Multi-objective learning (MOL) often arises in emerging machine learning problems when multiple learning criteria or tasks need to be addressed. Recent works have developed various _dynamic weighting_ algorithms for MOL, including MGDA and its variants, whose central idea is to find an update direction that _avoids conflicts_ among objectives. Albeit its appealing intuition, empirical studies show that dynamic weighting methods may not always outperform static alternatives. To bridge this gap between theory and practice, we focus on a new variant of stochastic MGDA - the Multi-objective gradient with Double sampling (MoDo) algorithm and study its generalization performance and the interplay with optimization through the lens of algorithm stability. We find that the rationale behind MGDA -- updating along conflict-avoidant direction - may \emph{impede} dynamic weighting algorithms from achieving the optimal ${\cal O}(1/\sqrt{n})$ population risk, where $n$ is the number of training samples. We further highlight the variability of dynamic weights and their impact on the three-way trade-off among optimization, generalization, and conflict avoidance that is unique in MOL.

Activity cliff prediction is a critical task in drug discovery and material design. Existing computational methods are limited to handling single binding targets, which restricts the applicability of these prediction models. In this paper, we present the Multi-Grained Target Perception network (MTPNet) to incorporate the prior knowledge of interactions between the molecules and their target proteins. Specifically, MTPNet is a unified framework for activity cliff prediction, which consists of two components: Macro-level Target Semantic (MTS) guidance and Micro-level Pocket Semantic (MPS) guidance. By this way, MTPNet dynamically optimizes molecular representations through multi-grained protein semantic conditions. To our knowledge, it is the first time to employ the receptor proteins as guiding information to effectively capture critical interaction details. Extensive experiments on 30 representative activity cliff datasets demonstrate that MTPNet significantly outperforms previous approaches, achieving an average RMSE improvement of 18.95% on top of several mainstream GNN architectures. Overall, MTPNet internalizes interaction patterns through conditional deep learning to achieve unified predictions of activity cliffs, helping to accelerate compound optimization and design. Codes are available at: https://github.com/ZishanShu/MTPNet.

We study the problem of sampling from a $d$-dimensional distribution with density $p(x)\propto e^{-f(x)}$, which does not necessarily satisfy good isoperimetric conditions. Specifically, we show that for any $L,M$ satisfying $LM\ge d\ge 5$, $\epsilon\in \left(0,\frac{1}{32}\right)$, and any algorithm with query accesses to the value of $f(x)$ and $\nabla f(x)$, there exists an $L$-log-smooth distribution with second moment at most $M$ such that the algorithm requires $\left(\frac{LM}{d\epsilon}\right)^{\Omega(d)}$ queries to compute a sample whose distribution is within $\epsilon$ in total variation distance to the target distribution. We complement the lower bound with an algorithm requiring $\left(\frac{LM}{d\epsilon}\right)^{\mathcal O(d)}$ queries, thereby characterizing the tight (up to the constant in the exponent) query complexity for sampling from the family of non-log-concave distributions. Our results are in sharp contrast with the recent work of Huang et al. (COLT'24), where an algorithm with quasi-polynomial query complexity was proposed for sampling from a non-log-concave distribution when $M=\mathtt{poly}(d)$. Their algorithm works under the stronger condition that all distributions along the trajectory of the Ornstein-Uhlenbeck process, starting from the target distribution, are $\mathcal O(1)$-log-smooth. We investigate this condition and prove that it is strictly stronger than requiring the target distribution to be $\mathcal O(1)$-log-smooth. Additionally, we study this condition in the context of mixtures of Gaussians. Finally, we place our results within the broader theme of ``sampling versus optimization'', as studied in Ma et al. (PNAS'19). We show that for a wide range of parameters, sampling is strictly easier than optimization by a super-exponential factor in the dimension $d$.

Multi-objective learning (MOL) often arises in emerging machine learning problems when multiple learning criteria or tasks need to be addressed. Recent works have developed various _dynamic weighting_ algorithms for MOL, including MGDA and its variants, whose central idea is to find an update direction that _avoids conflicts_ among objectives. Albeit its appealing intuition, empirical studies show that dynamic weighting methods may not always outperform static alternatives. To bridge this gap between theory and practice, we focus on a new variant of stochastic MGDA - the Multi-objective gradient with Double sampling (MoDo) algorithm and study its generalization performance and the interplay with optimization through the lens of algorithm stability. We find that the rationale behind MGDA -- updating along conflict-avoidant direction - may \emph{impede} dynamic weighting algorithms from achieving the optimal {\cal O}(1/\sqrt{n}) population risk, where n is the number of training samples.

Retrieval plays a fundamental role in recommendation systems, search, and natural language processing by efficiently finding relevant items from a large corpus given a query. Dot products have been widely used as the similarity function in such retrieval tasks, thanks to Maximum Inner Product Search (MIPS) that enabled efficient retrieval based on dot products. However, state-of-the-art retrieval algorithms have migrated to learned similarities. Such algorithms vary in form; the queries can be represented with multiple embeddings, complex neural networks can be deployed, the item ids can be decoded directly from queries using beam search, and multiple approaches can be combined in hybrid solutions. Unfortunately, we lack efficient solutions for retrieval in these state-of-the-art setups. Our work investigates techniques for approximate nearest neighbor search with learned similarity functions. We first prove that Mixture-of-Logits (MoL) is a universal approximator, and can express all learned similarity functions. We next propose techniques to retrieve the approximate top K results using MoL with a tight bound. We finally compare our techniques with existing approaches, showing that MoL sets new state-of-the-art results on recommendation retrieval tasks, and our approximate top-k retrieval with learned similarities outperforms baselines by up to 91 in latency, while achieving >.99 recall rate of exact algorithms.

Retrieval finds a small number of relevant candidates from a large corpus for information retrieval and recommendation applications. A key component of retrieval is to model (user, item) similarity, which is commonly represented as the dot product of two learned embeddings. This formulation permits efficient inference, commonly known as Maximum Inner Product Search (MIPS). Despite its popularity, dot products cannot capture complex user-item interactions, which are multifaceted and likely high rank. We hence examine non-dot-product retrieval settings on accelerators, and propose \textit{mixture of logits} (MoL), which models (user, item) similarity as an adaptive composition of elementary similarity functions. This new formulation is expressive, capable of modeling high rank (user, item) interactions, and further generalizes to the long tail. When combined with a hierarchical retrieval strategy, \textit{h-indexer}, we are able to scale up MoL to 100M corpus on a single GPU with latency comparable to MIPS baselines. On public datasets, our approach leads to uplifts of up to 77.3\% in hit rate (HR). Experiments on a large recommendation surface at Meta showed strong metric gains and reduced popularity bias, validating the proposed approach's performance and improved generalization.

Since a lexicon-based approach is more elegant scientifically, explaining the solution components and being easier to generalize to other applications, this paper provides a new approach for offensive language and hate speech detection on social media. Our approach embodies a lexicon of implicit and explicit offensive and swearing expressions annotated with contextual information. Due to the severity of the social media abusive comments in Brazil, and the lack of research in Portuguese, Brazilian Portuguese is the language used to validate the models. Nevertheless, our method may be applied to any other language. The conducted experiments show the effectiveness of the proposed approach, outperforming the current baseline methods for the Portuguese language.

In this paper we provide results on using integer programming (IP) and constraint programming (CP) to search for sets of mutually orthogonal latin squares (MOLS). Both programming paradigms have previously successfully been used to search for MOLS, but solvers for IP and CP solvers have significantly improved in recent years and data on how modern IP and CP solvers perform on the MOLS problem is lacking. Using state-of-the-art solvers as black boxes we were able to quickly find pairs of MOLS (or prove their nonexistence) in all orders up to ten. Moreover, we improve the effectiveness of the solvers by formulating an extended symmetry breaking method as well as an improvement to the straightforward CP encoding. We also analyze the effectiveness of using CP and IP solvers to search for triples of MOLS, compare our timings to those which have been previously published, and estimate the running time of using this approach to resolve the longstanding open problem of determining the existence of a triple of MOLS of order ten.