Continual Pre-Training (CPT) on Large Language Models (LLMs) has been widely used to expand the model's fundamental understanding of specific downstream domains (e.g., math and code). For the CPT on domain-specific LLMs, one important question is how to choose the optimal mixture ratio between the general-corpus (e.g., Dolma, Slim-pajama) and the downstream domain-corpus. Existing methods usually adopt laborious human efforts by grid-searching on a set of mixture ratios, which require high GPU training consumption costs. Besides, we cannot guarantee the selected ratio is optimal for the specific domain. To address the limitations of existing methods, inspired by the Scaling Law for performance prediction, we propose to investigate the Scaling Law of the Domain-specific Continual Pre-Training (D-CPT Law) to decide the optimal mixture ratio with acceptable training costs for LLMs of different sizes. Specifically, by fitting the D-CPT Law, we can easily predict the general and downstream performance of arbitrary mixture ratios, model sizes, and dataset sizes using small-scale training costs on limited experiments. Moreover, we also extend our standard D-CPT Law on cross-domain settings and propose the Cross-Domain D-CPT Law to predict the D-CPT law of target domains, where very small training costs (about 1\% of the normal training costs) are needed for the target domains. Comprehensive experimental results on six downstream domains demonstrate the effectiveness and generalizability of our proposed D-CPT Law and Cross-Domain D-CPT Law.

Large language models (LLMs) have exhibited impressive performance in language comprehension and various reasoning tasks. However, their abilities in spatial reasoning, a crucial aspect of human cognition, remain relatively unexplored. Human possess a remarkable ability to create mental images of unseen objects and actions through a process known as the Mind's Eye, enabling the imagination of the unseen world. Inspired by this cognitive capacity, we propose Visualization-of-Thought (VoT) prompting. VoT aims to elicit spatial reasoning of LLMs by visualizing their reasoning traces, thereby guiding subsequent reasoning steps.

Data augmentation creates new data points by transforming the original ones for an reinforcement learning (RL) agent to learn from, which has been shown to be effective for the objective of improving data efficiency of RL for continuous control. Prior work towards this objective has been largely restricted to perturbation-based data augmentation where new data points are created by perturbing the original ones,which has been impressively effective for tasks where the RL agent observe control states as images with perturbations including random cropping, shifting, etc. This work focuses on state-based control, where the RL agent can directly observe raw kinematic and task features, and considers an alternative data augmentation applied to these features based on Euclidean symmetries under transformations like rotations. We show that the default state features used in exiting benchmark tasks that are based on joint configurations are not amenable to Euclidean transformations. We therefore advocate using state features based on configurations of the limbs (i.e., rigid bodies connected by joints) that instead provides rich augmented data under Euclidean transformations. With minimal hyperparameter tuning, we show this new Euclidean data augmentation strategy significantly improve both data efficiency and asymptotic performance of RL on a wide range of continuous control tasks.

Processing multidomain data defined on multiple graphs holds significant potential in various practical applications in computer science. However, current methods are mostly limited to discrete graph filtering operations. Tensorial partial differential equations on graphs (TPDEGs) provide a principled framework for modeling structured data across multiple interacting graphs, addressing the limitations of the existing discrete methodologies. In this paper, we introduce Continuous Product Graph Neural Networks (CITRUS) that emerge as a natural solution to the TPDEG. CITRUS leverages the separability of continuous heat kernels from Cartesian graph products to efficiently implement graph spectral decomposition. We conduct thorough theoretical analyses of the stability and over-smoothing properties of CITRUS in response to domain-specific graph perturbations and graph spectra effects on the performance. We evaluate CITRUS on well-known traffic and weather spatiotemporal forecasting datasets, demonstrating superior performance over existing approaches.

In this paper, we point out that suboptimal noise-data mapping leads to slow training of diffusion models.

In 3D computer vision, translation averaging solves for absolute translations given a set of pairwise relative translation directions. While there has been much work on robustness to outliers and studies on the uniqueness of the solution, this paper deals with a distinctly different problem of sensitivity in translation averaging under uncertainty. We first analyze sensitivity in estimating scales corresponding to relative directions under small perturbations of the relative directions. Then, we formally define the conditioning of the translation averaging problem, which assesses the reliability of estimated translations based solely on the input directions. We give a sufficient criterion to ensure that the problem is well-conditioned. Subsequently, we provide an efficient algorithm to identify and remove combinations of directions which make the problem ill-conditioned while ensuring uniqueness of the solution. We demonstrate the utility of such analysis in global structure-from-motion pipelines for obtaining 3D reconstructions, which reveals the benefits of filtering the ill-conditioned set of directions in translation averaging in terms of reduced translation errors, a higher number of 3D points triangulated and faster convergence of bundle adjustment.

Federated Learning (FL) is a prevalent machine learning paradigm designed to address challenges posed by heterogeneous client data while preserving data privacy. Unlike distributed training, it typically orchestrates resource-constrained edge devices to communicate via a low-bandwidth communication network with a central server. This urges the development of more computation and communication efficient training algorithms. In this paper, we propose an efficient FL paradigm, where the local models in the clients are trained with low-precision operations and communicated with the server in low precision format, while only the model aggregation in the server is performed with high-precision computation. We surprisingly find that high precision models can be recovered from the low precision local models with proper aggregation in the server.

Learning of preference models from human feedback has been central to recent advances in artificial intelligence. Motivated by the cost of obtaining high-quality human annotations, we study efficient human preference elicitation for learning preference models. The key idea in our work is to generalize optimal designs, an approach to computing optimal information-gathering policies, to lists of items that represent potential questions with answers. The policy is a distribution over the lists and we elicit preferences from them proportionally to their probabilities. To show the generality of our ideas, we study both absolute and ranking feedback models on items in the list. We design efficient algorithms for both and analyze them. Finally, we demonstrate that our algorithms are practical by evaluating them on existing question-answering problems.

Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating population densities in a geographic region, a small Wasserstein distance means that the estimate is able to capture roughly where the population mass is. In this work we study differentially private density estimation in the Wasserstein distance. We design and analyze instance-optimal algorithms for this problem that can adapt to easy instances.For distributions $P$ over $\mathbb{R}$, we consider a strong notion of instance-optimality: an algorithm that uniformly achieves the instance-optimal estimation rate is competitive with an algorithm that is told that the distribution is either $P$ or $Q_P$ for some distribution $Q_P$ whose probability density function (pdf) is within a factor of 2 of the pdf of $P$.

A mainstream of Multi-modal Large Language Models (MLLMs) have two essential functions, i.e., visual recognition (e.g., grounding) and understanding (e.g., visual question answering). Presently, all these MLLMs integrate visual recognition and understanding in a same sequential manner in the LLM head, i.e., generating the response token-by-token for both recognition and understanding. We think unifying them in the same sequential manner is not optimal for two reasons: 1) parallel recognition is more efficient than sequential recognition and is actually prevailing in deep visual recognition, and 2) the recognition results can be integrated to help high-level cognition (while the current manner does not). Such motivated, this paper proposes a novel "parallel recognition sequential understanding" framework for MLLMs. The bottom LLM layers are utilized for parallel recognition and the recognition results are relayed into the top LLM layers for sequential understanding. Specifically, parallel recognition in the bottom LLM layers is implemented via object queries, a popular mechanism in DEtection TRansformer, which we find to harmonize well with the LLM layers. Empirical studies show our MLLM named Octopus improves accuracy on popular MLLM tasks and is up to 5 faster on visual grounding tasks.