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While the situation has improved for text-only models, it again seems to be the case currently that multimodal (text and image) models develop faster than ways to evaluate them. In this paper, we bring a recently developed evaluation paradigm from text models to multimodal models, namely evaluation through the goal-oriented game (self) play, complementing reference-based and preference-based evaluation. Specifically, we define games that challenge a model's capability to represent a situation from visual information and align such representations through dialogue. We find that the largest closed models perform rather well on the games that we define, while even the best open-weight models struggle with them. On further analysis, we find that the exceptional deep captioning capabilities of the largest models drive some of the performance. There is still room to grow for both kinds of models, ensuring the continued relevance of the benchmark.

Abstractive summarization has made significant strides in condensing and rephrasing large volumes of text into coherent summaries. However, summarizing administrative documents presents unique challenges due to domain-specific terminology, OCR-generated errors, and the scarcity of annotated datasets for model fine-tuning. Existing models often struggle to adapt to the intricate structure and specialized content of such documents. To address these limitations, we introduce DocSum, a domain-adaptive abstractive summarization framework tailored for administrative documents. Leveraging pre-training on OCR-transcribed text and fine-tuning with an innovative integration of question-answer pairs, DocSum enhances summary accuracy and relevance. This approach tackles the complexities inherent in administrative content, ensuring outputs that align with real-world business needs. To evaluate its capabilities, we define a novel downstream task setting-Document Abstractive Summarization-which reflects the practical requirements of business and organizational settings. Comprehensive experiments demonstrate DocSum's effectiveness in producing high-quality summaries, showcasing its potential to improve decision-making and operational workflows across the public and private sectors.

Given a point set $P$ in a metric space and a real number $t \geq 1$, an \emph{oriented $t$-spanner} is an oriented graph $\overrightarrow{G}=(P,\overrightarrow{E})$, where for every pair of distinct points $p$ and $q$ in $P$, the shortest oriented closed walk in $\overrightarrow{G}$ that contains $p$ and $q$ is at most a factor $t$ longer than the perimeter of the smallest triangle in $P$ containing $p$ and $q$. The \emph{oriented dilation} of a graph $\overrightarrow{G}$ is the minimum $t$ for which $\overrightarrow{G}$ is an oriented $t$-spanner. We present the first algorithm that computes, in Euclidean space, a sparse oriented spanner whose oriented dilation is bounded by a constant. More specifically, for any set of $n$ points in $\mathbb{R}^d$, where $d$ is a constant, we construct an oriented $(2+\varepsilon)$-spanner with $\mathcal{O}(n)$ edges in $\mathcal{O}(n \log n)$ time and $\mathcal{O}(n)$ space. Our construction uses the well-separated pair decomposition and an algorithm that computes a $(1+\varepsilon)$-approximation of the minimum-perimeter triangle in $P$ containing two given query points in $\mathcal{O}(\log n)$ time. While our algorithm is based on first computing a suitable undirected graph and then orienting it, we show that, in general, computing the orientation of an undirected graph that minimises its oriented dilation is NP-hard, even for point sets in the Euclidean plane. We further prove that even if the orientation is already given, computing the oriented dilation is APSP-hard for points in a general metric space. We complement this result with an algorithm that approximates the oriented dilation of a given graph in subcubic time for point sets in $\mathbb{R}^d$, where $d$ is a constant.

The growing demand for larger-scale models in the development of \textbf{L}arge \textbf{L}anguage \textbf{M}odels (LLMs) poses challenges for efficient training within limited computational resources. Traditional fine-tuning methods often exhibit instability in multi-task learning and rely heavily on extensive training resources. Here, we propose MoDULA (\textbf{M}ixture \textbf{o}f \textbf{D}omain-Specific and \textbf{U}niversal \textbf{L}oR\textbf{A}), a novel \textbf{P}arameter \textbf{E}fficient \textbf{F}ine-\textbf{T}uning (PEFT) \textbf{M}ixture-\textbf{o}f-\textbf{E}xpert (MoE) paradigm for improved fine-tuning and parameter efficiency in multi-task learning. The paradigm effectively improves the multi-task capability of the model by training universal experts, domain-specific experts, and routers separately. MoDULA-Res is a new method within the MoDULA paradigm, which maintains the model's general capability by connecting universal and task-specific experts through residual connections. The experimental results demonstrate that the overall performance of the MoDULA-Flan and MoDULA-Res methods surpasses that of existing fine-tuning methods on various LLMs. Notably, MoDULA-Res achieves more significant performance improvements in multiple tasks while reducing training costs by over 80\% without losing general capability. Moreover, MoDULA displays flexible pluggability, allowing for the efficient addition of new tasks without retraining existing experts from scratch. This progressive training paradigm circumvents data balancing issues, enhancing training efficiency and model stability. Overall, MoDULA provides a scalable, cost-effective solution for fine-tuning LLMs with enhanced parameter efficiency and generalization capability.

Multimodal semantic communication, which integrates various data modalities such as text, images, and audio, significantly enhances communication efficiency and reliability. It has broad application prospects in fields such as artificial intelligence, autonomous driving, and smart homes. However, current research primarily relies on analog channels and assumes constant channel states (perfect CSI), which is inadequate for addressing dynamic physical channels and noise in real-world scenarios. Existing methods often focus on single modality tasks and fail to handle multimodal stream data, such as video and audio, and their corresponding tasks. Furthermore, current semantic encoding and decoding modules mainly transmit single modality features, neglecting the need for multimodal semantic enhancement and recognition tasks. To address these challenges, this paper proposes a pilot-guided framework for multimodal semantic communication specifically tailored for audio-visual event localization tasks. This framework utilizes digital pilot codes and channel modules to guide the state of analog channels in real-wold scenarios and designs Euler-based multimodal semantic encoding and decoding that consider time-frequency characteristics based on dynamic channel state. This approach effectively handles multimodal stream source data, especially for audio-visual event localization tasks. Extensive numerical experiments demonstrate the robustness of the proposed framework in channel changes and its support for various communication scenarios. The experimental results show that the framework outperforms existing benchmark methods in terms of Signal-to-Noise Ratio (SNR), highlighting its advantage in semantic communication quality.

In this paper, we describe an algorithm for approximating functions of the form $f(x)=\int_{a}^{b} x^{\mu} \sigma(\mu) \, d \mu$ over $[0,1]$, where $\sigma(\mu)$ is some signed Radon measure, or, more generally, of the form $f(x) = <\sigma(\mu),\, x^\mu>$, where $\sigma(\mu)$ is some distribution supported on $[a,b]$, with $0 <a < b < \infty$. One example from this class of functions is $x^c (\log{x})^m=(-1)^m <\delta^{(m)}(\mu-c), \, x^\mu>$, where $a\leq c \leq b$ and $m \geq 0$ is an integer. Given the desired accuracy $\epsilon$ and the values of $a$ and $b$, our method determines a priori a collection of non-integer powers $t_1$, $t_2$, $\ldots$, $t_N$, so that the functions are approximated by series of the form $f(x)\approx \sum_{j=1}^N c_j x^{t_j}$, and a set of collocation points $x_1$, $x_2$, $\ldots$, $x_N$, such that the expansion coefficients can be found by collocating the function at these points. We prove that our method has a small uniform approximation error which is proportional to $\epsilon$ multiplied by some small constants, and that the number of singular powers and collocation points grows as $N=O(\log{\frac{1}{\epsilon}})$. We demonstrate the performance of our algorithm with several numerical experiments.

Recently, Miller and Wu introduced the positive $\lambda$-calculus, a call-by-value $\lambda$-calculus with sharing obtained by assigning proof terms to the positively polarized focused proofs for minimal intuitionistic logic. The positive $\lambda$-calculus stands out among $\lambda$-calculi with sharing for a compactness property related to the sharing of variables. We show that -- thanks to compactness -- the positive calculus neatly captures the core of useful sharing, a technique for the study of reasonable time cost models.

Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods. However, one drawback of the $\ell_1$ penalty is bias: nonzero parameters are underestimated in magnitude, motivating techniques such as the Adaptive Lasso which endow each parameter with its own penalty coefficient. But it's not clear how these parameter-specific penalties should be set in complex models. In this article, we study the approach of treating the penalty coefficients as additional decision variables to be learned in a \textit{Maximum a Posteriori} manner, developing a proximal gradient approach to joint optimization of these together with the parameters of any differentiable cost function. Beyond reducing bias in estimates, this procedure can also encourage arbitrary sparsity structure via a prior on the penalty coefficients. We compare our method to implementations of specific sparsity structures for non-Gaussian regression on synthetic and real datasets, finding our more general method to be competitive in terms of both speed and accuracy. We then consider nonlinear models for two case studies: COVID-19 vaccination behavior and international refugee movement, highlighting the applicability of this approach to complex problems and intricate sparsity structures.

We derive universal approximation results for the class of (countably) $m$-rectifiable measures. Specifically, we prove that $m$-rectifiable measures can be approximated as push-forwards of the one-dimensional Lebesgue measure on $[0,1]$ using ReLU neural networks with arbitrarily small approximation error in terms of Wasserstein distance. What is more, the weights in the networks under consideration are quantized and bounded and the number of ReLU neural networks required to achieve an approximation error of $\varepsilon$ is no larger than $2^{b(\varepsilon)}$ with $b(\varepsilon)=\mathcal{O}(\varepsilon^{-m}\log^2(\varepsilon))$. This result improves Lemma IX.4 in Perekrestenko et al. as it shows that the rate at which $b(\varepsilon)$ tends to infinity as $\varepsilon$ tends to zero equals the rectifiability parameter $m$, which can be much smaller than the ambient dimension. We extend this result to countably $m$-rectifiable measures and show that this rate still equals the rectifiability parameter $m$ provided that, among other technical assumptions, the measure decays exponentially on the individual components of the countably $m$-rectifiable support set.

Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental design problem, the goal is to pick $k$ out of the given $n$ experiments so as to make the most accurate estimate of the unknown parameters, denoted as $\hat{\beta}$. In this paper, we will study one of the most robust measures of error estimation - $D$-optimality criterion, which corresponds to minimizing the volume of the confidence ellipsoid for the estimation error $\beta-\hat{\beta}$. The problem gives rise to two natural variants depending on whether repetitions of experiments are allowed or not. We first propose an approximation algorithm with a $\frac1e$-approximation for the $D$-optimal design problem with and without repetitions, giving the first constant factor approximation for the problem. We then analyze another sampling approximation algorithm and prove that it is $(1-\epsilon)$-approximation if $k\geq \frac{4m}{\epsilon}+\frac{12}{\epsilon^2}\log(\frac{1}{\epsilon})$ for any $\epsilon \in (0,1)$. Finally, for $D$-optimal design with repetitions, we study a different algorithm proposed by literature and show that it can improve this asymptotic approximation ratio.