Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space

We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is to the problem of mean-field variational inference, which seeks to approximate a distribution $\pi$ over $\mathbb{R}^d$ by a product measure $\pi^\star$. When $\pi$ is strongly log-concave and log-smooth, we provide (1) approximation rates certifying that $\pi^\star$ is close to the minimizer $\pi^\star_\diamond$ of the KL divergence over a \emph{polyhedral} set $\mathcal{P}_\diamond$, and (2) an algorithm for minimizing $\text{KL}(\cdot\|\pi)$ over $\mathcal{P}_\diamond$ with accelerated complexity $O(\sqrt \kappa \log(\kappa d/\varepsilon^2))$, where $\kappa$ is the condition number of $\pi$.

Revenge of MLP in Sequential Recommendation

Sequential recommendation models sequences of historical user-item interactive behaviors (or referred as token) to better infer dynamic preferences. Fueled by the improved neural network architectures such as RNN, CNN and Transformer, this field has enjoyed rapid performance boost in the past years. Recent progress on all-MLP models lights on an efficient method with less intensive computation, token-mixing MLP, to learn the transformation patterns among historical behaviors. However, due to the inherent fully-connection design that allows the unrestricted cross-token communication and ignores the chronological order, we find that directly applying token-mixing MLP into sequential recommendation leads to subpar performance. In this paper, we present a purely MLP-based sequential recommendation architecture TriMLP with a novel \underline{Tri}angular Mixer where the modified \underline{MLP} endows tokens with ordered interactions. As the cross-token interaction in MLP is actually matrix multiplication, Triangular Mixer drops the lower-triangle neurons in the weight matrix and thus blocks the connections from future tokens, which prevents information leakage and improves prediction capability under the standard auto-regressive training fashion. To further model long and short-term preferences on fine-grained level, the mixer adopts a dual-branch structure based on the delicate MLP described above, namely global and local mixing, to separately capture the sequential long-range dependencies and local patterns. Empirical study on 9 different scale datasets (contain 50K\textasciitilde20M behaviors) of various benchmarks, including MovieLens, Amazon and Tenrec, demonstrates that TriMLP attains promising and stable accuracy/efficiency trade-off, i.e., averagely surpasses several state-of-the-art baselines by 5.32\% and saves 8.44\% inference time cost.