Z. Ma

Shang Liu, Hanzhao Wang, Zhongyao Ma et al.

Human-annotated preference data play an important role in aligning large language models (LLMs). In this paper, we investigate the questions of assessing the performance of human annotators and incentivizing them to provide high-quality annotations. The quality assessment of language/text annotation faces two challenges: (i) the intrinsic heterogeneity among annotators, which prevents the classic methods that assume the underlying existence of a true label; and (ii) the unclear relationship between the annotation quality and the performance of downstream tasks, which excludes the possibility of inferring the annotators' behavior based on the model performance trained from the annotation data. Then we formulate a principal-agent model to characterize the behaviors of and the interactions between the company and the human annotators. The model rationalizes a practical mechanism of a bonus scheme to incentivize annotators which benefits both parties and it underscores the importance of the joint presence of an assessment system and a proper contract scheme. From a technical perspective, our analysis extends the existing literature on the principal-agent model by considering a continuous action space for the agent. We show the gap between the first-best and the second-best solutions (under the continuous action space) is of $Θ(1/\sqrt{n \log n})$ for the binary contracts and $Θ(1/n)$ for the linear contracts, where $n$ is the number of samples used for performance assessment; this contrasts with the known result of $\exp(-Θ(n))$ for the binary contracts when the action space is discrete. Throughout the paper, we use real preference annotation data to accompany our discussions.

Zailin Ma, Jiansheng Yang, Yaodong Yang

Random feature (RF) method is a powerful kernel approximation technique, but is typically equipped with fixed activation functions, limiting its adaptability across diverse tasks. To overcome this limitation, we introduce the Random Feature Model with Learnable Activation Functions (RFLAF), a novel statistical model that parameterizes activation functions as weighted sums of basis functions within the random feature framework. Examples of basis functions include radial basis functions, spline functions, polynomials, and so forth. For theoretical results, we consider RBFs as representative basis functions. We start with a single RBF as the activation, and then extend the results to multiple RBFs, demonstrating that RF models with learnable activation component largely expand the represented function space. We provide estimates on the required number of samples and random features to achieve low excess risks. For experiments, we test RFLAF with three types of bases: radial basis functions, spline functions and polynomials. Experimental results show that RFLAFs with RBFs and splines consistently outperform other RF models, where RBFs show 3 times faster computational efficiency than splines. We then unfreeze the first-layer parameters and retrain the models, validating the expressivity advantage of learnable activation components on regular two-layer neural networks. Our work provides a deeper understanding of the component of learnable activation functions within modern neural network architectures.

Zailin Ma, Jiansheng Yang, Yaodong Yang

This paper studies the generalization properties of a recently proposed kernel method, the Random Feature models with Learnable Activation Functions (RFLAF). By applying a data-dependent sampling scheme for generating features, we provide by far the sharpest bounds on the required number of features for learning RFLAF in both the regression and classification tasks. We provide a unified theorem that describes the complexity of the feature number $s$, and discuss the results for the plain sampling scheme and the data-dependent leverage weighted scheme. Through weighted sampling, the bound on $s$ in the MSE loss case is improved from $Ω(1/ε^2)$ to $\tildeΩ((1/ε)^{1/t})$ in general $(t\geq 1)$, and even to $Ω(1)$ when the Gram matrix has a finite rank. For the Lipschitz loss case, the bound is improved from $Ω(1/ε^2)$ to $\tildeΩ((1/ε^2)^{1/t})$. To learn the weighted RFLAF, we also propose an algorithm to find an approximate kernel and then apply the leverage weighted sampling. Empirical results show that the weighted RFLAF achieves the same performances with a significantly fewer number of features compared to the plainly sampled RFLAF, validating our theories and the effectiveness of this method.