Generalization Bounds via Conditional $f$-Information

In this work, we introduce novel information-theoretic generalization bounds using the conditional $f$-information framework, an extension of the traditional conditional mutual information (MI) framework. We provide a generic approach to derive generalization bounds via $f$-information in the supersample setting, applicable to both bounded and unbounded loss functions. Unlike previous MI-based bounds, our proof strategy does not rely on upper bounding the cumulant-generating function (CGF) in the variational formula of MI. Instead, we set the CGF or its upper bound to zero by carefully selecting the measurable function invoked in the variational formula. Although some of our techniques are partially inspired by recent advances in the coin-betting framework (e.g., Jang et al. (2023)), our results are independent of any previous findings from regret guarantees of online gambling algorithms. Additionally, our newly derived MI-based bound recovers many previous results and improves our understanding of their potential limitations. Finally, we empirically compare various $f$-information measures for generalization, demonstrating the improvement of our new bounds over the previous bounds.

Universally Optimal Watermarking Schemes for LLMs: from Theory to Practice

Large Language Models (LLMs) boosts human efficiency but also poses misuse risks, with watermarking serving as a reliable method to differentiate AI-generated content from human-created text. In this work, we propose a novel theoretical framework for watermarking LLMs. Particularly, we jointly optimize both the watermarking scheme and detector to maximize detection performance, while controlling the worst-case Type-I error and distortion in the watermarked text. Within our framework, we characterize the universally minimum Type-II error, showing a fundamental trade-off between detection performance and distortion. More importantly, we identify the optimal type of detectors and watermarking schemes. Building upon our theoretical analysis, we introduce a practical, model-agnostic and computationally efficient token-level watermarking algorithm that invokes a surrogate model and the Gumbel-max trick. Empirical results on Llama-13B and Mistral-8$\times$7B demonstrate the effectiveness of our method. Furthermore, we also explore how robustness can be integrated into our theoretical framework, which provides a foundation for designing future watermarking systems with improved resilience to adversarial attacks.

Activated Parameter Locating via Causal Intervention for Model Merging

Model merging combines multiple homologous models into one model, achieving convincing generalization without the necessity of additional training. A key challenge in this problem is resolving parameter redundancies and conflicts across multiple models. Existing models have demonstrated that dropping a portion of delta parameters can alleviate conflicts while maintaining performance. However, these methods often drop parameters either randomly or based on magnitude, overlooking task-specific information embedded in fine-tuned models. In this paper, we propose an Activated Parameter Locating (APL) method that utilizes causal intervention to estimate parameter importance, enabling more precise parameter drops and better conflict mitigation. Moreover, to reduce the computational complexity associated with a large number of parameter partitions, we also introduce a theoretically supported gradient approximation strategy for APL. Experiments on model merging within both in-domain and out-of-domain settings, along with associated analyses, showcase the effectiveness of APL.

Cross-Modal and Uni-Modal Soft-Label Alignment for Image-Text Retrieval

Current image-text retrieval methods have demonstrated impressive performance in recent years. However, they still face two problems: the inter-modal matching missing problem and the intra-modal semantic loss problem. These problems can significantly affect the accuracy of image-text retrieval. To address these challenges, we propose a novel method called Cross-modal and Uni-modal Soft-label Alignment (CUSA). Our method leverages the power of uni-modal pre-trained models to provide soft-label supervision signals for the image-text retrieval model. Additionally, we introduce two alignment techniques, Cross-modal Soft-label Alignment (CSA) and Uni-modal Soft-label Alignment (USA), to overcome false negatives and enhance similarity recognition between uni-modal samples. Our method is designed to be plug-and-play, meaning it can be easily applied to existing image-text retrieval models without changing their original architectures. Extensive experiments on various image-text retrieval models and datasets, we demonstrate that our method can consistently improve the performance of image-text retrieval and achieve new state-of-the-art results. Furthermore, our method can also boost the uni-modal retrieval performance of image-text retrieval models, enabling it to achieve universal retrieval. The code and supplementary files can be found at https://github.com/lerogo/aaai24_itr_cusa.

On f-Divergence Principled Domain Adaptation: An Improved Framework

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 by Acuna et al. (2021) by refining their f-divergence-based discrepancy and additionally introducing a new measure, f-domain discrepancy (f-DD). By removing the absolute value function and incorporating a scaling parameter, f-DD yields novel target error and sample complexity bounds, allowing us to recover previous KL-based results and bridging the gap between algorithms and theory presented in Acuna et al. (2021). Leveraging a localization technique, we also develop a fast-rate generalization bound. Empirical results demonstrate the superior performance of f-DD-based domain learning algorithms over previous works in popular UDA benchmarks.

Sample-Conditioned Hypothesis Stability Sharpens Information-Theoretic Generalization Bounds

We present new information-theoretic generalization guarantees through the a novel construction of the "neighboring-hypothesis" matrix and a new family of stability notions termed sample-conditioned hypothesis (SCH) stability. Our approach yields sharper bounds that improve upon previous information-theoretic bounds in various learning scenarios. Notably, these bounds address the limitations of existing information-theoretic bounds in the context of stochastic convex optimization (SCO) problems, as explored in the recent work by Haghifam et al. (2023).

Over-training with Mixup May Hurt Generalization

Mixup, which creates synthetic training instances by linearly interpolating random sample pairs, is a simple and yet effective regularization technique to boost the performance of deep models trained with SGD. In this work, we report a previously unobserved phenomenon in Mixup training: on a number of standard datasets, the performance of Mixup-trained models starts to decay after training for a large number of epochs, giving rise to a U-shaped generalization curve. This behavior is further aggravated when the size of original dataset is reduced. To help understand such a behavior of Mixup, we show theoretically that Mixup training may introduce undesired data-dependent label noises to the synthesized data. Via analyzing a least-square regression problem with a random feature model, we explain why noisy labels may cause the U-shaped curve to occur: Mixup improves generalization through fitting the clean patterns at the early training stage, but as training progresses, Mixup becomes over-fitting to the noise in the synthetic data. Extensive experiments are performed on a variety of benchmark datasets, validating this explanation.

Tighter Information-Theoretic Generalization Bounds from Supersamples

We present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

Two Facets of SDE Under an Information-Theoretic Lens: Generalization of SGD via Training Trajectories and via Terminal States

Stochastic differential equations (SDEs) have been shown recently to well characterize the dynamics of training machine learning models with SGD. This provides two opportunities for better understanding the generalization behaviour of SGD through its SDE approximation. First, under the SDE characterization, SGD may be regarded as the full-batch gradient descent with Gaussian gradient noise. This allows the application of the generalization bounds developed by Xu & Raginsky (2017) to analyzing the generalization behaviour of SGD, resulting in upper bounds in terms of the mutual information between the training set and the training trajectory. Second, under mild assumptions, it is possible to obtain an estimate of the steady-state weight distribution of SDE. Using this estimate, we apply the PAC-Bayes-like information-theoretic bounds developed in both Xu & Raginsky (2017) and Negrea et al. (2019) to obtain generalization upper bounds in terms of the KL divergence between the steady-state weight distribution of SGD with respect to a prior distribution. Among various options, one may choose the prior as the steady-state weight distribution obtained by SGD on the same training set but with one example held out. In this case, the bound can be elegantly expressed using the influence function (Koh & Liang, 2017), which suggests that the generalization of the SGD is related to the stability of SGD. Various insights are presented along the development of these bounds, which are subsequently validated numerically.

Information-Theoretic Analysis of Unsupervised Domain Adaptation

This paper uses information-theoretic tools to analyze the generalization error in unsupervised domain adaptation (UDA). We present novel upper bounds for two notions of generalization errors. The first notion measures the gap between the population risk in the target domain and that in the source domain, and the second measures the gap between the population risk in the target domain and the empirical risk in the source domain. While our bounds for the first kind of error are in line with the traditional analysis and give similar insights, our bounds on the second kind of error are algorithm-dependent, which also provide insights into algorithm designs. Specifically, we present two simple techniques for improving generalization in UDA and validate them experimentally.