Many-to-Many Matching via Sparsity Controlled Optimal Transport

Many-to-many matching seeks to match multiple points in one set and multiple points in another set, which is a basis for a wide range of data mining problems. It can be naturally recast in the framework of Optimal Transport (OT). However, existing OT methods either lack the ability to accomplish many-to-many matching or necessitate careful tuning of a regularization parameter to achieve satisfactory results. This paper proposes a novel many-to-many matching method to explicitly encode many-to-many constraints while preventing the degeneration into one-to-one matching. The proposed method consists of the following two components. The first component is the matching budget constraints on each row and column of a transport plan, which specify how many points can be matched to a point at most. The second component is the deformed $q$-entropy regularization, which encourages a point to meet the matching budget maximally. While the deformed $q$-entropy was initially proposed to sparsify a transport plan, we employ it to avoid the degeneration into one-to-one matching. We optimize the objective via a penalty algorithm, which is efficient and theoretically guaranteed to converge. Experimental results on various tasks demonstrate that the proposed method achieves good performance by gleaning meaningful many-to-many matchings.

Efficient Model Editing with Task Vector Bases: A Theoretical Framework and Scalable Approach

Task vectors, which are derived from the difference between pre-trained and fine-tuned model weights, enable flexible task adaptation and model merging through arithmetic operations such as addition and negation. However, existing approaches often rely on heuristics with limited theoretical support, often leading to performance gaps comparing to direct task fine tuning. Meanwhile, although it is easy to manipulate saved task vectors with arithmetic for different purposes, such compositional flexibility demands high memory usage, especially when dealing with a huge number of tasks, limiting scalability. This work addresses these issues with a theoretically grounded framework that explains task vector arithmetic and introduces the task vector bases framework. Building upon existing task arithmetic literature, our method significantly reduces the memory cost for downstream arithmetic with little effort, while achieving competitive performance and maintaining compositional advantage, providing a practical solution for large-scale task arithmetic.

On Verbalized Confidence Scores for LLMs

The rise of large language models (LLMs) and their tight integration into our daily life make it essential to dedicate efforts towards their trustworthiness. Uncertainty quantification for LLMs can establish more human trust into their responses, but also allows LLM agents to make more informed decisions based on each other's uncertainty. To estimate the uncertainty in a response, internal token logits, task-specific proxy models, or sampling of multiple responses are commonly used. This work focuses on asking the LLM itself to verbalize its uncertainty with a confidence score as part of its output tokens, which is a promising way for prompt- and model-agnostic uncertainty quantification with low overhead. Using an extensive benchmark, we assess the reliability of verbalized confidence scores with respect to different datasets, models, and prompt methods. Our results reveal that the reliability of these scores strongly depends on how the model is asked, but also that it is possible to extract well-calibrated confidence scores with certain prompt methods. We argue that verbalized confidence scores can become a simple but effective and versatile uncertainty quantification method in the future. Our code is available at https://github.com/danielyxyang/llm-verbalized-uq .

Learning Structured Representations with Hyperbolic Embeddings

Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this hierarchy, treating labels as permutation invariant. Recent work [Zeng et al., 2022] proposes using this structured information explicitly, but the use of Euclidean distance may distort the underlying semantic context [Chen et al., 2013]. In this work, motivated by the advantage of hyperbolic spaces in modeling hierarchical relationships, we propose a novel approach HypStructure: a Hyperbolic Structured regularization approach to accurately embed the label hierarchy into the learned representations. HypStructure is a simple-yet-effective regularizer that consists of a hyperbolic tree-based representation loss along with a centering loss, and can be combined with any standard task loss to learn hierarchy-informed features. Extensive experiments on several large-scale vision benchmarks demonstrate the efficacy of HypStructure in reducing distortion and boosting generalization performance especially under low dimensional scenarios. For a better understanding of structured representation, we perform eigenvalue analysis that links the representation geometry to improved Out-of-Distribution (OOD) detection performance seen empirically. The code is available at \url{https://github.com/uiuctml/HypStructure}.

Fast unsupervised ground metric learning with tree-Wasserstein distance

The performance of unsupervised methods such as clustering depends on the choice of distance metric between features, or ground metric. Commonly, ground metrics are decided with heuristics or learned via supervised algorithms. However, since many datasets are unlabelled, unsupervised ground metric learning approaches have been introduced. One recent, promising option uses Wasserstein singular vectors (WSV), which emerge when computing optimal transport distances between features and samples simultaneously. While WSV is effective, it has complexity $\mathcal{O}(n^5)$, which is prohibitively expensive in some applications. In this work, we propose to augment the WSV method by embedding samples and features on trees, on which we compute the tree-Wasserstein distance (TWD). We demonstrate theoretically and empirically that the algorithm converges to a better approximation of the full WSV approach than the best known alternatives, and does so with $\mathcal{O}(n^3)$ complexity. In addition, we prove that the initial tree structure can be chosen flexibly, since tree geometry does not constrain the richness of the approximation up to the number of edge weights. This proof suggests a fast, recursive algorithm for computing the tree parameter basis set, which we find crucial to realising the efficiency gains at scale. Finally, we employ the tree-WSV algorithm to several single-cell RNA sequencing genomics datasets, demonstrating its scalability and utility for unsupervised cell-type clustering problems. These results poise unsupervised ground metric learning with TWD as a low-rank approximation of WSV with the potential for widespread low-compute application.

Towards the Effect of Examples on In-Context Learning: A Theoretical Case Study

In-context learning (ICL) has emerged as a powerful capability for large language models (LLMs) to adapt to downstream tasks by leveraging a few (demonstration) examples. Despite its effectiveness, the mechanism behind ICL remains underexplored. To better understand how ICL integrates the examples with the knowledge learned by the LLM during pre-training (i.e., pre-training knowledge) and how the examples impact ICL, this paper conducts a theoretical study in binary classification tasks. In particular, we introduce a probabilistic model extending from the Gaussian mixture model to exactly quantify the impact of pre-training knowledge, label frequency, and label noise on the prediction accuracy. Based on our analysis, when the pre-training knowledge contradicts the knowledge in the examples, whether ICL prediction relies more on the pre-training knowledge or the examples depends on the number of examples. In addition, the label frequency and label noise of the examples both affect the accuracy of the ICL prediction, where the minor class has a lower accuracy, and how the label noise impacts the accuracy is determined by the specific noise level of the two classes. Extensive simulations are conducted to verify the correctness of the theoretical results, and real-data experiments also align with the theoretical insights. Our work reveals the role of pre-training knowledge and examples in ICL, offering a deeper understanding of LLMs' behaviors in classification tasks.

Learning Structured Representations by Embedding Class Hierarchy with Fast Optimal Transport

To embed structured knowledge within labels into feature representations, prior work (Zeng et al., 2022) proposed to use the Cophenetic Correlation Coefficient (CPCC) as a regularizer during supervised learning. This regularizer calculates pairwise Euclidean distances of class means and aligns them with the corresponding shortest path distances derived from the label hierarchy tree. However, class means may not be good representatives of the class conditional distributions, especially when they are multi-mode in nature. To address this limitation, under the CPCC framework, we propose to use the Earth Mover's Distance (EMD) to measure the pairwise distances among classes in the feature space. We show that our exact EMD method generalizes previous work, and recovers the existing algorithm when class-conditional distributions are Gaussian in the feature space. To further improve the computational efficiency of our method, we introduce the Optimal Transport-CPCC family by exploring four EMD approximation variants. Our most efficient OT-CPCC variant runs in linear time in the size of the dataset, while maintaining competitive performance across datasets and tasks.

Towards Understanding Jailbreak Attacks in LLMs: A Representation Space Analysis

Large language models (LLMs) are susceptible to a type of attack known as jailbreaking, which misleads LLMs to output harmful contents. Although there are diverse jailbreak attack strategies, there is no unified understanding on why some methods succeed and others fail. This paper explores the behavior of harmful and harmless prompts in the LLM's representation space to investigate the intrinsic properties of successful jailbreak attacks. We hypothesize that successful attacks share some similar properties: They are effective in moving the representation of the harmful prompt towards the direction to the harmless prompts. We leverage hidden representations into the objective of existing jailbreak attacks to move the attacks along the acceptance direction, and conduct experiments to validate the above hypothesis using the proposed objective. We hope this study provides new insights into understanding how LLMs understand harmfulness information.

Polyak Meets Parameter-free Clipped Gradient Descent

Gradient descent and its variants are de facto standard algorithms for training machine learning models. As gradient descent is sensitive to its hyperparameters, we need to tune the hyperparameters carefully using a grid search, but it is time-consuming, especially when multiple hyperparameters exist. Recently, parameter-free methods that adjust the hyperparameters on the fly have been studied. However, the existing work only studied parameter-free methods for the stepsize, and parameter-free methods for other hyperparameters have not been explored. For instance, the gradient clipping threshold is also a crucial hyperparameter in addition to the stepsize to prevent gradient explosion issues, but none of the existing studies investigated the parameter-free methods for clipped gradient descent. In this work, we study the parameter-free methods for clipped gradient descent. Specifically, we propose Inexact Polyak Stepsize, which converges to the optimal solution without any hyperparameters tuning, and its convergence rate is asymptotically independent of L under L-smooth and $(L_0, L_1)$-smooth assumptions of the loss function as that of clipped gradient descent with well-tuned hyperparameters. We numerically validated our convergence results using a synthetic function and demonstrated the effectiveness of our proposed methods using LSTM, Nano-GPT, and T5.

PhiNets: Brain-inspired Non-contrastive Learning Based on Temporal Prediction Hypothesis

SimSiam is a prominent self-supervised learning method that achieves impressive results in various vision tasks under static environments. However, it has two critical issues: high sensitivity to hyperparameters, especially weight decay, and unsatisfactory performance in online and continual learning, where neuroscientists believe that powerful memory functions are necessary, as in brains. In this paper, we propose PhiNet, inspired by a hippocampal model based on the temporal prediction hypothesis. Unlike SimSiam, which aligns two augmented views of the original image, PhiNet integrates an additional predictor block that estimates the original image representation to imitate the CA1 region in the hippocampus. Moreover, we model the neocortex inspired by the Complementary Learning Systems theory with a momentum encoder block as a slow learner, which works as long-term memory. We demonstrate through analysing the learning dynamics that PhiNet benefits from the additional predictor to prevent the complete collapse of learned representations, a notorious challenge in non-contrastive learning. This dynamics analysis may partially corroborate why this hippocampal model is biologically plausible. Experimental results demonstrate that PhiNet is more robust to weight decay and performs better than SimSiam in memory-intensive tasks like online and continual learning.