Related papers: Sums and differences of sets (improvement over Alp…
Deep learning has become very popular for tasks such as predictive modeling and pattern recognition in handling big data. Deep learning is a powerful machine learning method that extracts lower level features and feeds them forward for the…
Deep ensembles excel in large-scale image classification tasks both in terms of prediction accuracy and calibration. Despite being simple to train, the computation and memory cost of deep ensembles limits their practicability. While some…
Unsupervised domain adaptation (UDA) plays a crucial role in addressing distribution shifts in machine learning. In this work, we improve the theoretical foundations of UDA proposed in Acuna et al. (2021) by refining their…
Large language models (LLMs) have significantly improved their reasoning capabilities; however, they still struggle with complex multi-step mathematical problem-solving due to error propagation, lack of self-correction, and limited…
Fine-tuning pre-trained language models, particularly large language models, demands extensive computing resources and can result in varying performance outcomes across different domains and datasets. This paper examines the approach of…
Fast estimates of model uncertainty are required for many robust robotics applications. Deep Ensembles provides state of the art uncertainty without requiring Bayesian methods, but still it is computationally expensive. In this paper we…
Deep learning and deep architectures are emerging as the best machine learning methods so far in many practical applications such as reducing the dimensionality of data, image classification, speech recognition or object segmentation. In…
Machine learning-based Deepfake detection models have achieved impressive results on benchmark datasets, yet their performance often deteriorates significantly when evaluated on out-of-distribution data. In this work, we investigate an…
A finite horizon variant of the quickest change detection problem is studied, in which the goal is to minimize a delay threshold (latency), under constraints on the probability of false alarm and the probability that the latency is…
We study the question of finding big Bruhat intervals that are poset hypercubes in the symmetric group $S_n$. Using permutations suggested by AlphaEvolve (an evolutionary coding agent developed by Google DeepMind), we were led to an unusual…
Sumsets are central objects in additive combinatorics. In 2007, Granville asked whether one can efficiently recognize whether a given set $S$ is a sumset, i.e. whether there is a set $A$ such that $A+A=S$. Granville suggested an algorithm…
Neural networks are increasingly being used to solve partial differential equations (PDEs), replacing slower numerical solvers. However, a critical issue is that neural PDE solvers require high-quality ground truth data, which usually must…
Recent advances in LLM-guided evolutionary computation, particularly AlphaEvolve (Novikov et al., 2025; Georgiev et al., 2025), have demonstrated remarkable success in discovering novel mathematical constructions and solving challenging…
Let $0< n,\alpha,\beta\in\mathbb{N}$ be such that $\gcd{(\alpha,\beta)}=1$. We carry out the evaluation of the convolution sums $\underset{\substack{ {(k,l)\in\mathbb{N}^{2}} \\ {\alpha\,k+\beta\,l=n} } }{\sum}\sigma(k)\sigma_{3}(l)$ and…
General-purpose Large Language Models (LLMs) are frequently fine-tuned through supervised fine-tuning (SFT) to enhance performance in specific domains. Better results can be achieved by distilling the chain-of-thought of a larger model at…
We propose a new finetuning method to provide pre-trained large language models (LMs) the ability to scale test-time compute through the diffusion framework. By increasing the number of diffusion steps, we show our finetuned models achieve…
In a previous paper {GN2} an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean ergodic theorem for the…
The sequence of 1/2-discrepancy sums of $\{x + i \theta \bmod 1\}$ is realized through a sequence of substitutions on an alphabet of three symbols; particular attention is paid to $x=0$. The first application is to show that any asymptotic…
This paper discovers that the neural network with lower decision boundary (DB) variability has better generalizability. Two new notions, algorithm DB variability and $(\epsilon, \eta)$-data DB variability, are proposed to measure the…
Evolutionary agentic systems intensify the trade-off between computational efficiency and reasoning capability by repeatedly invoking large language models (LLMs) during inference. This setting raises a central question: how can an agent…