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We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In a typical existing approach, one first tries to make a good initial guess for the parameter values. Then, in a loop, the corresponding outputs are computed by solving the ODE numerically, followed by computing the error from the given time series data. If the error is small, the loop terminates and the parameter values are returned. Otherwise, heuristics/theories are used to possibly improve the guess and continue the loop. A downside of this approach is non-robustness, as there are no guarantees for the result of the loop iterations to be predictably close to the true parameter values. In this paper, we propose a new approach, which does not suffer from the above non-robustness. In particular, it does not require making good initial guesses for the parameter values. Instead, it uses differential algebra, interpolation of the data using rational functions, and multivariate polynomial system solving, and has a potential for a complete user control over the error of the estimation (the actual error analysis is left for the future research). We also compare the performance of the resulting software with several other estimation software packages.

In multilingual translation research, the comprehension and utilization of language families are of paramount importance. Nevertheless, clustering languages based solely on their ancestral families can yield suboptimal results due to variations in the datasets employed during the model's training phase. To mitigate this challenge, we introduce an innovative method that leverages the fisher information matrix (FIM) to cluster language families, anchored on the multilingual translation model's characteristics. We hypothesize that language pairs with similar effects on model parameters exhibit a considerable degree of linguistic congruence and should thus be grouped cohesively. This concept has led us to define pseudo language families. We provide an in-depth discussion regarding the inception and application of these pseudo language families. Empirical evaluations reveal that employing these pseudo language families enhances performance over conventional language families in adapting a multilingual translation model to unfamiliar language pairs. The proposed methodology may also be extended to scenarios requiring language similarity measurements. The source code and associated scripts can be accessed at //github.com/ecoli-hit/PseudoFamily.

We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus the computational task is to estimate a time-evolving density $\rho(v, t)$ given noisy observations of the true density $\rho^\dagger$; this contrasts with the standard filtering problem based on observations of the state $v$. The task is naturally formulated as an infinite-dimensional filtering problem in the space of densities $\rho$. However, for the purposes of tractability, we seek algorithms in state space; specifically we introduce a mean field state space model and, using interacting particle system approximations to this model, we propose an ensemble method. We refer to the resulting methodology as the ensemble Fokker-Planck filter (EnFPF). Under certain restrictive assumptions we show that the EnFPF approximates the Kalman-Bucy filter for the Fokker-Planck equation, which is the exact solution of the infinite-dimensional filtering problem; our numerical experiments show that the methodology is useful beyond this restrictive setting. Specifically the experiments show that the EnFPF is able to correct ensemble statistics, to accelerate convergence to the invariant density for autonomous systems, and to accelerate convergence to time-dependent invariant densities for non-autonomous systems. We discuss possible applications of the EnFPF to climate ensembles and to turbulence modelling.

Recent language models generate false but plausible-sounding text with surprising frequency. Such "hallucinations" are an obstacle to the usability of language-based AI systems and can harm people who rely upon their outputs. This work shows shows that there is an inherent statistical lower-bound on the rate that pretrained language models hallucinate certain types of facts, having nothing to do with the transformer LM architecture or data quality. For "arbitrary" facts whose veracity cannot be determined from the training data, we show that hallucinations must occur at a certain rate for language models that satisfy a statistical calibration condition appropriate for generative language models. Specifically, if the maximum probability of any fact is bounded, we show that the probability of generating a hallucination is close to the fraction of facts that occur exactly once in the training data (a "Good-Turing" estimate), even assuming ideal training data without errors. One conclusion is that models pretrained to be sufficiently good predictors (i.e., calibrated) may require post-training to mitigate hallucinations on the type of arbitrary facts that tend to appear once in the training set. However, our analysis also suggests that there is no statistical reason that pretraining will lead to hallucination on facts that tend to appear more than once in the training data (like references to publications such as articles and books, whose hallucinations have been particularly notable and problematic) or on systematic facts (like arithmetic calculations). Therefore, different architectures and learning algorithms may mitigate these latter types of hallucinations.

Semantic communication, recognized as a promising technology for future intelligent applications, has received widespread research attention. Despite the potential of semantic communication to enhance transmission reliability, especially in low signal-to-noise (SNR) environments, the critical issue of resource allocation and compatibility in the dynamic wireless environment remains largely unexplored. In this paper, we propose an adaptive semantic resource allocation paradigm with semantic-bit quantization (SBQ) compatibly for existing wireless communications, where the inaccurate environment perception introduced by the additional mapping relationship between semantic metrics and transmission metrics is solved. In order to investigate the performance of semantic communication networks, the quality of service for semantic communication (SC-QoS), including the semantic quantization efficiency (SQE) and transmission latency, is proposed for the first time. A problem of maximizing the overall effective SC-QoS is formulated by jointly optimizing the transmit beamforming of the base station, the bits for semantic representation, the subchannel assignment, and the bandwidth resource allocation. To address the non-convex formulated problem, an intelligent resource allocation scheme is proposed based on a hybrid deep reinforcement learning (DRL) algorithm, where the intelligent agent can perceive both semantic tasks and dynamic wireless environments. Simulation results demonstrate that our design can effectively combat semantic noise and achieve superior performance in wireless communications compared to several benchmark schemes. Furthermore, compared to mapping-guided paradigm based resource allocation schemes, our proposed adaptive scheme can achieve up to 13% performance improvement in terms of SC-QoS.

While existing large vision-language multimodal models focus on whole image understanding, there is a prominent gap in achieving region-specific comprehension. Current approaches that use textual coordinates or spatial encodings often fail to provide a user-friendly interface for visual prompting. To address this challenge, we introduce a novel multimodal model capable of decoding arbitrary visual prompts. This allows users to intuitively mark images and interact with the model using natural cues like a "red bounding box" or "pointed arrow". Our simple design directly overlays visual markers onto the RGB image, eliminating the need for complex region encodings, yet achieves state-of-the-art performance on region-understanding tasks like Visual7W, PointQA, and Visual Commonsense Reasoning benchmark. Furthermore, we present ViP-Bench, a comprehensive benchmark to assess the capability of models in understanding visual prompts across multiple dimensions, enabling future research in this domain. Code, data, and model are publicly available.

In recent studies on MRI reconstruction, advances have shown significant promise for further accelerating the MRI acquisition. Most state-of-the-art methods require a large amount of fully-sampled data to optimise reconstruction models, which is impractical and expensive under certain clinical settings. On the other hand, for unsupervised scan-specific reconstruction methods, overfitting is likely to happen due to insufficient supervision, while restrictions on acceleration rates and under-sampling patterns further limit their applicability. To this end, we propose an unsupervised, adaptive coarse-to-fine framework that enhances reconstruction quality without being constrained by the sparsity levels or patterns in under-sampling. The framework employs an implicit neural representation for scan-specific MRI reconstruction, learning a mapping from multi-dimensional coordinates to their corresponding signal intensities. Moreover, we integrate a novel learning strategy that progressively refines the use of acquired k-space signals for self-supervision. This approach effectively adjusts the proportion of supervising signals from unevenly distributed information across different frequency bands, thus mitigating the issue of overfitting while improving the overall reconstruction. Comprehensive evaluation on a public dataset, including both 2D and 3D data, has shown that our method outperforms current state-of-the-art scan-specific MRI reconstruction techniques, for up to 8-fold under-sampling.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.

Text Classification is an important and classical problem in natural language processing. There have been a number of studies that applied convolutional neural networks (convolution on regular grid, e.g., sequence) to classification. However, only a limited number of studies have explored the more flexible graph convolutional neural networks (e.g., convolution on non-grid, e.g., arbitrary graph) for the task. In this work, we propose to use graph convolutional networks for text classification. We build a single text graph for a corpus based on word co-occurrence and document word relations, then learn a Text Graph Convolutional Network (Text GCN) for the corpus. Our Text GCN is initialized with one-hot representation for word and document, it then jointly learns the embeddings for both words and documents, as supervised by the known class labels for documents. Our experimental results on multiple benchmark datasets demonstrate that a vanilla Text GCN without any external word embeddings or knowledge outperforms state-of-the-art methods for text classification. On the other hand, Text GCN also learns predictive word and document embeddings. In addition, experimental results show that the improvement of Text GCN over state-of-the-art comparison methods become more prominent as we lower the percentage of training data, suggesting the robustness of Text GCN to less training data in text classification.