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3D cellular image segmentation methods are commonly divided into non-2D-based and 2D-based approaches, the latter reconstructing 3D shapes from the segmentation results of 2D layers. However, errors in 2D results often propagate, leading to oversegmentations in the final 3D results. To tackle this issue, we introduce an interpretable geometric framework that addresses the oversegmentations by correcting the 2D segmentation results based on geometric information from adjacent layers. Leveraging both geometric (layer-to-layer, 2D) and topological (3D shape) features, we use binary classification to determine whether neighboring cells should be stitched. We develop a pre-trained classifier on public plant cell datasets and validate its performance on animal cell datasets, confirming its effectiveness in correcting oversegmentations under the transfer learning setting. Furthermore, we demonstrate that our framework can be extended to correcting oversegmentation on non-2D-based methods. A clear pipeline is provided for end-users to build the pre-trained model to any labeled dataset., Comment: 17 pages, 16 figures

Optimal Transport (OT) theory seeks to determine the map $T:X \to Y$ that transports a source measure $P$ to a target measure $Q$, minimizing the cost $c(\mathbf{x}, T(\mathbf{x}))$ between $\mathbf{x}$ and its image $T(\mathbf{x})$. Building upon the Input Convex Neural Network OT solver and incorporating the concept of displacement-sparse maps, we introduce a sparsity penalty into the minimax Wasserstein formulation, promote sparsity in displacement vectors $\Delta(\mathbf{x}) := T(\mathbf{x}) - \mathbf{x}$, and enhance the interpretability of the resulting map. However, increasing sparsity often reduces feasibility, causing $T_{\#}(P)$ to deviate more significantly from the target measure. In low-dimensional settings, we propose a heuristic framework to balance the trade-off between sparsity and feasibility by dynamically adjusting the sparsity intensity parameter during training. For high-dimensional settings, we directly constrain the dimensionality of displacement vectors by enforcing $\dim(\Delta(\mathbf{x})) \leq l$, where $l < d$ for $X \subseteq \mathbb{R}^d$. Among maps satisfying this constraint, we aim to identify the most feasible one. This goal can be effectively achieved by adapting our low-dimensional heuristic framework without resorting to dimensionality reduction. We validate our method on both synthesized sc-RNA and real 4i cell perturbation datasets, demonstrating improvements over existing methods., Comment: 18 pages, 6 Figures

Cutting thin-walled deformable structures is common in daily life, but poses significant challenges for simulation due to the introduced spatial discontinuities. Traditional methods rely on mesh-based domain representations, which require frequent remeshing and refinement to accurately capture evolving discontinuities. These challenges are further compounded in reduced-space simulations, where the basis functions are inherently geometry- and mesh-dependent, making it difficult or even impossible for the basis to represent the diverse family of discontinuities introduced by cuts. Recent advances in representing basis functions with neural fields offer a promising alternative, leveraging their discretization-agnostic nature to represent deformations across varying geometries. However, the inherent continuity of neural fields is an obstruction to generalization, particularly if discontinuities are encoded in neural network weights. We present Wind Lifter, a novel neural representation designed to accurately model complex cuts in thin-walled deformable structures. Our approach constructs neural fields that reproduce discontinuities precisely at specified locations, without baking in the position of the cut line. Crucially, our approach does not embed the discontinuity in the neural network's weights, opening avenues to generalization of cut placement. Our method achieves real-time simulation speeds and supports dynamic updates to cut line geometry during the simulation. Moreover, the explicit representation of discontinuities makes our neural field intuitive to control and edit, offering a significant advantage over traditional neural fields, where discontinuities are embedded within the network's weights, and enabling new applications that rely on general cut placement.

Real-world open-domain questions can be complicated, particularly when answering them involves information from multiple information sources. LLMs have demonstrated impressive performance in decomposing complex tasks into simpler steps, and previous work has used it for better retrieval in support of complex questions. However, LLM's decomposition of questions is unaware of what data is available and how data is organized, often leading to a sub-optimal retrieval performance. Recent effort in agentic RAG proposes to perform retrieval in an iterative fashion, where a followup query is derived as an action based on previous rounds of retrieval. While this provides one way of interacting with the data collection, agentic RAG's exploration of data is inefficient because successive queries depend on previous results rather than being guided by the organization of available data in the collection. To address this problem, we propose an LLM-based retrieval method -- ARM, that aims to better align the question with the organization of the data collection by exploring relationships among data objects beyond matching the utterance of the query, thus leading to a retrieve-all-at-once solution for complex queries. We evaluated ARM on two datasets, Bird and OTT-QA. On Bird, it outperforms standard RAG with query decomposition by up to 5.2 pt in execution accuracy and agentic RAG (ReAct) by up to 15.9 pt. On OTT-QA, it achieves up to 5.5 pt and 19.3 pt higher F1 match scores compared to these approaches.

Query scheduling is a critical task that directly impacts query performance in database management systems (DBMS). Deeply integrated schedulers, which require changes to DBMS internals, are usually customized for a specific engine and can take months to implement. In contrast, non-intrusive schedulers make coarse-grained decisions, such as controlling query admission and re-ordering query execution, without requiring modifications to DBMS internals. They require much less engineering effort and can be applied across a wide range of DBMS engines, offering immediate benefits to end users. However, most existing non-intrusive scheduling systems rely on simplified cost models and heuristics that cannot accurately model query interactions under concurrency and different system states, possibly leading to suboptimal scheduling decisions. This work introduces IconqSched, a new, principled non-intrusive scheduler that optimizes the execution order and timing of queries to enhance total end-to-end runtime as experienced by the user query queuing time plus system runtime. Unlike previous approaches, IconqSched features a novel fine-grained predictor, Iconq, which treats the DBMS as a black box and accurately estimates the system runtime of concurrently executed queries under different system states. Using these predictions, IconqSched is able to capture system runtime variations across different query mixes and system loads. It then employs a greedy scheduling algorithm to effectively determine which queries to submit and when to submit them. We compare IconqSched to other schedulers in terms of end-to-end runtime using real workload traces. On Postgres, IconqSched reduces end-to-end runtime by 16.2%-28.2% on average and 33.6%-38.9% in the tail. Similarly, on Redshift, it reduces end-to-end runtime by 10.3%-14.1% on average and 14.9%-22.2% in the tail.

Differentiable simulation has become a powerful tool for system identification. While prior work has focused on identifying robot properties using robot-specific data or object properties using object-specific data, our approach calibrates object properties by using information from the robot, without relying on data from the object itself. Specifically, we utilize robot joint encoder information, which is commonly available in standard robotic systems. Our key observation is that by analyzing the robot's reactions to manipulated objects, we can infer properties of those objects, such as inertia and softness. Leveraging this insight, we develop differentiable simulations of robot-object interactions to inversely identify the properties of the manipulated objects. Our approach relies solely on proprioception -- the robot's internal sensing capabilities -- and does not require external measurement tools or vision-based tracking systems. This general method is applicable to any articulated robot and requires only joint position information. We demonstrate the effectiveness of our method on a low-cost robotic platform, achieving accurate mass and elastic modulus estimations of manipulated objects with just a few seconds of computation on a laptop., Comment: arXiv admin comment: This version has been removed by arXiv administrators as the submitter did not have the rights to agree to the license at the time of submission

Existing text-to-SQL benchmarks have largely been constructed from web tables with human-generated question-SQL pairs. LLMs typically show strong results on these benchmarks, leading to a belief that LLMs are effective at text-to-SQL tasks. However, how these results transfer to enterprise settings is unclear because tables in enterprise databases might differ substantially from web tables in structure and content. To contend with this problem, we introduce a new dataset BEAVER, the first enterprise text-to-SQL benchmark sourced from real private enterprise data warehouses. This dataset includes natural language queries and their correct SQL statements, which we collected from actual query logs. We then benchmark off-the-shelf LLMs on this dataset. LLMs perform poorly, even when augmented with standard prompt engineering and RAG techniques. We identify three main reasons for the poor performance: (1) schemas of enterprise tables are more complex than the schemas in public data, resulting in SQL-generation tasks intrinsically harder; (2) business-oriented questions are often more complex, requiring joins over multiple tables, aggregations, and nested queries; (3) public LLMs cannot train on private enterprise data warehouses that are not publicly accessible, and therefore it is difficult for the model to learn to solve (1) and (2). We believe BEAVER will facilitate future research in building text-to-SQL systems that perform better in enterprise settings., Comment: Dataset and code are available at https://peterbaile.github.io/beaver/

The eigenfunctions of the Laplace operator are essential in mathematical physics, engineering, and geometry processing. Typically, these are computed by discretizing the domain and performing eigendecomposition, tying the results to a specific mesh. However, this method is unsuitable for continuously-parameterized shapes. We propose a novel representation for eigenfunctions in continuously-parameterized shape spaces, where eigenfunctions are spatial fields with continuous dependence on shape parameters, defined by minimal Dirichlet energy, unit norm, and mutual orthogonality. We implement this with multilayer perceptrons trained as neural fields, mapping shape parameters and domain positions to eigenfunction values. A unique challenge is enforcing mutual orthogonality with respect to causality, where the causal ordering varies across the shape space. Our training method therefore requires three interwoven concepts: (1) learning $n$ eigenfunctions concurrently by minimizing Dirichlet energy with unit norm constraints; (2) filtering gradients during backpropagation to enforce causal orthogonality, preventing earlier eigenfunctions from being influenced by later ones; (3) dynamically sorting the causal ordering based on eigenvalues to track eigenvalue curve crossovers. We demonstrate our method on problems such as shape family analysis, predicting eigenfunctions for incomplete shapes, interactive shape manipulation, and computing higher-dimensional eigenfunctions, on all of which traditional methods fall short.

Large language models (LLMs) know little about enterprise database tables in the private data ecosystem, which substantially differ from web text in structure and content. As LLMs' performance is tied to their training data, a crucial question is how useful they can be in improving enterprise database management and analysis tasks. To address this, we contribute experimental results on LLMs' performance for text-to-SQL and semantic column-type detection tasks on enterprise datasets. The performance of LLMs on enterprise data is significantly lower than on benchmark datasets commonly used. Informed by our findings and feedback from industry practitioners, we identify three fundamental challenges -- latency, cost, and quality -- and propose potential solutions to use LLMs in enterprise data workflows effectively., Comment: Poster at North East Database Day 2024

We propose accelerating the simulation of Lagrangian dynamics, such as fluid flows, granular flows, and elastoplasticity, with neural-operator-based reduced-order modeling. While full-order approaches simulate the physics of every particle within the system, incurring high computation time for dense inputs, we propose to simulate the physics on sparse graphs constructed by sampling from the spatially discretized system. Our discretization-invariant reduced-order framework trains on any spatial discretizations and computes temporal dynamics on any sparse sampling of these discretizations through neural operators. Our proposed approach is termed Graph Informed Optimized Reduced-Order Modeling or \textit{GIOROM}. Through reduced order modeling, we ensure lower computation time by sparsifying the system by 6.6-32.0$\times$, while ensuring high-fidelity full-order inference via neural fields. We show that our model generalizes to a range of initial conditions, resolutions, and materials. The code and the demos are provided at \url{https://github.com/HrishikeshVish/GIOROM}

The same real-life questions posed to different individuals may lead to different answers based on their unique situations. For instance, whether a student is eligible for a scholarship depends on eligibility conditions, such as major or degree required. ConditionalQA was proposed to evaluate models' capability of reading a document and answering eligibility questions, considering unmentioned conditions. However, it is limited to questions on single documents, neglecting harder cases that may require cross-document reasoning and optimization, for example, "What is the maximum number of scholarships attainable?" Such questions over multiple documents are not only more challenging due to more context having to understand, but also because the model has to (1) explore all possible combinations of unmentioned conditions and (2) understand the relationship between conditions across documents, to reason about the optimal outcome. To evaluate models' capability of answering such questions, we propose a new dataset MDCR, which can reflect real-world challenges and serve as a new test bed for complex conditional reasoning that requires optimization. We evaluate this dataset using the most recent LLMs and demonstrate their limitations in solving this task. We believe this dataset will facilitate future research in answering optimization questions with unknown conditions.

Integrating multiple generative foundation models, especially those trained on different modalities, into something greater than the sum of its parts poses significant challenges. Two key hurdles are the availability of aligned data (concepts that contain similar meaning but is expressed differently in different modalities), and effectively leveraging unimodal representations in cross-domain generative tasks, without compromising their original unimodal capabilities. We propose Zipper, a multi-tower decoder architecture that addresses these concerns by using cross-attention to flexibly compose multimodal generative models from independently pre-trained unimodal decoders. In our experiments fusing speech and text modalities, we show the proposed architecture performs very competitively in scenarios with limited aligned text-speech data. We also showcase the flexibility of our model to selectively maintain unimodal (e.g., text-to-text generation) generation performance by freezing the corresponding modal tower (e.g. text). In cross-modal tasks such as automatic speech recognition (ASR) where the output modality is text, we show that freezing the text backbone results in negligible performance degradation. In cross-modal tasks such as text-to-speech generation (TTS) where the output modality is speech, we show that using a pre-trained speech backbone results in superior performance to the baseline., Comment: Under review at NeurIPS

A long-standing goal of data management systems has been to build systems which can compute quantitative insights over large corpora of unstructured data in a cost-effective manner. Until recently, it was difficult and expensive to extract facts from company documents, data from scientific papers, or metrics from image and video corpora. Today's models can accomplish these tasks with high accuracy. However, a programmer who wants to answer a substantive AI-powered query must orchestrate large numbers of models, prompts, and data operations. For even a single query, the programmer has to make a vast number of decisions such as the choice of model, the right inference method, the most cost-effective inference hardware, the ideal prompt design, and so on. The optimal set of decisions can change as the query changes and as the rapidly-evolving technical landscape shifts. In this paper we present Palimpzest, a system that enables anyone to process AI-powered analytical queries simply by defining them in a declarative language. The system uses its cost optimization framework to implement the query plan with the best trade-offs between runtime, financial cost, and output data quality. We describe the workload of AI-powered analytics tasks, the optimization methods that Palimpzest uses, and the prototype system itself. We evaluate Palimpzest on tasks in Legal Discovery, Real Estate Search, and Medical Schema Matching. We show that even our simple prototype offers a range of appealing plans, including one that is 3.3x faster and 2.9x cheaper than the baseline method, while also offering better data quality. With parallelism enabled, Palimpzest can produce plans with up to a 90.3x speedup at 9.1x lower cost relative to a single-threaded GPT-4 baseline, while obtaining an F1-score within 83.5% of the baseline. These require no additional work by the user., Comment: 29 pages, 9 figures

Retrieving relevant tables containing the necessary information to accurately answer a given question over tables is critical to open-domain question-answering (QA) systems. Previous methods assume the answer to such a question can be found either in a single table or multiple tables identified through question decomposition or rewriting. However, neither of these approaches is sufficient, as many questions require retrieving multiple tables and joining them through a join plan that cannot be discerned from the user query itself. If the join plan is not considered in the retrieval stage, the subsequent steps of reasoning and answering based on those retrieved tables are likely to be incorrect. To address this problem, we introduce a method that uncovers useful join relations for any query and database during table retrieval. We use a novel re-ranking method formulated as a mixed-integer program that considers not only table-query relevance but also table-table relevance that requires inferring join relationships. Our method outperforms the state-of-the-art approaches for table retrieval by up to 9.3% in F1 score and for end-to-end QA by up to 5.4% in accuracy., Comment: ACL 2024. Dataset and code are available at https://peterbaile.github.io/jar

While self-correction has shown promise in improving LLM outputs in terms of style and quality (e.g. Chen et al., 2023b; Madaan et al., 2023), recent attempts to self-correct logical or reasoning errors often cause correct answers to become incorrect, resulting in worse performances overall (Huang et al., 2023). In this paper, we show that poor self-correction performance stems from LLMs' inability to find logical mistakes, rather than their ability to correct a known mistake. Firstly, we benchmark several state-of-the-art LLMs on their mistake-finding ability and demonstrate that they generally struggle with the task, even in highly objective, unambiguous cases. Secondly, we test the correction abilities of LLMs -- separately from mistake finding -- using a backtracking setup that feeds ground truth mistake location information to the model. We show that this boosts downstream task performance across our 5 reasoning tasks, indicating that LLMs' correction abilities are robust. Finally, we show that it is possible to obtain mistake location information without ground truth labels or in-domain training data. We train a small classifier with out-of-domain data, which exhibits stronger mistake-finding performance than prompting a large model. We release our dataset of LLM-generated logical mistakes, BIG-Bench Mistake, to enable further research into locating LLM reasoning mistakes., Comment: ACL 2024 Findings

Over the past few years, self-supervised monocular depth estimation that does not depend on ground-truth during the training phase has received widespread attention. Most efforts focus on designing different types of network architectures and loss functions or handling edge cases, e.g., occlusion and dynamic objects. In this work, we introduce a novel self-supervised depth estimation framework, dubbed MonoDiffusion, by formulating it as an iterative denoising process. Because the depth ground-truth is unavailable in the training phase, we develop a pseudo ground-truth diffusion process to assist the diffusion in MonoDiffusion. The pseudo ground-truth diffusion gradually adds noise to the depth map generated by a pre-trained teacher model. Moreover,the teacher model allows applying a distillation loss to guide the denoised depth. Further, we develop a masked visual condition mechanism to enhance the denoising ability of model. Extensive experiments are conducted on the KITTI and Make3D datasets and the proposed MonoDiffusion outperforms prior state-of-the-art competitors. The source code will be available at https://github.com/ShuweiShao/MonoDiffusion., Comment: 10 pages, 8 figures

Over the past few years, monocular depth estimation and completion have been paid more and more attention from the computer vision community because of their widespread applications. In this paper, we introduce novel physics (geometry)-driven deep learning frameworks for these two tasks by assuming that 3D scenes are constituted with piece-wise planes. Instead of directly estimating the depth map or completing the sparse depth map, we propose to estimate the surface normal and plane-to-origin distance maps or complete the sparse surface normal and distance maps as intermediate outputs. To this end, we develop a normal-distance head that outputs pixel-level surface normal and distance. Meanwhile, the surface normal and distance maps are regularized by a developed plane-aware consistency constraint, which are then transformed into depth maps. Furthermore, we integrate an additional depth head to strengthen the robustness of the proposed frameworks. Extensive experiments on the NYU-Depth-v2, KITTI and SUN RGB-D datasets demonstrate that our method exceeds in performance prior state-of-the-art monocular depth estimation and completion competitors. The source code will be available at https://github.com/ShuweiShao/NDDepth., Comment: Extension of previous work arXiv:2309.10592

We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. State-of-the-art scientific computing models like the Material Point Method (MPM) faithfully simulate large-deformation elastoplasticity and fracture mechanics. However, their long runtime and large memory consumption render them unsuitable for applications constrained by computation time and memory usage, e.g., virtual reality. To overcome these barriers, we propose a reduced-order framework. Our key innovation is training a low-dimensional manifold for the Kirchhoff stress field via an implicit neural representation. This low-dimensional neural stress field (NSF) enables efficient evaluations of stress values and, correspondingly, internal forces at arbitrary spatial locations. In addition, we also train neural deformation and affine fields to build low-dimensional manifolds for the deformation and affine momentum fields. These neural stress, deformation, and affine fields share the same low-dimensional latent space, which uniquely embeds the high-dimensional simulation state. After training, we run new simulations by evolving in this single latent space, which drastically reduces the computation time and memory consumption. Our general continuum-mechanics-based reduced-order framework is applicable to any phenomena governed by the elastodynamics equation. To showcase the versatility of our framework, we simulate a wide range of material behaviors, including elastica, sand, metal, non-Newtonian fluids, fracture, contact, and collision. We demonstrate dimension reduction by up to 100,000X and time savings by up to 10X.

Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial discretization, and then serves to accelerate simulations with the same discretization. This discretization-dependence is restrictive. Becoming independent of a specific discretization would provide flexibility to mix and match mesh resolutions, connectivity, and type (tetrahedral, hexahedral) in training data; to accelerate simulations with novel discretizations unseen during training; and to accelerate adaptive simulations that temporally or parametrically change the discretization. We present a flexible, discretization-independent approach to reduced-order modeling. Like traditional ROM, we represent the configuration as a linear combination of displacement fields. Unlike traditional ROM, our displacement fields are continuous maps from every point on the reference domain to a corresponding displacement vector; these maps are represented as implicit neural fields. With linear continuous ROM (LiCROM), our training set can include multiple geometries undergoing multiple loading conditions, independent of their discretization. This opens the door to novel applications of reduced order modeling. We can now accelerate simulations that modify the geometry at runtime, for instance via cutting, hole punching, and even swapping the entire mesh. We can also accelerate simulations of geometries unseen during training. We demonstrate one-shot generalization, training on a single geometry and subsequently simulating various unseen geometries.

The advancement of Large Language Models (LLMs), including GPT-4, provides exciting new opportunities for generative design. We investigate the application of this tool across the entire design and manufacturing workflow. Specifically, we scrutinize the utility of LLMs in tasks such as: converting a text-based prompt into a design specification, transforming a design into manufacturing instructions, producing a design space and design variations, computing the performance of a design, and searching for designs predicated on performance. Through a series of examples, we highlight both the benefits and the limitations of the current LLMs. By exposing these limitations, we aspire to catalyze the continued improvement and progression of these models.

We introduce AudioPaLM, a large language model for speech understanding and generation. AudioPaLM fuses text-based and speech-based language models, PaLM-2 [Anil et al., 2023] and AudioLM [Borsos et al., 2022], into a unified multimodal architecture that can process and generate text and speech with applications including speech recognition and speech-to-speech translation. AudioPaLM inherits the capability to preserve paralinguistic information such as speaker identity and intonation from AudioLM and the linguistic knowledge present only in text large language models such as PaLM-2. We demonstrate that initializing AudioPaLM with the weights of a text-only large language model improves speech processing, successfully leveraging the larger quantity of text training data used in pretraining to assist with the speech tasks. The resulting model significantly outperforms existing systems for speech translation tasks and has the ability to perform zero-shot speech-to-text translation for many languages for which input/target language combinations were not seen in training. AudioPaLM also demonstrates features of audio language models, such as transferring a voice across languages based on a short spoken prompt. We release examples of our method at https://google-research.github.io/seanet/audiopalm/examples, Comment: Technical report

Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given precision level. One challenge in PCG solvers is the selection of preconditioners, as different problem-dependent systems can benefit from different preconditioners. We present a new method to introduce \emph{inductive bias} in preconditioning conjugate gradient algorithm. Given a system matrix and a set of solution vectors arise from an underlying distribution, we train a graph neural network to obtain an approximate decomposition to the system matrix to be used as a preconditioner in the context of PCG solvers. We conduct extensive experiments to demonstrate the efficacy and generalizability of our proposed approach in solving various 2D and 3D linear second-order PDEs.

We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method's ability to learn constitutive laws from videos., Comment: Homepage: https://sites.google.com/view/nclaw

Image keypoints and descriptors play a crucial role in many visual measurement tasks. In recent years, deep neural networks have been widely used to improve the performance of keypoint and descriptor extraction. However, the conventional convolution operations do not provide the geometric invariance required for the descriptor. To address this issue, we propose the Sparse Deformable Descriptor Head (SDDH), which learns the deformable positions of supporting features for each keypoint and constructs deformable descriptors. Furthermore, SDDH extracts descriptors at sparse keypoints instead of a dense descriptor map, which enables efficient extraction of descriptors with strong expressiveness. In addition, we relax the neural reprojection error (NRE) loss from dense to sparse to train the extracted sparse descriptors. Experimental results show that the proposed network is both efficient and powerful in various visual measurement tasks, including image matching, 3D reconstruction, and visual relocalization., Comment: Accepted by IEEE Transactions on Instrumentation & Measurement

We consider a class of reinforcement-learning systems in which the agent follows a behavior policy to explore a discrete state-action space to find an optimal policy while adhering to some restriction on its behavior. Such restriction may prevent the agent from visiting some state-action pairs, possibly leading to the agent finding only a sub-optimal policy. To address this problem we introduce the concept of constrained exploration with optimality preservation, whereby the exploration behavior of the agent is constrained to meet a specification while the optimality of the (original) unconstrained learning process is preserved. We first establish a feedback-control structure that models the dynamics of the unconstrained learning process. We then extend this structure by adding a supervisor to ensure that the behavior of the agent meets the specification, and establish (for a class of reinforcement-learning problems with a known deterministic environment) a necessary and sufficient condition under which optimality is preserved. This work demonstrates the utility and the prospect of studying reinforcement-learning problems in the context of the theories of discrete-event systems, automata and formal languages., Comment: 33 pages, and 6 figures

Existing approaches to system identification (estimating the physical parameters of an object) from videos assume known object geometries. This precludes their applicability in a vast majority of scenes where object geometries are complex or unknown. In this work, we aim to identify parameters characterizing a physical system from a set of multi-view videos without any assumption on object geometry or topology. To this end, we propose "Physics Augmented Continuum Neural Radiance Fields" (PAC-NeRF), to estimate both the unknown geometry and physical parameters of highly dynamic objects from multi-view videos. We design PAC-NeRF to only ever produce physically plausible states by enforcing the neural radiance field to follow the conservation laws of continuum mechanics. For this, we design a hybrid Eulerian-Lagrangian representation of the neural radiance field, i.e., we use the Eulerian grid representation for NeRF density and color fields, while advecting the neural radiance fields via Lagrangian particles. This hybrid Eulerian-Lagrangian representation seamlessly blends efficient neural rendering with the material point method (MPM) for robust differentiable physics simulation. We validate the effectiveness of our proposed framework on geometry and physical parameter estimation over a vast range of materials, including elastic bodies, plasticine, sand, Newtonian and non-Newtonian fluids, and demonstrate significant performance gain on most tasks., Comment: ICLR 2023 Spotlight. Project page: https://sites.google.com/view/PAC-NeRF

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/, Comment: ICML 2023. Project page: http://www.cs.columbia.edu/cg/INSR-PDE/

This data snapshot is a second report in a two-part series, "Newark Kids Count Data Snapshot: The Impact of COVID-19." In 2021, data releases from the U.S. Bureau of Labor Statistics, as well as the U.S. Census Bureau, have demonstrated the ways in which college students have shifted their educational plans as a result of COVID-19. This snapshot seeks to investigate these trends at a more local level by examining the experiences of Newark's 2019 and 2020 high school graduates as they navigated their freshman and sophomore years in college during a global pandemic. [For the first data snapshot, see ED613560.]

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce the dimensionality of discretized vector fields, our continuous reduced-order modeling (CROM) approach builds a low-dimensional embedding of the continuous vector fields themselves, not their discretization. We represent this reduced manifold using continuously differentiable neural fields, which may train on any and all available numerical solutions of the continuous system, even when they are obtained using diverse methods or discretizations. We validate our approach on an extensive range of PDEs with training data from voxel grids, meshes, and point clouds. Compared to prior discretization-dependent ROM methods, such as linear subspace proper orthogonal decomposition (POD) and nonlinear manifold neural-network-based autoencoders, CROM features higher accuracy, lower memory consumption, dynamically adaptive resolutions, and applicability to any discretization. For equal latent space dimension, CROM exhibits 79$\times$ and 49$\times$ better accuracy, and 39$\times$ and 132$\times$ smaller memory footprint, than POD and autoencoder methods, respectively. Experiments demonstrate 109$\times$ and 89$\times$ wall-clock speedups over unreduced models on CPUs and GPUs, respectively. Videos and codes are available on the project page: https://crom-pde.github.io

Deep stereo matching has made significant progress in recent years. However, state-of-the-art methods are based on expensive 4D cost volume, which limits their use in real-world applications. To address this issue, 3D correlation maps and iterative disparity updates have been proposed. Regarding that in real-world platforms, such as self-driving cars and robots, the Lidar is usually installed. Thus we further introduce the sparse Lidar point into the iterative updates, which alleviates the burden of network updating the disparity from zero states. Furthermore, we propose training the network in a self-supervised way so that it can be trained on any captured data for better generalization ability. Experiments and comparisons show that the presented method is effective and achieves comparable results with related methods.

Existing methods detect the keypoints in a non-differentiable way, therefore they can not directly optimize the position of keypoints through back-propagation. To address this issue, we present a partially differentiable keypoint detection module, which outputs accurate sub-pixel keypoints. The reprojection loss is then proposed to directly optimize these sub-pixel keypoints, and the dispersity peak loss is presented for accurate keypoints regularization. We also extract the descriptors in a sub-pixel way, and they are trained with the stable neural reprojection error loss. Moreover, a lightweight network is designed for keypoint detection and descriptor extraction, which can run at 95 frames per second for 640x480 images on a commercial GPU. On homography estimation, camera pose estimation, and visual (re-)localization tasks, the proposed method achieves equivalent performance with the state-of-the-art approaches, while greatly reduces the inference time., Comment: 11 pages, 11 figures

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the $\textit{kinematics}$ by approximating the deformation map using an implicit neural representation that restricts deformation trajectories to reside on a low-dimensional manifold. By explicitly approximating the deformation map, its spatiotemporal gradients -- in particular the deformation gradient and the velocity -- can be computed via analytical differentiation. In contrast to typical model-reduction techniques that construct a linear or nonlinear manifold to approximate the (finite number of) degrees of freedom characterizing a given spatial discretization, the use of an implicit neural representation enables the proposed method to approximate the $\textit{continuous}$ deformation map. This allows the kinematic approximation to remain agnostic to the discretization. Consequently, the technique supports dynamic discretizations -- including resolution changes -- during the course of the online reduced-order-model simulation. To generate $\textit{dynamics}$ for the generalized coordinates, we propose a family of projection techniques. At each time step, these techniques: (1) Calculate full-space kinematics at quadrature points, (2) Calculate the full-space dynamics for a subset of `sample' material points, and (3) Calculate the reduced-space dynamics by projecting the updated full-space position and velocity onto the low-dimensional manifold and tangent space, respectively. We achieve significant computational speedup via hyper-reduction that ensures all three steps execute on only a small subset of the problem's spatial domain. Large-scale numerical examples with millions of material points illustrate the method's ability to gain an order of magnitude computational-cost saving -- indeed $\textit{real-time simulations}$ -- with negligible errors.