Generalization Bound of Gradient Flow through Training Trajectory and Data-dependent Kernel

Gradient-based optimization methods have shown remarkable empirical success, yet their theoretical generalization properties remain only partially understood. In this paper, we establish a generalization bound for gradient flow that aligns with the classical Rademacher complexity bounds for kernel methods-specifically those based on the RKHS norm and kernel trace-through a data-dependent kernel called the loss path kernel (LPK). Unlike static kernels such as NTK, the LPK captures the entire training trajectory, adapting to both data and optimization dynamics, leading to tighter and more informative generalization guarantees. Moreover, the bound highlights how the norm of the training loss gradients along the optimization trajectory influences the final generalization performance. The key technical ingredients in our proof combine stability analysis of gradient flow with uniform convergence via Rademacher complexity. Our bound recovers existing kernel regression bounds for overparameterized neural networks and shows the feature learning capability of neural networks compared to kernel methods. Numerical experiments on real-world datasets validate that our bounds correlate well with the true generalization gap.

Federated Unlearning with Gradient Descent and Conflict Mitigation

Federated Learning (FL) has received much attention in recent years. However, although clients are not required to share their data in FL, the global model itself can implicitly remember clients' local data. Therefore, it's necessary to effectively remove the target client's data from the FL global model to ease the risk of privacy leakage and implement ``the right to be forgotten". Federated Unlearning (FU) has been considered a promising way to remove data without full retraining. But the model utility easily suffers significant reduction during unlearning due to the gradient conflicts. Furthermore, when conducting the post-training to recover the model utility, the model is prone to move back and revert what has already been unlearned. To address these issues, we propose Federated Unlearning with Orthogonal Steepest Descent (FedOSD). We first design an unlearning Cross-Entropy loss to overcome the convergence issue of the gradient ascent. A steepest descent direction for unlearning is then calculated in the condition of being non-conflicting with other clients' gradients and closest to the target client's gradient. This benefits to efficiently unlearn and mitigate the model utility reduction. After unlearning, we recover the model utility by maintaining the achievement of unlearning. Finally, extensive experiments in several FL scenarios verify that FedOSD outperforms the SOTA FU algorithms in terms of unlearning and model utility.

Optimal Exact Recovery in Semi-Supervised Learning: A Study of Spectral Methods and Graph Convolutional Networks

We delve into the challenge of semi-supervised node classification on the Contextual Stochastic Block Model (CSBM) dataset. Here, nodes from the two-cluster Stochastic Block Model (SBM) are coupled with feature vectors, which are derived from a Gaussian Mixture Model (GMM) that corresponds to their respective node labels. With only a subset of the CSBM node labels accessible for training, our primary objective becomes the accurate classification of the remaining nodes. Venturing into the transductive learning landscape, we, for the first time, pinpoint the information-theoretical threshold for the exact recovery of all test nodes in CSBM. Concurrently, we design an optimal spectral estimator inspired by Principal Component Analysis (PCA) with the training labels and essential data from both the adjacency matrix and feature vectors. We also evaluate the efficacy of graph ridge regression and Graph Convolutional Networks (GCN) on this synthetic dataset. Our findings underscore that graph ridge regression and GCN possess the ability to achieve the information threshold of exact recovery in a manner akin to the optimal estimator when using the optimal weighted self-loops. This highlights the potential role of feature learning in augmenting the proficiency of GCN, especially in the realm of semi-supervised learning.

Rate, Explain and Cite (REC): Enhanced Explanation and Attribution in Automatic Evaluation by Large Language Models

LLMs have demonstrated impressive proficiency in generating coherent and high-quality text, making them valuable across a range of text-generation tasks. However, rigorous evaluation of this generated content is crucial, as ensuring its quality remains a significant challenge due to persistent issues such as factual inaccuracies and hallucinations. This paper introduces two fine-tuned general-purpose LLM autoevaluators, REC-12B and REC-70B, specifically designed to evaluate generated text across several dimensions: faithfulness, instruction following, coherence, and completeness. These models not only provide ratings for these metrics but also offer detailed explanations and verifiable citations, thereby enhancing trust in the content. Moreover, the models support various citation modes, accommodating different requirements for latency and granularity. Extensive evaluations on diverse benchmarks demonstrate that our general-purpose LLM auto-evaluator, REC-70B, outperforms state-of-the-art LLMs, excelling in content evaluation by delivering better quality explanations and citations with minimal bias. It achieves Rank \#1 as a generative model on the RewardBench leaderboard\footnote{\url{https://huggingface.co/spaces/allenai/reward-bench}} under the model name \texttt{TextEval-Llama3.1-70B}. Our REC dataset and models are released at \url{https://github.com/adelaidehsu/REC}.

UFT: Unifying Fine-Tuning of SFT and RLHF/DPO/UNA through a Generalized Implicit Reward Function

By pretraining on trillions of tokens, an LLM gains the capability of text generation. However, to enhance its utility and reduce potential harm, SFT and alignment are applied sequentially to the pretrained model. Due to the differing nature and objective functions of SFT and alignment, catastrophic forgetting has become a significant issue. To address this, we introduce Unified Fine-Tuning (UFT), which integrates SFT and alignment into a single training stage using the same objective and loss functions through an implicit reward function. Our experimental results demonstrate that UFT outperforms SFT on instruction-tuning data alone. Moreover, when combining instruction-tuning data with alignment data, UFT effectively prevents catastrophic forgetting across these two stages and shows a clear advantage over sequentially applying SFT and alignment. This is evident in the significant improvements observed in the \textbf{ifeval} task for instruction-following and the \textbf{truthful-qa} task for factuality. The proposed general fine-tuning framework UFT establishes an effective and efficient pretraining-UFT paradigm for LLM training.

FedMABA: Towards Fair Federated Learning through Multi-Armed Bandits Allocation

The increasing concern for data privacy has driven the rapid development of federated learning (FL), a privacy-preserving collaborative paradigm. However, the statistical heterogeneity among clients in FL results in inconsistent performance of the server model across various clients. Server model may show favoritism towards certain clients while performing poorly for others, heightening the challenge of fairness. In this paper, we reconsider the inconsistency in client performance distribution and introduce the concept of adversarial multi-armed bandit to optimize the proposed objective with explicit constraints on performance disparities. Practically, we propose a novel multi-armed bandit-based allocation FL algorithm (FedMABA) to mitigate performance unfairness among diverse clients with different data distributions. Extensive experiments, in different Non-I.I.D. scenarios, demonstrate the exceptional performance of FedMABA in enhancing fairness.

UNA: Unifying Alignments of RLHF/PPO, DPO and KTO by a Generalized Implicit Reward Function

An LLM is pretrained on trillions of tokens, but the pretrained LLM may still generate undesired responses. To solve this problem, alignment techniques such as RLHF, DPO and KTO are proposed. However, these alignment techniques have limitations. For example, RLHF requires training the reward model and policy separately, which is complex, time-consuming, memory intensive and unstable during training processes. DPO proposes a mapping between an optimal policy and a reward, greatly simplifying the training process of RLHF. However, it can not take full advantages of a reward model and it is limited to pairwise preference data. In this paper, we propose \textbf{UN}ified \textbf{A}lignment (UNA) which unifies RLHF/PPO, DPO and KTO. Firstly, we mathematically prove that given the classical RLHF objective, the optimal policy is induced by a generalize implicit reward function. With this novel mapping between a reward model and an optimal policy, UNA can 1. unify RLHF/PPO, DPO and KTO into a supervised learning of minimizing the difference between an implicit reward and an explicit reward; 2. outperform RLHF/PPO while simplify, stabilize, speed up and reduce memory burden of RL fine-tuning process; 3. accommodate different feedback types including pairwise, binary and scalar feedback. Downstream experiments show UNA outperforms DPO, KTO and RLHF.

StreamVoice+: Evolving into End-to-end Streaming Zero-shot Voice Conversion

StreamVoice has recently pushed the boundaries of zero-shot voice conversion (VC) in the streaming domain. It uses a streamable language model (LM) with a context-aware approach to convert semantic features from automatic speech recognition (ASR) into acoustic features with the desired speaker timbre. Despite its innovations, StreamVoice faces challenges due to its dependency on a streaming ASR within a cascaded framework, which complicates system deployment and optimization, affects VC system's design and performance based on the choice of ASR, and struggles with conversion stability when faced with low-quality semantic inputs. To overcome these limitations, we introduce StreamVoice+, an enhanced LM-based end-to-end streaming framework that operates independently of streaming ASR. StreamVoice+ integrates a semantic encoder and a connector with the original StreamVoice framework, now trained using a non-streaming ASR. This model undergoes a two-stage training process: initially, the StreamVoice backbone is pre-trained for voice conversion and the semantic encoder for robust semantic extraction. Subsequently, the system is fine-tuned end-to-end, incorporating a LoRA matrix to activate comprehensive streaming functionality. Furthermore, StreamVoice+ mainly introduces two strategic enhancements to boost conversion quality: a residual compensation mechanism in the connector to ensure effective semantic transmission and a self-refinement strategy that leverages pseudo-parallel speech pairs generated by the conversion backbone to improve speech decoupling. Experiments demonstrate that StreamVoice+ not only achieves higher naturalness and speaker similarity in voice conversion than its predecessor but also provides versatile support for both streaming and non-streaming conversion scenarios.

Universality of kernel random matrices and kernel regression in the quadratic regime

Kernel ridge regression (KRR) is a popular class of machine learning models that has become an important tool for understanding deep learning. Much of the focus has been on studying the proportional asymptotic regime, $n \asymp d$, where $n$ is the number of training samples and $d$ is the dimension of the dataset. In this regime, under certain conditions on the data distribution, the kernel random matrix involved in KRR exhibits behavior akin to that of a linear kernel. In this work, we extend the study of kernel regression to the quadratic asymptotic regime, where $n \asymp d^2$. In this regime, we demonstrate that a broad class of inner-product kernels exhibit behavior similar to a quadratic kernel. Specifically, we establish an operator norm approximation bound for the difference between the original kernel random matrix and a quadratic kernel random matrix with additional correction terms compared to the Taylor expansion of the kernel functions. The approximation works for general data distributions under a Gaussian-moment-matching assumption with a covariance structure. This new approximation is utilized to obtain a limiting spectral distribution of the original kernel matrix and characterize the precise asymptotic training and generalization errors for KRR in the quadratic regime when $n/d^2$ converges to a non-zero constant. The generalization errors are obtained for both deterministic and random teacher models. Our proof techniques combine moment methods, Wick's formula, orthogonal polynomials, and resolvent analysis of random matrices with correlated entries.

McGAN: Generating Manufacturable Designs by Embedding Manufacturing Rules into Conditional Generative Adversarial Network

Generative design (GD) methods aim to automatically generate a wide variety of designs that satisfy functional or aesthetic design requirements. However, research to date generally lacks considerations of manufacturability of the generated designs. To this end, we propose a novel GD approach by using deep neural networks to encode design for manufacturing (DFM) rules, thereby modifying part designs to make them manufacturable by a given manufacturing process. Specifically, a three-step approach is proposed: first, an instance segmentation method, Mask R-CNN, is used to decompose a part design into subregions. Second, a conditional generative adversarial neural network (cGAN), Pix2Pix, transforms unmanufacturable decomposed subregions into manufacturable subregions. The transformed subregions of designs are subsequently reintegrated into a unified manufacturable design. These three steps, Mask-RCNN, Pix2Pix, and reintegration, form the basis of the proposed Manufacturable conditional GAN (McGAN) framework. Experimental results show that McGAN can transform existing unmanufacturable designs to generate their corresponding manufacturable counterparts automatically that realize the specified manufacturing rules in an efficient and robust manner. The effectiveness of McGAN is demonstrated through two-dimensional design case studies of an injection molding process.