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Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in applications where generating each particle is costly. This paper develops a non-asymptotic analysis of ensemble Kalman updates that rigorously explains why a small ensemble size suffices if the prior covariance has moderate effective dimension due to fast spectrum decay or approximate sparsity. We present our theory in a unified framework, comparing several implementations of ensemble Kalman updates that use perturbed observations, square root filtering, and localization. As part of our analysis, we develop new dimension-free covariance estimation bounds for approximately sparse matrices that may be of independent interest.

Self-supervised learning (SSL) models have recently demonstrated remarkable performance across various tasks, including image segmentation. This study delves into the emergent characteristics of the Self-Distillation with No Labels (DINO) algorithm and its application to Synthetic Aperture Radar (SAR) imagery. We pre-train a vision transformer (ViT)-based DINO model using unlabeled SAR data, and later fine-tune the model to predict high-resolution land cover maps. We rigorously evaluate the utility of attention maps generated by the ViT backbone, and compare them with the model's token embedding space. We observe a small improvement in model performance with pre-training compared to training from scratch, and discuss the limitations and opportunities of SSL for remote sensing and land cover segmentation. Beyond small performance increases, we show that ViT attention maps hold great intrinsic value for remote sensing, and could provide useful inputs to other algorithms. With this, our work lays the ground-work for bigger and better SSL models for Earth Observation.

This paper proposes a novel controllable human motion synthesis method for fine-level deformation based on static point-based radiance fields. Although previous editable neural radiance field methods can generate impressive results on novel-view synthesis and allow naive deformation, few algorithms can achieve complex 3D human editing such as forward kinematics. Our method exploits the explicit point cloud to train the static 3D scene and apply the deformation by encoding the point cloud translation using a deformation MLP. To make sure the rendering result is consistent with the canonical space training, we estimate the local rotation using SVD and interpolate the per-point rotation to the query view direction of the pre-trained radiance field. Extensive experiments show that our approach can significantly outperform the state-of-the-art on fine-level complex deformation which can be generalized to other 3D characters besides humans.

The paper presents a comprehensive performance evaluation of some heuristic search algorithms in the context of autonomous systems and robotics. The objective of the study is to evaluate and compare the performance of different search algorithms in different problem settings on the pathfinding domain. Experiments give us insight into the behavior of the evaluated heuristic search algorithms, over the variation of different parameters: domain size, obstacle density, and distance between the start and the goal states. Results are then used to design a selection algorithm that, on the basis of problem characteristics, suggests the best search algorithm to use.

Long-range context modeling is crucial to both dialogue understanding and generation. The most popular method for dialogue context representation is to concatenate the last-$k$ utterances in chronological order. However, this method may not be ideal for conversations containing long-range dependencies, i.e., when there is a need to look beyond last-$k$ utterances to generate a meaningful response. In this work, we propose DialoGen, a novel encoder-decoder based framework for dialogue generation with a generalized context representation that can look beyond the last-$k$ utterances. The main idea of our approach is to identify and utilize the most relevant historical utterances instead of last-$k$, which also enables the compact representation of dialogue history with fewer tokens. We study the effectiveness of our proposed method on both dialogue generation (open-domain) and understanding (DST). Even with a compact context representation, DialoGen performs comparably to the state-of-the-art models on the open-domain DailyDialog dataset. We observe a similar behavior on the DST task of the MultiWOZ dataset when the proposed context representation is applied to existing DST models. We also discuss the generalizability and interpretability of DialoGen and show that the relevance score of previous utterances agrees well with human cognition.

We propose Joint MLP/Attention (JoMA) dynamics, a novel mathematical framework to understand the training procedure of multilayer Transformer architectures. This is achieved by integrating out the self-attention layer in Transformers, producing a modified dynamics of MLP layers only. JoMA removes unrealistic assumptions in previous analysis (e.g., lack of residual connection) and predicts that the attention first becomes sparse (to learn salient tokens), then dense (to learn less salient tokens) in the presence of nonlinear activations, while in the linear case, it is consistent with existing works that show attention becomes sparse over time. We leverage JoMA to qualitatively explains how tokens are combined to form hierarchies in multilayer Transformers, when the input tokens are generated by a latent hierarchical generative model. Experiments on models trained from real-world dataset (Wikitext2/Wikitext103) and various pre-trained models (OPT, Pythia) verify our theoretical findings.

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where $M^* \in \mathbb{R}^{n \times n}$ is a positive semi-definite unknown matrix of rank $r \ll n$, and one uses a symmetric parameterization $XX^\top$ to learn $M^*$. Here $X \in \mathbb{R}^{n \times k}$ with $k > r$ is the factor matrix. We give a novel $\Omega (1/T^2)$ lower bound of randomly initialized GD for the over-parameterized case ($k >r$) where $T$ is the number of iterations. This is in stark contrast to the exact-parameterization scenario ($k=r$) where the convergence rate is $\exp (-\Omega (T))$. Next, we study asymmetric setting where $M^* \in \mathbb{R}^{n_1 \times n_2}$ is the unknown matrix of rank $r \ll \min\{n_1,n_2\}$, and one uses an asymmetric parameterization $FG^\top$ to learn $M^*$ where $F \in \mathbb{R}^{n_1 \times k}$ and $G \in \mathbb{R}^{n_2 \times k}$. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case ($k=r$) with an $\exp (-\Omega(T))$ rate. Furthermore, we give the first global exact convergence result for the over-parameterization case ($k>r$) with an $\exp(-\Omega(\alpha^2 T))$ rate where $\alpha$ is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from $\Omega (1/T^2)$ to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of $\alpha$, recovering the rate in the exact-parameterization case.

We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 16% and 32%. Remarkably, our MAmmoTH-7B model reaches 33% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 23%, and the MAmmoTH-34B model achieves 44% accuracy on MATH, even surpassing GPT-4's CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.

The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this logic are used in blocks, each block consisting only of existential quantifiers or only of universal quantifiers. In this paper we consider the possibility of mixing quantifiers in blocks. We identify a non-trivial variation of the logic with mixed blocks of quantifiers which retains some good properties of the two-variable fragment and of the uniform one-dimensional fragment: it has the finite (exponential) model property and hence decidable, NExpTime-complete satisfiability problem.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.