Dmitry Rybin

Zhiwei Tang, Dmitry Rybin, Tsung-Hui Chang

In this study, we delve into an emerging optimization challenge involving a black-box objective function that can only be gauged via a ranking oracle-a situation frequently encountered in real-world scenarios, especially when the function is evaluated by human judges. Such challenge is inspired from Reinforcement Learning with Human Feedback (RLHF), an approach recently employed to enhance the performance of Large Language Models (LLMs) using human guidance. We introduce ZO-RankSGD, an innovative zeroth-order optimization algorithm designed to tackle this optimization problem, accompanied by theoretical assurances. Our algorithm utilizes a novel rank-based random estimator to determine the descent direction and guarantees convergence to a stationary point. Moreover, ZO-RankSGD is readily applicable to policy optimization problems in Reinforcement Learning (RL), particularly when only ranking oracles for the episode reward are available. Last but not least, we demonstrate the effectiveness of ZO-RankSGD in a novel application: improving the quality of images generated by a diffusion generative model with human ranking feedback. Throughout experiments, we found that ZO-RankSGD can significantly enhance the detail of generated images with only a few rounds of human feedback. Overall, our work advances the field of zeroth-order optimization by addressing the problem of optimizing functions with only ranking feedback, and offers a new and effective approach for aligning Artificial Intelligence (AI) with human intentions.

Dmitry Rybin, Ruoyu Sun, Zhi-Quan Luo

Neural networks that satisfy invariance with respect to input permutations have been widely studied in machine learning literature. However, in many applications, only a subset of all input permutations is of interest. For heterogeneous graph data, one can focus on permutations that preserve node types. We fully characterize linear layers invariant to such permutations. We verify experimentally that implementing these layers in graph neural network architectures allows learning important node interactions more effectively than existing techniques. We show that the dimension of space of these layers is given by a generalization of Bell numbers, extending the work (Maron et al., 2019). We further narrow the invariant network design space by addressing a question about the sizes of tensor layers necessary for function approximation on graph data. Our findings suggest that function approximation on a graph with $n$ nodes can be done with tensors of sizes $\leq n$, which is tighter than the best-known bound $\leq n(n-1)/2$. For $d \times d$ image data with translation symmetry, our methods give a tight upper bound $2d - 1$ (instead of $d^{4}$) on sizes of invariant tensor generators via a surprising connection to Davenport constants.

Dmitry Rybin, Yushun Zhang, Ding Tian et al.

We present Exact Causal Attention (ECA), a Strassen-style algorithm that computes exact Causal Attention using 10\% fewer operations. ECA improves a special class of matrix multiplications where either one operand or the output matrix is upper- or lower-triangular. This includes all matrix multiplication operations in the forward and backward pass of Causal Attention, such as masked product $\mathrm{Mask}(QK^{T})$. ECA is built upon algebraic identities discovered via machine learning and combinatorial search. We note that ECA cannot accelerate fused kernels such as FlashAttention on GPU. This is because ECA requires materialization of large intermediate expressions in the memory, while FlashAttention does not. However, it provides an alternative approach for compute-bound applications and can potentially be useful in scenarios with FLOPs considerations.

Dmitry Rybin, Yushun Zhang, Zhi-Quan Luo

We present RXTX, a new algorithm for computing the product of matrix by its transpose $XX^{t}$ for $X\in \mathbb{R}^{n\times m}$. RXTX uses $5\%$ fewer multiplications and $5\%$ fewer operations (additions and multiplications) than State-of-the-Art algorithms. Note that the accelerations not only holds asymptotically for large matrices with $n \rightarrow \infty$, but also for small matrices including $n = 4$. The algorithm was discovered by combining Machine Learning-based search methods with Combinatorial Optimization.