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Beyond scaling base models with more data or parameters, fine-tuned adapters provide an alternative way to generate high fidelity, custom images at reduced costs. As such, adapters have been widely adopted by open-source communities, accumulating a database of over 100K adapters-most of which are highly customized with insufficient descriptions. This paper explores the problem of matching the prompt to a set of relevant adapters, built on recent work that highlight the performance gains of composing adapters. We introduce Stylus, which efficiently selects and automatically composes task-specific adapters based on a prompt's keywords. Stylus outlines a three-stage approach that first summarizes adapters with improved descriptions and embeddings, retrieves relevant adapters, and then further assembles adapters based on prompts' keywords by checking how well they fit the prompt. To evaluate Stylus, we developed StylusDocs, a curated dataset featuring 75K adapters with pre-computed adapter embeddings. In our evaluation on popular Stable Diffusion checkpoints, Stylus achieves greater CLIP-FID Pareto efficiency and is twice as preferred, with humans and multimodal models as evaluators, over the base model. See stylus-diffusion.github.io for more.

Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods. However, each technique possesses inherent limitations, underscoring the critical importance of selecting an appropriate approximation method tailored to specific problem domains. This article delves into the utilization of Chebyshev polynomials at Chebyshev nodes for approximation. For sufficiently smooth functions, the partial sum of Chebyshev series expansion offers optimal polynomial approximation, rendering it a preferred choice in various applications such as digital signal processing and graph filters due to its computational efficiency. In this article, we focus on functions of bounded variation, which find numerous applications across mathematical physics, hyperbolic conservations, and optimization. We present two optimal error estimations associated with Chebyshev polynomial approximations tailored for such functions. To validate our theoretical assertions, we conduct numerical experiments. Additionally, we delineate promising future avenues aligned with this research, particularly within the realms of machine learning and related fields.

Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines. However, discovering such insightful equations from data presents significant challenges due to the necessity of navigating extremely high-dimensional combinatorial and nonlinear hypothesis spaces. Traditional methods of equation discovery largely focus on extracting equations from data alone, often neglecting the rich domain-specific prior knowledge that scientists typically depend on. To bridge this gap, we introduce LLM-SR, a novel approach that leverages the extensive scientific knowledge and robust code generation capabilities of Large Language Models (LLMs) to discover scientific equations from data in an efficient manner. Specifically, LLM-SR treats equations as programs with mathematical operators and combines LLMs' scientific priors with evolutionary search over equation programs. The LLM iteratively proposes new equation skeletons, drawing from its physical understanding, which are then optimized against data to estimate skeleton parameters. We demonstrate LLM-SR's effectiveness across three diverse scientific domains, where it discovers physically accurate equations that provide significantly better fits to in-domain and out-of-domain data compared to the well-established equation discovery baselines

Large Language Models (LLMs) have highlighted the necessity of effective unlearning mechanisms to comply with data regulations and ethical AI practices. LLM unlearning aims at removing undesired data influences and associated model capabilities without compromising utility out of the scope of unlearning. While interest in studying LLM unlearning is growing,the impact of the optimizer choice for LLM unlearning remains under-explored. In this work, we shed light on the significance of optimizer selection in LLM unlearning for the first time, establishing a clear connection between {second-order optimization} and influence unlearning (a classical approach using influence functions to update the model for data influence removal). This insight propels us to develop a second-order unlearning framework, termed SOUL, built upon the second-order clipped stochastic optimization (Sophia)-based LLM training method. SOUL extends the static, one-shot model update using influence unlearning to a dynamic, iterative unlearning process. Our extensive experiments show that SOUL consistently outperforms conventional first-order methods across various unlearning tasks, models, and metrics, suggesting the promise of second-order optimization in providing a scalable and easily implementable solution for LLM unlearning.

Image-text matching remains a challenging task due to heterogeneous semantic diversity across modalities and insufficient distance separability within triplets. Different from previous approaches focusing on enhancing multi-modal representations or exploiting cross-modal correspondence for more accurate retrieval, in this paper we aim to leverage the knowledge transfer between peer branches in a boosting manner to seek a more powerful matching model. Specifically, we propose a brand-new Deep Boosting Learning (DBL) algorithm, where an anchor branch is first trained to provide insights into the data properties, with a target branch gaining more advanced knowledge to develop optimal features and distance metrics. Concretely, an anchor branch initially learns the absolute or relative distance between positive and negative pairs, providing a foundational understanding of the particular network and data distribution. Building upon this knowledge, a target branch is concurrently tasked with more adaptive margin constraints to further enlarge the relative distance between matched and unmatched samples. Extensive experiments validate that our DBL can achieve impressive and consistent improvements based on various recent state-of-the-art models in the image-text matching field, and outperform related popular cooperative strategies, e.g., Conventional Distillation, Mutual Learning, and Contrastive Learning. Beyond the above, we confirm that DBL can be seamlessly integrated into their training scenarios and achieve superior performance under the same computational costs, demonstrating the flexibility and broad applicability of our proposed method. Our code is publicly available at: //github.com/Paranioar/DBL.

State estimation for legged robots is challenging due to their highly dynamic motion and limitations imposed by sensor accuracy. By integrating Kalman filtering, optimization, and learning-based modalities, we propose a hybrid solution that combines proprioception and exteroceptive information for estimating the state of the robot's trunk. Leveraging joint encoder and IMU measurements, our Kalman filter is enhanced through a single-rigid body model that incorporates ground reaction force control outputs from convex Model Predictive Control optimization. The estimation is further refined through Gated Recurrent Units, which also considers semantic insights and robot height from a Vision Transformer autoencoder applied on depth images. This framework not only furnishes accurate robot state estimates, including uncertainty evaluations, but can minimize the nonlinear errors that arise from sensor measurements and model simplifications through learning. The proposed methodology is evaluated in hardware using a quadruped robot on various terrains, yielding a 65% improvement on the Root Mean Squared Error compared to our VIO SLAM baseline. Code example: //github.com/AlexS28/OptiState

We study two modifications of the trapezoidal product cubature formulae, approximating double integrals over the square domain $[a,b]^2=[a,b]\times [a,b]$. Our modified cubature formulae use mixed type data: except evaluations of the integrand on the points forming a uniform grid on $[a,b]^2$, they involve two or four univariate integrals. An useful property of these cubature formulae is that they are definite of order $(2,2)$, that is, they provide one-sided approximation to the double integral for real-valued integrands from the class $$ \mathcal{C}^{2,2}[a,b]=\{f(x,y)\,:\,\frac{\partial^4 f}{\partial x^2\partial y^2}\ \text{continuous and does not change sign in}\ (a,b)^2\}. $$ For integrands from $\mathcal{C}^{2,2}[a,b]$ we prove monotonicity of the remainders and derive a-posteriori error estimates.

We study set selection problems where the weights are uncertain. Instead of its exact weight, only an uncertainty interval containing its true weight is available for each element. In some cases, some solutions are universally optimal; i.e., they are optimal for every weight that lies within the uncertainty intervals. However, it may be that no universal optimal solution exists, unless we are revealed additional information on the precise values of some elements. In the minimum cost admissible query problem, we are tasked to (non-adaptively) find a minimum-cost subset of elements that, no matter how they are revealed, guarantee the existence of a universally optimal solution. We introduce thresholds under uncertainty to analyze problems of minimum cost admissible queries. Roughly speaking, for every element e, there is a threshold for its weight, below which e is included in all optimal solutions and a second threshold above which e is excluded from all optimal solutions. We show that computing thresholds and finding minimum cost admissible queries are essentially equivalent problems. Thus, the analysis of the minimum admissible query problem reduces to the problem of computing thresholds. We provide efficient algorithms for computing thresholds in the settings of minimum spanning trees, matroids, and matchings in trees; and NP-hardness results in the settings of s-t shortest paths and bipartite matching. By making use of the equivalence between the two problems these results translate into efficient algorithms for minimum cost admissible queries in the settings of minimum spanning trees, matroids, and matchings in trees; and NP-hardness results in the settings of s-t shortest paths and bipartite matching.

We investigate the role of various demonstration components in the in-context learning (ICL) performance of large language models (LLMs). Specifically, we explore the impacts of ground-truth labels, input distribution, and complementary explanations, particularly when these are altered or perturbed. We build on previous work, which offers mixed findings on how these elements influence ICL. To probe these questions, we employ explainable NLP (XNLP) methods and utilize saliency maps of contrastive demonstrations for both qualitative and quantitative analysis. Our findings reveal that flipping ground-truth labels significantly affects the saliency, though it's more noticeable in larger LLMs. Our analysis of the input distribution at a granular level reveals that changing sentiment-indicative terms in a sentiment analysis task to neutral ones does not have as substantial an impact as altering ground-truth labels. Finally, we find that the effectiveness of complementary explanations in boosting ICL performance is task-dependent, with limited benefits seen in sentiment analysis tasks compared to symbolic reasoning tasks. These insights are critical for understanding the functionality of LLMs and guiding the development of effective demonstrations, which is increasingly relevant in light of the growing use of LLMs in applications such as ChatGPT. Our research code is publicly available at //github.com/paihengxu/XICL.

The increasing complexity of modern deep neural network models and the expanding sizes of datasets necessitate the development of optimized and scalable training methods. In this white paper, we addressed the challenge of efficiently training neural network models using sequences of varying sizes. To address this challenge, we propose a novel training scheme that enables efficient distributed data-parallel training on sequences of different sizes with minimal overhead. By using this scheme we were able to reduce the padding amount by more than 100$x$ while not deleting a single frame, resulting in an overall increased performance on both training time and Recall in our experiments.