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For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the expectation of the logarithm of an importance sampling estimate of the likelihood with respect to both the latent variable model parameters and the importance distribution parameters, the expectation being itself with respect to the importance samples. Despite its great empirical success in machine learning, a theoretical analysis of the limit properties of the resulting estimates is still lacking. We fill this gap by establishing consistency when both the Monte Carlo and the observed data sample sizes go to infinity simultaneously. We also establish asymptotic normality and efficiency under additional conditions relating the rate of growth between the Monte Carlo and the observed data samples sizes. We distinguish several regimes related to the smoothness of the importance ratio., Comment: 25 pages, 2 figures

Let $D$ be an integral domain with quotient field $K$ and $E$ a subset of $K$. The \textit{ring of integer-valued rational functions on} $E$ is defined as $$\mathrm{int}_R(E,D):=\lbrace \varphi \in K(X);\; \varphi(E)\subseteq D\rbrace.$$ The main goal of this paper is to investigate the Krull dimension of the ring $\mathrm{int}_R(E,D).$ Particularly, we are interested in domains that are either Jaffard or PVDs. Interesting results are established with some illustrating examples., Comment: To appear in Archiv der Mathematik, DOI : 10.1007/s00013-024-02086-7

We report on the successful design and fabrication of optical modules using a 50 micron pitch polymer waveguide interface, integrated for low loss, high density optical data transfer with very low space requirements on a Si photonics die. This prototype module meets JEDEC reliability standards and promises to increase the number of optical fibers that can be connected at the edge of a chip, a measure known as beachfront density, by six times compared to state of the art technology. Scalability of the polymer waveguide to less than 20 micron pitch stands to improve the bandwidth density upwards of 10 Tbps/mm.

This paper tackles the pressing challenge of mutagenicity prediction by introducing three ground-breaking approaches. First, it showcases the superior performance of 2D scattering coefficients extracted from molecular images, compared to traditional molecular descriptors. Second, it presents a hybrid approach that combines geometric graph scattering (GGS), Graph Isomorphism Networks (GIN), and machine learning models, achieving strong results in mutagenicity prediction. Third, it introduces a novel graph neural network architecture, MOLG3-SAGE, which integrates GGS node features into a fully connected graph structure, delivering outstanding predictive accuracy. Experimental results on the ZINC dataset demonstrate significant improvements, emphasizing the effectiveness of blending 2D and geometric scattering techniques with graph neural networks. This study illustrates the potential of GNNs and GGS for mutagenicity prediction, with broad implications for drug discovery and chemical safety assessment.

Large language models (LLMs) exhibit remarkable capabilities on not just language tasks, but also various tasks that are not linguistic in nature, such as logical reasoning and social inference. In the human brain, neuroscience has identified a core language system that selectively and causally supports language processing. We here ask whether similar specialization for language emerges in LLMs. We identify language-selective units within 18 popular LLMs, using the same localization approach that is used in neuroscience. We then establish the causal role of these units by demonstrating that ablating LLM language-selective units -- but not random units -- leads to drastic deficits in language tasks. Correspondingly, language-selective LLM units are more aligned to brain recordings from the human language system than random units. Finally, we investigate whether our localization method extends to other cognitive domains: while we find specialized networks in some LLMs for reasoning and social capabilities, there are substantial differences among models. These findings provide functional and causal evidence for specialization in large language models, and highlight parallels with the functional organization in the brain., Comment: Preprint

While today's large language models exhibit impressive abilities in generating human-like text, they require massive amounts of data during training. We here take inspiration from human cognitive development to train models in limited data conditions. Specifically we present a self-synthesis approach that iterates through four phases: Phase 1 sets up fundamental language abilities, training the model from scratch on a small corpus. Language is then associated with the visual environment in phase 2, integrating the model with a vision encoder to generate descriptive captions from labeled images. In the "self-synthesis" phase 3, the model generates captions for unlabeled images, that it then uses to further train its language component with a mix of synthetic, and previous real-world text. This phase is meant to expand the model's linguistic repertoire, similar to humans self-annotating new experiences. Finally, phase 4 develops advanced cognitive skills, by training the model on specific tasks such as visual question answering and reasoning. Our approach offers a proof of concept for training a multimodal model using a developmentally plausible amount of data., Comment: Accepted to BabyLM Challenge at CoNLL 2024

Let $D\subseteq B$ be an extension of integral domains and $E$ a subset of the quotient field of $D$. We introduce the ring of \textit{$D$-valued $B$-rational functions on $E$}, denoted by $Int^R_B(E,D)$, which naturally extends the concepts of integer-valued polynomials, defined as $ Int^R_B(E,D) \:=\lbrace f \in B(X);\; f(E)\subseteq D\rbrace.$ The notion of $Int^R_B(E,D)$ boils down to the usual notion of integer-valued rational functions when the subset $E$ is infinite. In this paper, we aim to investigate various properties of these rings, such as prime ideals, localization, and the module structure. Furthermore, we study the transfer of some ring-theoretic properties from $Int^R(E,D)$ to $D$., Comment: 21 pages. To appear in Communications in Algebra, https://doi.org/10.1080/00927872.2024.2422035

Breast cancer remains a significant global health challenge, with prognosis and treatment decisions largely dependent on clinical characteristics. Accurate prediction of patient outcomes is crucial for personalized treatment strategies. This study employs survival analysis techniques, including Cox proportional hazards and parametric survival models, to enhance the prediction of the log odds of survival in breast cancer patients. Clinical variables such as tumor size, hormone receptor status, HER2 status, age, and treatment history were analyzed to assess their impact on survival outcomes. Data from 1557 breast cancer patients were obtained from a publicly available dataset provided by the University College Hospital, Ibadan, Nigeria. This dataset was preprocessed and analyzed using both univariate and multivariate approaches to evaluate survival outcomes. Kaplan-Meier survival curves were generated to visualize survival probabilities, while the Cox proportional hazards model identified key risk factors influencing mortality. The results showed that older age, larger tumor size, and HER2-positive status were significantly associated with an increased risk of mortality. In contrast, estrogen receptor positivity and breast-conserving surgery were linked to better survival outcomes. The findings suggest that integrating these clinical variables into predictive models improvesthe accuracy of survival predictions, helping to identify high-risk patients who may benefit from more aggressive interventions. This study demonstrates the potential of survival analysis in optimizing breast cancer care, particularly in resource-limited settings. Future research should focus on integrating genomic data and real-world clinical outcomes to further refine these models., Comment: 17 pages

Neurons in the brain are spatially organized such that neighbors on tissue often exhibit similar response profiles. In the human language system, experimental studies have observed clusters for syntactic and semantic categories, but the mechanisms underlying this functional organization remain unclear. Here, building on work from the vision literature, we develop TopoLM, a transformer language model with an explicit two-dimensional spatial representation of model units. By combining a next-token prediction objective with a spatial smoothness loss, representations in this model assemble into clusters that correspond to semantically interpretable groupings of text and closely match the functional organization in the brain's language system. TopoLM successfully predicts the emergence of the spatio-functional organization of a cortical language system as well as the organization of functional clusters selective for fine-grained linguistic features empirically observed in human cortex. Our results suggest that the functional organization of the human language system is driven by a unified spatial objective, and provide a functionally and spatially aligned model of language processing in the brain.

Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable terms. To tackle this issue, state-of-the-art approaches formulate the problem as that of sampling from a surrogate diffusion model targeting the posterior and decompose its scores into two terms: the prior score and an intractable guidance term. While the former is replaced by the pre-trained score of the considered diffusion model, the guidance term has to be estimated. In this paper, we propose a novel approach that utilises a decomposition of the transitions which, in contrast to previous methods, allows a trade-off between the complexity of the intractable guidance term and that of the prior transitions. We validate the proposed approach through extensive experiments on linear and nonlinear inverse problems, including challenging cases with latent diffusion models as priors. We then demonstrate its applicability to various modalities and its promising impact on public health by tackling cardiovascular disease diagnosis through the reconstruction of incomplete electrocardiograms. The code is publicly available at \url{https://github.com/yazidjanati/mgps}.

Designing expressive typography that visually conveys a word's meaning while maintaining readability is a complex task, known as semantic typography. It involves selecting an idea, choosing an appropriate font, and balancing creativity with legibility. We introduce an end-to-end system that automates this process. First, a Large Language Model (LLM) generates imagery ideas for the word, useful for abstract concepts like freedom. Then, the FontCLIP pre-trained model automatically selects a suitable font based on its semantic understanding of font attributes. The system identifies optimal regions of the word for morphing and iteratively transforms them using a pre-trained diffusion model. A key feature is our OCR-based loss function, which enhances readability and enables simultaneous stylization of multiple characters. We compare our method with other baselines, demonstrating great readability enhancement and versatility across multiple languages and writing scripts.

This work proposes a strategy for organising quadrotors around a payload to enable hovering without external stimuli, together with a MATLAB software for modelling the dynamics of a quadrotor-payload system. Based on geometric concepts, the proposed design keeps the payload and system centre of mass aligned. Hovering tests that are successful confirm the method's efficiency. Moreover, the algorithm is improved to take thrust capacities and propeller distances into account, calculating the minimum number of quadrotors needed for hovering. The algorithm's effectiveness is demonstrated by numerical examples, which reveal that larger quadrotors may require fewer units while smaller ones give greater flexibility. Our code can be found at: \href{https://github.com/Hosnooo/Swarm-Slung-Payload}{https://github.com/Hosnooo/Swarm-Slung-Payload}, Comment: accepted for publication at AIAA SCITECH 2025

Bitcoin's global success has led to the rise of blockchain, but many systems labeled as "blockchain" deviate from its core principles, adding complexity to the ecosystem. This survey addresses the need for a comprehensive review and taxonomy to clarify the differences between blockchain and blockchain-like systems. We propose a reference model with four key layers: data, consensus, execution, and application, and introduce a new taxonomy for better classification. Through a qualitative and quantitative analysis of 44 DLT solutions and 26 consensus mechanisms, we highlight key challenges and offer research directions in the field.

The proliferation of machine learning models in critical decision making processes has underscored the need for bias discovery and mitigation strategies. Identifying the reasons behind a biased system is not straightforward, since in many occasions they are associated with hidden spurious correlations which are not easy to spot. Standard approaches rely on bias audits performed by analyzing model performance in pre-defined subgroups of data samples, usually characterized by common attributes like gender or ethnicity when it comes to people, or other specific attributes defining semantically coherent groups of images. However, it is not always possible to know a-priori the specific attributes defining the failure modes of visual recognition systems. Recent approaches propose to discover these groups by leveraging large vision language models, which enable the extraction of cross-modal embeddings and the generation of textual descriptions to characterize the subgroups where a certain model is underperforming. In this work, we argue that incorporating visual explanations (e.g. heatmaps generated via GradCAM or other approaches) can boost the performance of such bias discovery and mitigation frameworks. To this end, we introduce Visually Grounded Bias Discovery and Mitigation (ViG-Bias), a simple yet effective technique which can be integrated to a variety of existing frameworks to improve both, discovery and mitigation performance. Our comprehensive evaluation shows that incorporating visual explanations enhances existing techniques like DOMINO, FACTS and Bias-to-Text, across several challenging datasets, including CelebA, Waterbirds, and NICO++., Comment: ECCV 2024

Large Language Models (LLMs) have been shown to be effective models of the human language system, with some models predicting most explainable variance of brain activity in current datasets. Even in untrained models, the representations induced by architectural priors can exhibit reasonable alignment to brain data. In this work, we investigate the key architectural components driving the surprising alignment of untrained models. To estimate LLM-to-brain similarity, we first select language-selective units within an LLM, similar to how neuroscientists identify the language network in the human brain. We then benchmark the brain alignment of these LLM units across five different brain recording datasets. By isolating critical components of the Transformer architecture, we identify tokenization strategy and multihead attention as the two major components driving brain alignment. A simple form of recurrence further improves alignment. We further demonstrate this quantitative brain alignment of our model by reproducing landmark studies in the language neuroscience field, showing that localized model units -- just like language voxels measured empirically in the human brain -- discriminate more reliably between lexical than syntactic differences, and exhibit similar response profiles under the same experimental conditions. Finally, we demonstrate the utility of our model's representations for language modeling, achieving improved sample and parameter efficiency over comparable architectures. Our model's estimates of surprisal sets a new state-of-the-art in the behavioral alignment to human reading times. Taken together, we propose a highly brain- and behaviorally-aligned model that conceptualizes the human language system as an untrained shallow feature encoder, with structural priors, combined with a trained decoder to achieve efficient and performant language processing., Comment: Preprint

While existing literature relies on performance differences to uncover gender biases in ASR models, a deeper analysis is essential to understand how gender is encoded and utilized during transcript generation. This work investigates the encoding and utilization of gender in the latent representations of two transformer-based ASR models, Wav2Vec2 and HuBERT. Using linear erasure, we demonstrate the feasibility of removing gender information from each layer of an ASR model and show that such an intervention has minimal impacts on the ASR performance. Additionally, our analysis reveals a concentration of gender information within the first and last frames in the final layers, explaining the ease of erasing gender in these layers. Our findings suggest the prospect of creating gender-neutral embeddings that can be integrated into ASR frameworks without compromising their efficacy., Comment: Accepted at Interspeech 2024

In this paper, we investigate the deterministic multidimensional Skorokhod problem with normal reflection in a family of time-dependent convex domains that are c\`adl\`ag with respect to the Hausdorff metric. We then show the existence and uniqueness of solutions to multidimensional McKean-Vlasov stochastic differential equations reflected in these time-dependent domains. Additionally, we derive stability properties with respect to the initial condition and the coefficients. Finally, we establish a propagation of chaos result.

PAC-Bayesian analysis is a frequentist framework for incorporating prior knowledge into learning. It was inspired by Bayesian learning, which allows sequential data processing and naturally turns posteriors from one processing step into priors for the next. However, despite two and a half decades of research, the ability to update priors sequentially without losing confidence information along the way remained elusive for PAC-Bayes. While PAC-Bayes allows construction of data-informed priors, the final confidence intervals depend only on the number of points that were not used for the construction of the prior, whereas confidence information in the prior, which is related to the number of points used to construct the prior, is lost. This limits the possibility and benefit of sequential prior updates, because the final bounds depend only on the size of the final batch. We present a novel and, in retrospect, surprisingly simple and powerful PAC-Bayesian procedure that allows sequential prior updates with no information loss. The procedure is based on a novel decomposition of the expected loss of randomized classifiers. The decomposition rewrites the loss of the posterior as an excess loss relative to a downscaled loss of the prior plus the downscaled loss of the prior, which is bounded recursively. As a side result, we also present a generalization of the split-kl and PAC-Bayes-split-kl inequalities to discrete random variables, which we use for bounding the excess losses, and which can be of independent interest. In empirical evaluation the new procedure significantly outperforms state-of-the-art.

We report on an experimental platform based on an atom chip encompassing a coplanar waveguide which enables to manipulate a quantum gas of sodium atoms with strong microwave fields. We describe the production with this setup of a very elongated degenerate quantum gas with typically 10^6 atoms, that can be prepared all along the cross-over from the three-dimensional to the one-dimensional regime depending on the atom number and trapping geometry. Using the microwave field radiated by the waveguide, we drive Rabi oscillations between the hyperfine ground states, with the atoms trapped at various distances from the waveguide. At the closest position explored, the field amplitude exceeds 5 G, corresponding to a Rabi frequency larger than 6 MHz. This enables fast manipulation of the atomic internal state.

The Method of Successive Approximations (MSA) is a fixed-point iterative method used to solve stochastic optimal control problems. It is an indirect method based on the conditions derived from the Stochastic Maximum Principle (SMP), an extension of the Pontryagin Maximum Principle (PMP) to stochastic control problems. In this study, we investigate the contractivity and the convergence of MSA for a specific and interesting class of stochastic dynamical systems (when the drift coefficient is one-sided-Lipschitz with a negative constant and the diffusion coefficient is Lipschitz continuous). Our analysis unfolds in three key steps: firstly, we prove the stability of the state process with respect to the control process. Secondly, we establish the stability of the adjoint process. Finally, we present rigorous evidence to prove the contractivity and then the convergence of MSA. This study contributes to enhancing the understanding of MSA's applicability and effectiveness in addressing stochastic optimal control problems.