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Inferring causal structure from data is a challenging task of fundamental importance in science. Observational data are often insufficient to identify a system's causal structure uniquely. While conducting interventions (i.e., experiments) can improve the identifiability, such samples are usually challenging and expensive to obtain. Hence, experimental design approaches for causal discovery aim to minimize the number of interventions by estimating the most informative intervention target. In this work, we propose a novel Gradient-based Intervention Targeting method, abbreviated GIT, that 'trusts' the gradient estimator of a gradient-based causal discovery framework to provide signals for the intervention acquisition function. We provide extensive experiments in simulated and real-world datasets and demonstrate that GIT performs on par with competitive baselines, surpassing them in the low-data regime.

The current landscape of research leveraging large language models (LLMs) is experiencing a surge. Many works harness the powerful reasoning capabilities of these models to comprehend various modalities, such as text, speech, images, videos, etc. They also utilize LLMs to understand human intention and generate desired outputs like images, videos, and music. However, research that combines both understanding and generation using LLMs is still limited and in its nascent stage. To address this gap, we introduce a Multi-modal Music Understanding and Generation (M$^{2}$UGen) framework that integrates LLM's abilities to comprehend and generate music for different modalities. The M$^{2}$UGen framework is purpose-built to unlock creative potential from diverse sources of inspiration, encompassing music, image, and video through the use of pretrained MERT, ViT, and ViViT models, respectively. To enable music generation, we explore the use of AudioLDM 2 and MusicGen. Bridging multi-modal understanding and music generation is accomplished through the integration of the LLaMA 2 model. Furthermore, we make use of the MU-LLaMA model to generate extensive datasets that support text/image/video-to-music generation, facilitating the training of our M$^{2}$UGen framework. We conduct a thorough evaluation of our proposed framework. The experimental results demonstrate that our model achieves or surpasses the performance of the current state-of-the-art models.

Natural language processing research has begun to embrace the notion of annotator subjectivity, motivated by variations in labelling. This approach understands each annotator's view as valid, which can be highly suitable for tasks that embed subjectivity, e.g., sentiment analysis. However, this construction may be inappropriate for tasks such as hate speech detection, as it affords equal validity to all positions on e.g., sexism or racism. We argue that the conflation of hate and offence can invalidate findings on hate speech, and call for future work to be situated in theory, disentangling hate from its orthogonal concept, offence.

We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains $\mathrm{D} \subset \mathbb{R}^d$, $d=2,3$. We prove exponential emulation rates in Sobolev spaces in terms of the number of neurons and in terms of the number of nonzero coefficients for Gevrey-regular solution classes defined in terms of weighted Sobolev scales in $\mathrm{D}$, comprising the countably-normed spaces of I.M. Babu\v{s}ka and B.Q. Guo. As intermediate result, we prove that continuous, piecewise polynomial high order (``$p$-version'') finite elements with elementwise polynomial degree $p\in\mathbb{N}$ on arbitrary, regular, simplicial partitions of polyhedral domains $\mathrm{D} \subset \mathbb{R}^d$, $d\geq 2$ can be exactly emulated by neural networks combining ReLU and ReLU$^2$ activations. On shape-regular, simplicial partitions of polytopal domains $\mathrm{D}$, both the number of neurons and the number of nonzero parameters are proportional to the number of degrees of freedom of the finite element space, in particular for the $hp$-Finite Element Method of I.M. Babu\v{s}ka and B.Q. Guo.

Geometric matching is an important topic in computational geometry and has been extensively studied over decades. In this paper, we study a geometric-matching problem, known as geometric many-to-many matching. In this problem, the input is a set $S$ of $n$ colored points in $\mathbb{R}^d$, which implicitly defines a graph $G = (S,E(S))$ where $E(S) = \{(p,q): p,q \in S \text{ have different colors}\}$, and the goal is to compute a minimum-cost subset $E^* \subseteq E(S)$ of edges that cover all points in $S$. Here the cost of $E^*$ is the sum of the costs of all edges in $E^*$, where the cost of a single edge $e$ is the Euclidean distance (or more generally, the $L_p$-distance) between the two endpoints of $e$. Our main result is a $(1+\varepsilon)$-approximation algorithm with an optimal running time $O_\varepsilon(n \log n)$ for geometric many-to-many matching in any fixed dimension, which works under any $L_p$-norm. This is the first near-linear approximation scheme for the problem in any $d \geq 2$. Prior to this work, only the bipartite case of geometric many-to-many matching was considered in $\mathbb{R}^1$ and $\mathbb{R}^2$, and the best known approximation scheme in $\mathbb{R}^2$ takes $O_\varepsilon(n^{1.5} \cdot \mathsf{poly}(\log n))$ time.

This paper introduces $\infty$-Diff, a generative diffusion model defined in an infinite-dimensional Hilbert space, which can model infinite resolution data. By training on randomly sampled subsets of coordinates and denoising content only at those locations, we learn a continuous function for arbitrary resolution sampling. Unlike prior neural field-based infinite-dimensional models, which use point-wise functions requiring latent compression, our method employs non-local integral operators to map between Hilbert spaces, allowing spatial context aggregation. This is achieved with an efficient multi-scale function-space architecture that operates directly on raw sparse coordinates, coupled with a mollified diffusion process that smooths out irregularities. Through experiments on high-resolution datasets, we found that even at an $8\times$ subsampling rate, our model retains high-quality diffusion. This leads to significant run-time and memory savings, delivers samples with lower FID scores, and scales beyond the training resolution while retaining detail.

Assessing the quality of summarizers poses significant challenges. In response, we propose a novel task-oriented evaluation approach that assesses summarizers based on their capacity to produce summaries that are useful for downstream tasks, while preserving task outcomes. We theoretically establish a direct relationship between the resulting error probability of these tasks and the mutual information between source texts and generated summaries. We introduce $\texttt{COSMIC}$ as a practical implementation of this metric, demonstrating its strong correlation with human judgment-based metrics and its effectiveness in predicting downstream task performance. Comparative analyses against established metrics like $\texttt{BERTScore}$ and $\texttt{ROUGE}$ highlight the competitive performance of $\texttt{COSMIC}$.

Object-oriented programming (OOP) is one of the most popular paradigms used for building software systems. However, despite its industrial and academic popularity, OOP is still missing a formal apparatus similar to $\lambda$-calculus, which functional programming is based on. There were a number of attempts to formalize OOP, but none of them managed to cover all the features available in modern OO programming languages, such as C++ or Java. We have made yet another attempt and created $\varphi$-calculus. We also created EOLANG (also called EO), an experimental programming language based on $\varphi$-calculus.

Motif finding is an important step for the detection of rare events occurring in a set of DNA or protein sequences. Extraction of information about these rare events can lead to new biological discoveries. Motifs are some important patterns that have numerous applications including the identification of transcription factors and their binding sites, composite regulatory patterns, similarity between families of proteins, etc. Although several flavors of motif searching algorithms have been studied in the literature, we study the version known as $ (l, d) $-motif search or Planted Motif Search (PMS). In PMS, given two integers $ l $, $ d $ and $ n $ input sequences we try to find all the patterns of length $ l $ that appear in each of the $ n $ input sequences with at most $ d $ mismatches. We also discuss the quorum version of PMS in our work that finds motifs that are not planted in all the input sequences but at least in $ q $ of the sequences. Our algorithm is mainly based on the algorithms qPMSPrune, qPMS7, TraverStringRef and PMS8. We introduce some techniques to compress the input strings and make faster comparison between strings with bitwise operations. Our algorithm performs a little better than the existing exact algorithms to solve the qPMS problem in DNA sequence. We have also proposed an idea for parallel implementation of our algorithm.