smart exploration of the search space for such cases. We conduct comprehensive experiments using real-world and synthetic datasets alongside the theoretical analysis. Our experiment results demonstrate the effectiveness of our proposed solutions in mining the unknown, under-represented, and under-performing minorities.

Mohsen Dehghankar, Mahdi Erfanian, Abolfazl Asudeh

Despite their tremendous success and versatility, Deep Neural Networks (DNNs) such as Large Language Models (LLMs) suffer from inference inefficiency and rely on advanced computational infrastructure. To address these challenges and make these models more accessible and cost-effective, in this paper, we propose algorithms to improve the inference time and memory efficiency of DNNs with binary and ternary weight matrices. Particularly focusing on matrix multiplication as the bottleneck operation of inference, we observe that, once trained, the weight matrices of a model no longer change. This allows us to preprocess these matrices and create indices that help reduce the storage requirements by a logarithmic factor while enabling our efficient inference algorithms. Specifically, for a $n\times n$ weight matrix, our efficient algorithm guarantees a time complexity of $O(\frac{n^2}{\log n})$, a logarithmic factor improvement over the standard vector-matrix multiplication. Besides theoretical analysis, we conduct extensive experiments to evaluate the practical efficiency of our algorithms. Our results confirm the superiority of our approach both with respect to time and memory, as we observed a reduction in the multiplication time up to 29x and memory usage up to 6x. When applied to LLMs, our experiments show up to a 5.24x speedup in the inference time.