相关论文: $\text{#NFA}$ admits an FPRAS: Efficient Enumerati…

Graph neural networks (GNNs), which capture graph structures via a feature aggregation mechanism following the graph embedding framework, have demonstrated a powerful ability to support various tasks. According to the topology properties…

In this thesis we develop FPTASs for the counting problems of m-tuples, contingency tables with two rows, and 0/1 knapsack. For the problem of counting m-tuples, we design two algorithms, one is strongly polynomial. As far as we know, these…

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel…

We revisit the popular \emph{delayed deterministic finite automaton} (\ddfa{}) compression algorithm introduced by Kumar~et~al.~[SIGCOMM 2006] for compressing deterministic finite automata (DFAs) used in intrusion detection systems. This…

Large language models (LLMs) often benefit from verbalized reasoning at inference time, but it remains unclear which aspects of task difficulty these extra reasoning tokens address. To investigate this question, we formalize a framework…

An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…

The long-lived renaming problem appears in shared-memory systems where a set of threads need to register and deregister frequently from the computation, while concurrent operations scan the set of currently registered threads. Instances of…

Unlearning the data observed during the training of a machine learning (ML) model is an important task that can play a pivotal role in fortifying the privacy and security of ML-based applications. This paper raises the following questions:…

We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

When comparing human with artificial intelligence, one major difference is apparent: Humans can generalize very broadly from sparse data sets because they are able to recombine and reintegrate data components in compositional manners. To…

This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…

We study the problems of counting the homomorphisms, counting the copies, and counting the induced copies of a $k$-vertex graph $H$ in a $d$-degenerate $n$-vertex graph $G$. Our main result establishes exhaustive and explicit complexity…

We consider the class of counting problems,i.e. functions in $\#$P, which are self reducible, and have easy decision version, i.e. for every input it is easy to decide if the value of the function $f(x)$ is zero. For example,…

We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…

Running LLMs with extended reasoning on every problem is expensive, but determining which inputs actually require additional compute remains challenging. We investigate whether their own likelihood of success is recoverable from their…

Weakly supervised learning generally faces challenges in applicability to various scenarios with diverse weak supervision and in scalability due to the complexity of existing algorithms, thereby hindering the practical deployment. This…

Can deep neural networks learn to solve any task, and in particular problems of high complexity? This question attracts a lot of interest, with recent works tackling computationally hard tasks such as the traveling salesman problem and…

In natural language processing (NLP), the "Transformer" architecture was proposed as the first transduction model replying entirely on self-attention mechanisms without using sequence-aligned recurrent neural networks (RNNs) or convolution,…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…