Supervised fine-tuning (SFT) has become a crucial step for aligning pretrained large language models (LLMs) using supervised datasets of input-output pairs. However, despite being supervised, SFT is inherently limited by its generative training objective. To address its limitations, the existing common strategy is to follow SFT with a separate phase of preference optimization (PO), which relies on either human-labeled preference data or a strong reward model to guide the learning process. In this paper, we address the limitations of SFT by exploring one of the most successful techniques in conventional supervised learning: discriminative learning. We introduce Discriminative Fine-Tuning (DFT), an improved variant of SFT, which mitigates the burden of collecting human-labeled preference data or training strong reward models. Unlike SFT that employs a generative approach and overlooks negative data, DFT adopts a discriminative paradigm that increases the probability of positive answers while suppressing potentially negative ones, aiming for data prediction instead of token prediction. Our contributions include: (i) a discriminative probabilistic framework for fine-tuning LLMs by explicitly modeling the discriminative likelihood of an answer among all possible outputs given an input; (ii) efficient algorithms to optimize this discriminative likelihood; and (iii) extensive experiments demonstrating DFT’s effectiveness, achieving performance better than SFT and comparable to if not better than SFT$\rightarrow$PO. The code can be found at https://github.com/Optimization-AI/DFT.

In self-supervised contrastive learning, negative pairs are typically constructed using an anchor image and a sample drawn from the entire dataset, excluding the anchor. However, this approach can result in the creation of negative pairs with similar semantics, referred to as "false negatives", leading to their embeddings being falsely pushed apart. To address this issue, we introduce GloFND, an optimization-based approach that automatically learns on the fly the threshold for each anchor data to identify its false negatives during training. In contrast to previous methods for false negative discovery, our approach globally detects false negatives across the entire dataset rather than locally within the mini-batch. Moreover, its per-iteration computation cost remains independent of the dataset size. Experimental results on image and image-text data demonstrate the effectiveness of the proposed method. Our implementation is available at https://github.com/vibalcam/GloFND.

Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a tighter analysis of two previous approximation algorithms, improving their approximation guarantees from 4 to 3. Moreover, we show that both algorithms can be derandomized in a surprisingly simple way, by greedily taking a vertex of maximum degree in an auxiliary graph and forming a cluster around it. One of these algorithms relies on solving a linear program. Our final contribution is to design a new and purely combinatorial approach for doing so that is far more scalable in theory and practice.