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Most pronouns are referring expressions, computers need to resolve what do the pronouns refer to, and there are divergences on pronoun usage across languages. Thus, dealing with these divergences and translating pronouns is a challenge in machine translation. Mentions are referring candidates of pronouns and have closer relations with pronouns compared to general tokens. We assume that extracting additional mention features can help pronoun translation. Therefore, we introduce an additional mention attention module in the decoder to pay extra attention to source mentions but not non-mention tokens. Our mention attention module not only extracts features from source mentions, but also considers target-side context which benefits pronoun translation. In addition, we also introduce two mention classifiers to train models to recognize mentions, whose outputs guide the mention attention. We conduct experiments on the WMT17 English-German translation task, and evaluate our models on general translation and pronoun translation, using BLEU, APT, and contrastive evaluation metrics. Our proposed model outperforms the baseline Transformer model in terms of APT and BLEU scores, this confirms our hypothesis that we can improve pronoun translation by paying additional attention to source mentions, and shows that our introduced additional modules do not have negative effect on the general translation quality.

We consider a nonparametric model $\mathcal{E}^{n},$ generated by independent observations $X_{i},$ $i=1,...,n,$ with densities $p(x,\theta_{i}),$ $i=1,...,n,$ the parameters of which $\theta _{i}=f(i/n)\in \Theta $ are driven by the values of an unknown function $f:[0,1]\rightarrow \Theta $ in a smoothness class. The main result of the paper is that, under regularity assumptions, this model can be approximated, in the sense of the Le Cam deficiency pseudodistance, by a nonparametric Gaussian shift model $Y_{i}=\Gamma (f(i/n))+\varepsilon _{i},$ where $\varepsilon_{1},...,\varepsilon _{n}$ are i.i.d. standard normal r.v.'s, the function $\Gamma (\theta ):\Theta \rightarrow \mathrm{R}$ satisfies $\Gamma ^{\prime}(\theta )=\sqrt{I(\theta )}$ and $I(\theta )$ is the Fisher information corresponding to the density $p(x,\theta ).$

The Church Problem asks for the construction of a procedure which, given a logical specification A(I,O) between input omega-strings I and output omega-strings O, determines whether there exists an operator F that implements the specification in the sense that A(I, F(I)) holds for all inputs I. Buchi and Landweber provided a procedure to solve the Church problem for MSO specifications and operators computable by finite-state automata. We investigate a generalization of the Church synthesis problem to the continuous time domain of the non-negative reals. We show that in the continuous time domain there are phenomena which are very different from the canonical discrete time domain of the natural numbers.

Given a finite set satisfying condition $\mathcal{A}$, the subset selection problem asks, how large of a subset satisfying condition $\mathcal{B}$ can we find? We make progress on three instances of subset selection problems in planar point sets. Let $n,s\in\mathbb{N}$ with $n\geq s$, and let $P\subseteq\mathbb{R}^2$ be a set of $n$ points, where at most $s$ points lie on the same line. Firstly, we select a general position subset of $P$, i.e., a subset containing no $3$ points on the same line. This problem was proposed by Erd\H{o}s under the regime when $s$ is a constant. For $s$ being non-constant, we give new lower and upper bounds on the maximum size of such a subset. In particular, we show that in the worst case such a set can have size at most $O(n/s)$ when $n^{1/3}\leq s\leq n$ and $O(n^{5/6+o(1)}/\sqrt{s})$ when $3\leq s\leq n^{1/3}$. Secondly, we select a monotone general position subset of $P$, that is, a subset in general position where the points are ordered from left to right and their $y$-coordinates are either non-decreasing or non-increasing. We present bounds on the maximum size of such a subset. In particular, when $s=\Theta(\sqrt{n})$, our upper and lower bounds differ only by a logarithmic factor. Lastly, we select a subset of $P$ with pairwise distinct slopes. This problem was initially studied by Erd\H{o}s, Graham, Ruzsa, and Taylor on the grid. We show that for $s=O(\sqrt{n})$ such a subset of size $\Omega((n/\log{s})^{1/3})$ can always be found in $P$. When $s=\Theta(\sqrt{n})$, this matches a lower bound given by Zhang on the grid. As for the upper bound, we show that in the worst case such a subset has size at most $O(\sqrt{n})$ for $2\leq s\leq n^{3/8}$ and $O((n/s)^{4/5})$ for $n^{3/8}\leq s=O(\sqrt{n})$. The proofs use a wide range of tools such as incidence geometry, probabilistic methods, the hypergraph container method, and additive combinatorics.

We consider temporal numeric planning problems $\Pi$ expressed in PDDL2.1 level 3, and show how to produce SMT formulas $(i)$ whose models correspond to valid plans of $\Pi$, and $(ii)$ that extend the recently proposed planning with patterns approach from the numeric to the temporal case. We prove the correctness and completeness of the approach and show that it performs very well on 10 domains with required concurrency.

Magnetic Resonance Fingerprinting (MRF) is a time-efficient approach to quantitative MRI, enabling the mapping of multiple tissue properties from a single, accelerated scan. However, achieving accurate reconstructions remains challenging, particularly in highly accelerated and undersampled acquisitions, which are crucial for reducing scan times. While deep learning techniques have advanced image reconstruction, the recent introduction of diffusion models offers new possibilities for imaging tasks, though their application in the medical field is still emerging. Notably, diffusion models have not yet been explored for the MRF problem. In this work, we propose for the first time a conditional diffusion probabilistic model for MRF image reconstruction. Qualitative and quantitative comparisons on in-vivo brain scan data demonstrate that the proposed approach can outperform established deep learning and compressed sensing algorithms for MRF reconstruction. Extensive ablation studies also explore strategies to improve computational efficiency of our approach.

We present {\em generative clustering} (GC) for clustering a set of documents, $\mathrm{X}$, by using texts $\mathrm{Y}$ generated by large language models (LLMs) instead of by clustering the original documents $\mathrm{X}$. Because LLMs provide probability distributions, the similarity between two documents can be rigorously defined in an information-theoretic manner by the KL divergence. We also propose a natural, novel clustering algorithm by using importance sampling. We show that GC achieves the state-of-the-art performance, outperforming any previous clustering method often by a large margin. Furthermore, we show an application to generative document retrieval in which documents are indexed via hierarchical clustering and our method improves the retrieval accuracy.

Inductive reasoning - the process of inferring general rules from a small number of observations - is a fundamental aspect of human intelligence. Recent works suggest that large language models (LLMs) can engage in inductive reasoning by sampling multiple hypotheses about the rules and selecting the one that best explains the observations. However, due to the IID sampling, semantically redundant hypotheses are frequently generated, leading to significant wastage of compute. In this paper, we 1) demonstrate that increasing the temperature to enhance the diversity is limited due to text degeneration issue, and 2) propose a novel method to improve the diversity while maintaining text quality. We first analyze the effect of increasing the temperature parameter, which is regarded as the LLM's diversity control, on IID hypotheses. Our analysis shows that as temperature rises, diversity and accuracy of hypotheses increase up to a certain point, but this trend saturates due to text degeneration. To generate hypotheses that are more semantically diverse and of higher quality, we propose a novel approach inspired by human inductive reasoning, which we call Mixture of Concepts (MoC). When applied to several inductive reasoning benchmarks, MoC demonstrated significant performance improvements compared to standard IID sampling and other approaches.

Central to rough path theory is the signature transform of a path, an infinite series of tensors given by the iterated integrals of the underlying path. The signature poses an effective way to capture sequentially ordered information, thanks both to its rich analytic and algebraic properties as well as its universality when used as a basis to approximate functions on path space. Whilst a truncated version of the signature can be efficiently computed using Chen's identity, there is a lack of efficient methods for computing a sparse collection of iterated integrals contained in high levels of the signature. We address this problem by leveraging signature kernels, defined as the inner product of two signatures, and computable efficiently by means of PDE-based methods. By forming a filter in signature space with which to take kernels, one can effectively isolate specific groups of signature coefficients and, in particular, a singular coefficient at any depth of the transform. We show that such a filter can be expressed as a linear combination of suitable signature transforms and demonstrate empirically the effectiveness of our approach. To conclude, we give an example use case for sparse collections of signature coefficients based on the construction of N-step Euler schemes for sparse CDEs.

Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.