Unraveling the Gradient Descent Dynamics of Transformers

While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this understanding gap by answering the following two core questions: (1) Which types of Transformer architectures allow Gradient Descent (GD) to achieve guaranteed convergence? and (2) Under what initial conditions and architectural specifics does the Transformer achieve rapid convergence during training? By analyzing the loss landscape of a single Transformer layer using Softmax and Gaussian attention kernels, our work provides concrete answers to these questions. Our findings demonstrate that, with appropriate weight initialization, GD can train a Transformer model (with either kernel type) to achieve a global optimal solution, especially when the input embedding dimension is large. Nonetheless, certain scenarios highlight potential pitfalls: training a Transformer using the Softmax attention kernel may sometimes lead to suboptimal local solutions. In contrast, the Gaussian attention kernel exhibits a much favorable behavior. Our empirical study further validate the theoretical findings.

MAP: Multi-Human-Value Alignment Palette

Ensuring that generative AI systems align with human values is essential but challenging, especially when considering multiple human values and their potential trade-offs. Since human values can be personalized and dynamically change over time, the desirable levels of value alignment vary across different ethnic groups, industry sectors, and user cohorts. Within existing frameworks, it is hard to define human values and align AI systems accordingly across different directions simultaneously, such as harmlessness, helpfulness, and positiveness. To address this, we develop a novel, first-principle approach called Multi-Human-Value Alignment Palette (MAP), which navigates the alignment across multiple human values in a structured and reliable way. MAP formulates the alignment problem as an optimization task with user-defined constraints, which define human value targets. It can be efficiently solved via a primal-dual approach, which determines whether a user-defined alignment target is achievable and how to achieve it. We conduct a detailed theoretical analysis of MAP by quantifying the trade-offs between values, the sensitivity to constraints, the fundamental connection between multi-value alignment and sequential alignment, and proving that linear weighted rewards are sufficient for multi-value alignment. Extensive experiments demonstrate MAP's ability to align multiple values in a principled manner while delivering strong empirical performance across various tasks.

Drift to Remember

Lifelong learning in artificial intelligence (AI) aims to mimic the biological brain's ability to continuously learn and retain knowledge, yet it faces challenges such as catastrophic forgetting. Recent neuroscience research suggests that neural activity in biological systems undergoes representational drift, where neural responses evolve over time, even with consistent inputs and tasks. We hypothesize that representational drift can alleviate catastrophic forgetting in AI during new task acquisition. To test this, we introduce DriftNet, a network designed to constantly explore various local minima in the loss landscape while dynamically retrieving relevant tasks. This approach ensures efficient integration of new information and preserves existing knowledge. Experimental studies in image classification and natural language processing demonstrate that DriftNet outperforms existing models in lifelong learning. Importantly, DriftNet is scalable in handling a sequence of tasks such as sentiment analysis and question answering using large language models (LLMs) with billions of parameters on a single Nvidia A100 GPU. DriftNet efficiently updates LLMs using only new data, avoiding the need for full dataset retraining. Tested on GPT-2 and RoBERTa, DriftNet is a robust, cost-effective solution for lifelong learning in LLMs. This study not only advances AI systems to emulate biological learning, but also provides insights into the adaptive mechanisms of biological neural systems, deepening our understanding of lifelong learning in nature.

DynamicFL: Federated Learning with Dynamic Communication Resource Allocation

Federated Learning (FL) is a collaborative machine learning framework that allows multiple users to train models utilizing their local data in a distributed manner. However, considerable statistical heterogeneity in local data across devices often leads to suboptimal model performance compared with independently and identically distributed (IID) data scenarios. In this paper, we introduce DynamicFL, a new FL framework that investigates the trade-offs between global model performance and communication costs for two widely adopted FL methods: Federated Stochastic Gradient Descent (FedSGD) and Federated Averaging (FedAvg). Our approach allocates diverse communication resources to clients based on their data statistical heterogeneity, considering communication resource constraints, and attains substantial performance enhancements compared to uniform communication resource allocation. Notably, our method bridges the gap between FedSGD and FedAvg, providing a flexible framework leveraging communication heterogeneity to address statistical heterogeneity in FL. Through extensive experiments, we demonstrate that DynamicFL surpasses current state-of-the-art methods with up to a 10% increase in model accuracy, demonstrating its adaptability and effectiveness in tackling data statistical heterogeneity challenges.

Drop the beat! Freestyler for Accompaniment Conditioned Rapping Voice Generation

Rap, a prominent genre of vocal performance, remains underexplored in vocal generation. General vocal synthesis depends on precise note and duration inputs, requiring users to have related musical knowledge, which limits flexibility. In contrast, rap typically features simpler melodies, with a core focus on a strong rhythmic sense that harmonizes with accompanying beats. In this paper, we propose Freestyler, the first system that generates rapping vocals directly from lyrics and accompaniment inputs. Freestyler utilizes language model-based token generation, followed by a conditional flow matching model to produce spectrograms and a neural vocoder to restore audio. It allows a 3-second prompt to enable zero-shot timbre control. Due to the scarcity of publicly available rap datasets, we also present RapBank, a rap song dataset collected from the internet, alongside a meticulously designed processing pipeline. Experimental results show that Freestyler produces high-quality rapping voice generation with enhanced naturalness and strong alignment with accompanying beats, both stylistically and rhythmically.

Base Models for Parabolic Partial Differential Equations

Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often necessary to compute the solutions or a function of the solutions to a parametric PDE in multiple scenarios corresponding to different parameters of this PDE. This process often requires resolving the PDEs from scratch, which is time-consuming. To better employ existing simulations for the PDEs, we propose a framework for finding solutions to parabolic PDEs across different scenarios by meta-learning an underlying base distribution. We build upon this base distribution to propose a method for computing solutions to parametric PDEs under different parameter settings. Finally, we illustrate the application of the proposed methods through extensive experiments in generative modeling, stochastic control, and finance. The empirical results suggest that the proposed approach improves generalization to solving PDEs under new parameter regimes.

CroMo-Mixup: Augmenting Cross-Model Representations for Continual Self-Supervised Learning

Continual self-supervised learning (CSSL) learns a series of tasks sequentially on the unlabeled data. Two main challenges of continual learning are catastrophic forgetting and task confusion. While CSSL problem has been studied to address the catastrophic forgetting challenge, little work has been done to address the task confusion aspect. In this work, we show through extensive experiments that self-supervised learning (SSL) can make CSSL more susceptible to the task confusion problem, particularly in less diverse settings of class incremental learning because different classes belonging to different tasks are not trained concurrently. Motivated by this challenge, we present a novel cross-model feature Mixup (CroMo-Mixup) framework that addresses this issue through two key components: 1) Cross-Task data Mixup, which mixes samples across tasks to enhance negative sample diversity; and 2) Cross-Model feature Mixup, which learns similarities between embeddings obtained from current and old models of the mixed sample and the original images, facilitating cross-task class contrast learning and old knowledge retrieval. We evaluate the effectiveness of CroMo-Mixup to improve both Task-ID prediction and average linear accuracy across all tasks on three datasets, CIFAR10, CIFAR100, and tinyImageNet under different class-incremental learning settings. We validate the compatibility of CroMo-Mixup on four state-of-the-art SSL objectives. Code is available at \url{https://github.com/ErumMushtaq/CroMo-Mixup}.

Robust Score-Based Quickest Change Detection

Methods in the field of quickest change detection rapidly detect in real-time a change in the data-generating distribution of an online data stream. Existing methods have been able to detect this change point when the densities of the pre- and post-change distributions are known. Recent work has extended these results to the case where the pre- and post-change distributions are known only by their score functions. This work considers the case where the pre- and post-change score functions are known only to correspond to distributions in two disjoint sets. This work employs a pair of "least-favorable" distributions to robustify the existing score-based quickest change detection algorithm, the properties of which are studied. This paper calculates the least-favorable distributions for specific model classes and provides methods of estimating the least-favorable distributions for common constructions. Simulation results are provided demonstrating the performance of our robust change detection algorithm.

Additive-Effect Assisted Learning

It is quite popular nowadays for researchers and data analysts holding different datasets to seek assistance from each other to enhance their modeling performance. We consider a scenario where different learners hold datasets with potentially distinct variables, and their observations can be aligned by a nonprivate identifier. Their collaboration faces the following difficulties: First, learners may need to keep data values or even variable names undisclosed due to, e.g., commercial interest or privacy regulations; second, there are restrictions on the number of transmission rounds between them due to e.g., communication costs. To address these challenges, we develop a two-stage assisted learning architecture for an agent, Alice, to seek assistance from another agent, Bob. In the first stage, we propose a privacy-aware hypothesis testing-based screening method for Alice to decide on the usefulness of the data from Bob, in a way that only requires Bob to transmit sketchy data. Once Alice recognizes Bob's usefulness, Alice and Bob move to the second stage, where they jointly apply a synergistic iterative model training procedure. With limited transmissions of summary statistics, we show that Alice can achieve the oracle performance as if the training were from centralized data, both theoretically and numerically.

ColA: Collaborative Adaptation with Gradient Learning

A primary function of back-propagation is to compute both the gradient of hidden representations and parameters for optimization with gradient descent. Training large models requires high computational costs due to their vast parameter sizes. While Parameter-Efficient Fine-Tuning (PEFT) methods aim to train smaller auxiliary models to save computational space, they still present computational overheads, especially in Fine-Tuning as a Service (FTaaS) for numerous users. We introduce Collaborative Adaptation (ColA) with Gradient Learning (GL), a parameter-free, model-agnostic fine-tuning approach that decouples the computation of the gradient of hidden representations and parameters. In comparison to PEFT methods, ColA facilitates more cost-effective FTaaS by offloading the computation of the gradient to low-cost devices. We also provide a theoretical analysis of ColA and experimentally demonstrate that ColA can perform on par or better than existing PEFT methods on various benchmarks.