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The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However, rigorous edge storage might not always be essential to be able to draw the needed conclusions. A similar problem takes records with many variables and attempts to extract the most discernible features. It is said that the ``dimension'' of this data is reduced. Following an approach with the same objective in mind, we can map a graph representation to a $k$-dimensional space and answer queries of neighboring nodes mainly by measuring Euclidean distances. The accuracy of our answers would decrease but would be compensated for by fuzzy logic which gives an idea about the likelihood of error. This method allows for reasonable representation in memory while maintaining a fair amount of useful information, and allows for concise embedding in $k$-dimensional Euclidean space as well as solving some problems without having to decompress the graph. Of particular interest is the case where $k=2$. Promising highly accurate experimental results are obtained and reported.

We devise a version of Linear Temporal Logic (LTL) on a denotational domain of streams. We investigate this logic in terms of domain theory, (point-free) topology and geometric logic. This yields the first steps toward an extension of the "Domain Theory in Logical Form" paradigm to temporal liveness properties. We show that the negation-free formulae of LTL induce sober subspaces of streams, but that this is in general not the case in presence of negation. We propose a direct, inductive, translation of negation-free LTL to geometric logic. This translation reflects the approximations used to compute the usual fixpoint representations of LTL modalities. As a motivating example, we handle a natural input-output specification for the usual filter function on streams.

Transformer-based Large Language Models (LLMs) often impose limitations on the length of the text input to ensure the generation of fluent and relevant responses. This constraint restricts their applicability in scenarios involving long texts. We propose a novel semantic compression method that enables generalization to texts that are 6-8 times longer, without incurring significant computational costs or requiring fine-tuning. Our proposed framework draws inspiration from source coding in information theory and employs a pre-trained model to reduce the semantic redundancy of long inputs before passing them to the LLMs for downstream tasks. Experimental results demonstrate that our method effectively extends the context window of LLMs across a range of tasks including question answering, summarization, few-shot learning, and information retrieval. Furthermore, the proposed semantic compression method exhibits consistent fluency in text generation while reducing the associated computational overhead.

Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost over ambiguity sets, i.e., sets of distributions that are sufficiently compatible with the observed data. In this paper, the ambiguity sets capture the set of probability distributions whose convolution with the noise distribution remains within a ball centered at the empirical noisy distribution of data samples parameterized by the total variation distance. Using the prescribed ambiguity set, the solutions of the distributionally-robust optimizations converge to the solutions of the original stochastic programs when the numbers of the data samples grow to infinity. Therefore, the proposed distributionally-robust optimization problems are asymptotically consistent. This is proved under the assumption that the distribution of the noise is uniformly diagonally dominant. More importantly, the distributionally-robust optimization problems can be cast as tractable convex optimization problems and are therefore amenable to large-scale stochastic problems.

We introduce a framework for intrinsic latent diffusion models operating directly on the surfaces of 3D shapes, with the goal of synthesizing high-quality textures. Our approach is underpinned by two contributions: field latents, a latent representation encoding textures as discrete vector fields on the mesh vertices, and field latent diffusion models, which learn to denoise a diffusion process in the learned latent space on the surface. We consider a single-textured-mesh paradigm, where our models are trained to generate variations of a given texture on a mesh. We show the synthesized textures are of superior fidelity compared those from existing single-textured-mesh generative models. Our models can also be adapted for user-controlled editing tasks such as inpainting and label-guided generation. The efficacy of our approach is due in part to the equivariance of our proposed framework under isometries, allowing our models to seamlessly reproduce details across locally similar regions and opening the door to a notion of generative texture transfer.

Contact-rich manipulation tasks with stiff frictional elements like connector insertion are difficult to model with rigid-body simulators. In this work, we propose a new approach for modeling these environments by learning a quasi-static contact force model instead of a full simulator. Using a feature vector that contains information about the configuration and control, we find a linear mapping adequately captures the relationship between this feature vector and the sensed contact forces. A novel Linear Model Learning (LML) algorithm is used to solve for the globally optimal mapping in real time without any matrix inversions, resulting in an algorithm that runs in nearly constant time on a GPU as the model size increases. We validate the proposed approach for connector insertion both in simulation and hardware experiments, where the learned model is combined with an optimization-based controller to achieve smooth insertions in the presence of misalignments and uncertainty. Our website featuring videos, code, and more materials is available at //model-based-plugging.github.io/.

A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a polynomial (many-one) compression (PC) can be regarded as a restricted variant of PTC where the machine can query the oracle exactly once and must output the same answer as the oracle. Bodlaender et al. (ICALP 2008) and Fortnow and Santhanam (STOC 2008) initiated an impressive hardness theory for PC under the assumption coNP $\not\subseteq$ NP/poly. Since PTC is a generalization of PC, we define $\mathcal{C}$ as the set of all problems that have PTCs but have no PCs under the assumption coNP $\not\subseteq$ NP/poly. Based on the hardness theory for PC, Fernau et al. (STACS 2009) found the first problem Leaf Out-tree($k$) in $\mathcal{C}$. However, very little is known about $\mathcal{C}$, as only a dozen problems were shown to belong to the complexity class in the last ten years. Several problems are open, for example, whether CNF-SAT($n$) and $k$-path are in $\mathcal{C}$, and novel ideas are required to better understand the fundamental differences between PTCs and PCs. In this paper, we enrich our knowledge about $\mathcal{C}$ by showing that several problems parameterized by modular-width ($mw$) belong to $\mathcal{C}$. More specifically, exploiting the properties of the well-studied structural graph parameter $mw$, we demonstrate 17 problems parameterized by $mw$ are in $\mathcal{C}$, such as Chromatic Number($mw$) and Hamiltonian Cycle($mw$). In addition, we develop a general recipe to prove the existence of PTCs for a large class of problems, including our 17 problems.

Macro-level modeling is still the dominant approach in many demographic applications because of its simplicity. Individual-level models, on the other hand, provide a more comprehensive understanding of observed patterns; however, their estimation using real data has remained a challenge. The approach we introduce in this article attempts to overcome this limitation. Using likelihood-free inference techniques, we show that it is possible to estimate the parameters of a simple but demographically interpretable individual-level model of the reproductive process from a set of aggregate fertility rates. By estimating individual-level quantities from widely available aggregate data, this approach can contribute to a better understanding of reproductive behavior and its driving mechanisms. It also allows for a more direct link between individual-level and population-level processes. We illustrate our approach using data from three natural fertility populations.

Designing and generating new data under targeted properties has been attracting various critical applications such as molecule design, image editing and speech synthesis. Traditional hand-crafted approaches heavily rely on expertise experience and intensive human efforts, yet still suffer from the insufficiency of scientific knowledge and low throughput to support effective and efficient data generation. Recently, the advancement of deep learning induces expressive methods that can learn the underlying representation and properties of data. Such capability provides new opportunities in figuring out the mutual relationship between the structural patterns and functional properties of the data and leveraging such relationship to generate structural data given the desired properties. This article provides a systematic review of this promising research area, commonly known as controllable deep data generation. Firstly, the potential challenges are raised and preliminaries are provided. Then the controllable deep data generation is formally defined, a taxonomy on various techniques is proposed and the evaluation metrics in this specific domain are summarized. After that, exciting applications of controllable deep data generation are introduced and existing works are experimentally analyzed and compared. Finally, the promising future directions of controllable deep data generation are highlighted and five potential challenges are identified.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.