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Reinforcement learning (RL) has emerged as a promising strategy for finetuning small language models (SLMs) to solve targeted tasks such as math and coding. However, RL algorithms tend to be resource-intensive, taking a significant amount…
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…
This work studies post-training parameter quantization in large language models (LLMs). We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from $\textit{incoherent}$…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
The proliferation of edge devices has unlocked unprecedented opportunities for deep learning model deployment in computer vision applications. However, these complex models require considerable power, memory and compute resources that are…
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…
Rotations have become essential to state-of-the-art quantization pipelines for large language models (LLMs) by effectively smoothing outliers in weights and activations. However, further optimizing the rotation parameters offers only…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of…
Classical neural network approximation results take the form: for every function $f$ and every error tolerance $\epsilon > 0$, one constructs a neural network whose architecture and weights depend on $\epsilon$. This paper introduces a…
A loop invariant is a property of a loop that remains true before and after each execution of the loop. The identification of loop invariants is a critical step to support automated program safety assessment. Recent advancements in Large…
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pad\'e approximation, sometimes accompanied by the Schur decomposition. The main computational…
In many instances of fixed-point multiplication, a full precision result is not required. Instead it is sufficient to return a faithfully rounded result. Faithful rounding permits the machine representable number either immediately above or…
This paper presents RevOrder, a novel technique aimed at improving arithmetic operations in large language models (LLMs) by reversing the output digits in addition, subtraction, and n-digit by 1-digit (nD by 1D) multiplication tasks. Our…
Recent advancements in large reasoning models (LRMs) have demonstrated the effectiveness of scaling test-time computation to enhance reasoning capabilities on various tasks. However, LRMs often suffer from an ``overthinking'' problem, where…
We consider several extensions of the fractional bin packing problem, a relaxation of the traditional bin packing problem where the objects may be split across multiple bins. In these extensions, we introduce load-balancing constraints…
We present REMM, a rotation-equivariant framework for end-to-end multimodal image matching, which fully encodes rotational differences of descriptors in the whole matching pipeline. Previous learning-based methods mainly focus on extracting…
Large Language Models (LLMs) are increasingly deployed in high-stakes contexts where their outputs influence real-world decisions. However, evaluating bias in LLM outputs remains methodologically challenging due to sensitivity to prompt…