Haoyuan Sun

Haoyuan Sun, Kwangjun Ahn, Christos Thrampoulidis et al. · mit

Driven by the empirical success and wide use of deep neural networks, understanding the generalization performance of overparameterized models has become an increasingly popular question. To this end, there has been substantial effort to characterize the implicit bias of the optimization algorithms used, such as gradient descent (GD), and the structural properties of their preferred solutions. This paper answers an open question in this literature: For the classification setting, what solution does mirror descent (MD) converge to? Specifically, motivated by its efficient implementation, we consider the family of mirror descent algorithms with potential function chosen as the $p$-th power of the $\ell_p$-norm, which is an important generalization of GD. We call this algorithm $p$-$\textsf{GD}$. For this family, we characterize the solutions it obtains and show that it converges in direction to a generalized maximum-margin solution with respect to the $\ell_p$-norm for linearly separable classification. While the MD update rule is in general expensive to compute and perhaps not suitable for deep learning, $p$-$\textsf{GD}$ is fully parallelizable in the same manner as SGD and can be used to train deep neural networks with virtually no additional computational overhead. Using comprehensive experiments with both linear and deep neural network models, we demonstrate that $p$-$\textsf{GD}$ can noticeably affect the structure and the generalization performance of the learned models.

Haoyuan Sun, Khashayar Gatmiry, Kwangjun Ahn et al. · mit

Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how optimization algorithms impact generalization through their "preferred" solutions, a phenomenon commonly referred to as implicit regularization. In particular, it has been argued that gradient descent (GD) induces an implicit $\ell_2$-norm regularization in regression and classification problems. However, the implicit regularization of different algorithms are confined to either a specific geometry or a particular class of learning problems, indicating a gap in a general approach for controlling the implicit regularization. To address this, we present a unified approach using mirror descent (MD), a notable generalization of GD, to control implicit regularization in both regression and classification settings. More specifically, we show that MD with the general class of homogeneous potential functions converges in direction to a generalized maximum-margin solution for linear classification problems, thereby answering a long-standing question in the classification setting. Further, we show that MD can be implemented efficiently and enjoys fast convergence under suitable conditions. Through comprehensive experiments, we demonstrate that MD is a versatile method to produce learned models with different regularizers, which in turn have different generalization performances.

Devansh Jalota, Haoyuan Sun, Navid Azizan · mit

The computation of equilibrium prices at which the supply of goods matches their demand typically relies on complete information on agents' private attributes, e.g., suppliers' cost functions, which are often unavailable in practice. Motivated by this practical consideration, we consider the problem of learning equilibrium prices over a horizon of $T$ periods in the incomplete information setting wherein a market operator seeks to satisfy the customer demand for a commodity by purchasing it from competing suppliers with cost functions unknown to the operator. We first consider the setting when suppliers' cost functions are fixed and develop algorithms that, on three pertinent regret metrics, simultaneously achieve a regret of $O(1)$ when the customer demand is constant over time, and $O(\sqrt{T})$ when the demand varies over time. In the setting when the suppliers' cost functions vary over time, we demonstrate that, in general, no online algorithm can achieve sublinear regret on all three metrics. Thus, we consider an augmented setting wherein the operator has access to hints/contexts that reflect the variation in the cost functions and propose an algorithm with sublinear regret in this augmented setting. Finally, we present numerical experiments that validate our results and discuss various model extensions.

Haoyuan Sun, Bo Xia, Yongzhe Chang et al.

Direct Preference Optimization (DPO) has recently expanded its successful application from aligning large language models (LLMs) to aligning text-to-image models with human preferences, which has generated considerable interest within the community. However, we have observed that these approaches rely solely on minimizing the reverse Kullback-Leibler divergence during alignment process between the fine-tuned model and the reference model, neglecting the incorporation of other divergence constraints. In this study, we focus on extending reverse Kullback-Leibler divergence in the alignment paradigm of text-to-image models to $f$-divergence, which aims to garner better alignment performance as well as good generation diversity. We provide the generalized formula of the alignment paradigm under the $f$-divergence condition and thoroughly analyze the impact of different divergence constraints on alignment process from the perspective of gradient fields. We conduct comprehensive evaluation on image-text alignment performance, human value alignment performance and generation diversity performance under different divergence constraints, and the results indicate that alignment based on Jensen-Shannon divergence achieves the best trade-off among them. The option of divergence employed for aligning text-to-image models significantly impacts the trade-off between alignment performance (especially human value alignment) and generation diversity, which highlights the necessity of selecting an appropriate divergence for practical applications.

Tianyi Zeng, Jincheng Gao, Tianyi Wang et al.

Maintaining background consistency while enhancing foreground quality remains a core challenge in video editing. Injecting full-image information often leads to background artifacts, whereas rigid background locking severely constrains the model's capacity for foreground generation. To address this issue, we propose KV-Lock, a training-free framework tailored for DiT-based video diffusion models. Our core insight is that the hallucination metric (variance of denoising prediction) directly quantifies generation diversity, which is inherently linked to the classifier-free guidance (CFG) scale. Building upon this, KV-Lock leverages diffusion hallucination detection to dynamically schedule two key components: the fusion ratio between cached background key-values (KVs) and newly generated KVs, and the CFG scale. When hallucination risk is detected, KV-Lock strengthens background KV locking and simultaneously amplifies conditional guidance for foreground generation, thereby mitigating artifacts and improving generation fidelity. As a training-free, plug-and-play module, KV-Lock can be easily integrated into any pre-trained DiT-based models. Extensive experiments validate that our method outperforms existing approaches in improved foreground quality with high background fidelity across various video editing tasks.

Bo Fang, Yuxin Song, Qiangqiang Wu et al.

Complex video reasoning remains a significant challenge for Multimodal Large Language Models (MLLMs), as current R1-based methodologies often prioritize text-centric reasoning derived from text-based and image-based developments. In video tasks, such strategies frequently underutilize rich visual information, leading to potential shortcut learning and increased susceptibility to hallucination. To foster a more robust, visual-centric video understanding, we start by introducing a novel self-supervised reinforcement learning GRPO algorithm (Pretext-GRPO) within the standard R1 pipeline, in which positive rewards are assigned for correctly solving pretext tasks on transformed visual inputs, which makes the model to non-trivially process the visual information. Building on the effectiveness of Pretext-GRPO, we further propose the ViSS-R1 framework, which streamlines and integrates pretext-task-based self-supervised learning directly into the MLLM's R1 post-training paradigm. Instead of relying solely on sparse visual cues, our framework compels models to reason about transformed visual input by simultaneously processing both pretext questions (concerning transformations) and true user queries. This necessitates identifying the applied transformation and reconstructing the original video to formulate accurate final answers. Comprehensive evaluations on six widely-used video reasoning and understanding benchmarks demonstrate the effectiveness and superiority of our Pretext-GRPO and ViSS-R1 for complex video reasoning. Our codes and models will be publicly available.

Haoyuan Sun, Ali Jadbabaie, Navid Azizan · mit

Transformer-based models demonstrate a remarkable ability for in-context learning (ICL), where they can adapt to unseen tasks from a few prompt examples without parameter updates. Recent research has illuminated how Transformers perform ICL, showing that the optimal linear self-attention (LSA) mechanism can implement one step of gradient descent for linear least-squares objectives when trained on random linear regression tasks. Building on this, we investigate ICL for nonlinear function classes. We first prove that LSA is inherently incapable of outperforming linear predictors on nonlinear tasks, underscoring why prior solutions cannot readily extend to these problems. To overcome this limitation, we analyze a Transformer block consisting of LSA and feed-forward layers inspired by the gated linear units (GLU), which is a standard component of modern Transformers. We show that this block achieves nonlinear ICL by implementing one step of gradient descent on a polynomial kernel regression loss. Furthermore, our analysis reveals that the expressivity of a single block is inherently limited by its dimensions. We then show that a deep Transformer can overcome this bottleneck by distributing the computation of richer kernel functions across multiple blocks, performing block-coordinate descent in a high-dimensional feature space that a single block cannot represent. Our findings highlight that the feed-forward layers provide a crucial and scalable mechanism by which Transformers can express nonlinear representations for ICL.

Kai Qin, Jiaqi Wu, Jianxiang He et al.

As Large Language Models (LLMs) demonstrate remarkable capabilities learned from vast corpora, concerns regarding data privacy and safety are receiving increasing attention. LLM unlearning, which aims to remove the influence of specific data while preserving overall model utility, is becoming an important research area. One of the mainstream unlearning classes is optimization-based methods, which achieve forgetting directly through fine-tuning, exemplified by Negative Preference Optimization (NPO). However, NPO's effectiveness is limited by its inherent lack of explicit positive preference signals. Attempts to introduce such signals by constructing preferred responses often necessitate domain-specific knowledge or well-designed prompts, fundamentally restricting their generalizability. In this paper, we shift the focus to the distribution-level, directly targeting the next-token probability distribution instead of entire responses, and derive a novel unlearning algorithm termed \textbf{Di}stribution \textbf{P}reference \textbf{O}ptimization (DiPO). We show that the requisite preference distribution pairs for DiPO, which are distributions over the model's output tokens, can be constructed by selectively amplifying or suppressing the model's high-confidence output logits, thereby effectively overcoming NPO's limitations. We theoretically prove the consistency of DiPO's loss function with the desired unlearning direction. Extensive experiments demonstrate that DiPO achieves a strong trade-off between model utility and forget quality. Notably, DiPO attains the highest forget quality on the TOFU benchmark, and maintains leading scalability and sustainability in utility preservation on the MUSE benchmark.