Grammatical cues are sometimes redundant with word meanings in natural language. For instance, English word order rules constrain the word order of a sentence like "The dog chewed the bone" even though the status of "dog" as subject and "bone" as object can be inferred from world knowledge and plausibility. Quantifying how often this redundancy occurs, and how the level of redundancy varies across typologically diverse languages, can shed light on the function and evolution of grammar. To that end, we performed a behavioral experiment in English and Russian and a cross-linguistic computational analysis measuring the redundancy of grammatical cues in transitive clauses extracted from corpus text. English and Russian speakers (n=484) were presented with subjects, verbs, and objects (in random order and with morphological markings removed) extracted from naturally occurring sentences and were asked to identify which noun is the subject of the action. Accuracy was high in both languages (~89% in English, ~87% in Russian). Next, we trained a neural network machine classifier on a similar task: predicting which nominal in a subject-verb-object triad is the subject. Across 30 languages from eight language families, performance was consistently high: a median accuracy of 87%, comparable to the accuracy observed in the human experiments. The conclusion is that grammatical cues such as word order are necessary to convey subjecthood and objecthood in a minority of naturally occurring transitive clauses; nevertheless, they can (a) provide an important source of redundancy and (b) are crucial for conveying intended meaning that cannot be inferred from the words alone, including descriptions of human interactions, where roles are often reversible (e.g., Ray helped Lu/Lu helped Ray), and expressing non-prototypical meanings (e.g., "The bone chewed the dog.").
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Scale-free dynamics, formalized by selfsimilarity, provides a versatile paradigm massively and ubiquitously used to model temporal dynamics in real-world data. However, its practical use has mostly remained univariate so far. By contrast, modern applications often demand multivariate data analysis. Accordingly, models for multivariate selfsimilarity were recently proposed. Nevertheless, they have remained rarely used in practice because of a lack of available robust estimation procedures for the vector of selfsimilarity parameters. Building upon recent mathematical developments, the present work puts forth an efficient estimation procedure based on the theoretical study of the multiscale eigenstructure of the wavelet spectrum of multivariate selfsimilar processes. The estimation performance is studied theoretically in the asymptotic limits of large scale and sample sizes, and computationally for finite-size samples. As a practical outcome, a fully operational and documented multivariate signal processing estimation toolbox is made freely available and is ready for practical use on real-world data. Its potential benefits are illustrated in epileptic seizure prediction from multi-channel EEG data.
Simply-verifiable mathematical conditions for existence, uniqueness and explicit analytical computation of minimal adversarial paths (MAP) and minimal adversarial distances (MAD) for (locally) uniquely-invertible classifiers, for generalized linear models (GLM), and for entropic AI (EAI) are formulated and proven. Practical computation of MAP and MAD, their comparison and interpretations for various classes of AI tools (for neuronal networks, boosted random forests, GLM and EAI) are demonstrated on the common synthetic benchmarks: on a double Swiss roll spiral and its extensions, as well as on the two biomedical data problems (for the health insurance claim predictions, and for the heart attack lethality classification). On biomedical applications it is demonstrated how MAP provides unique minimal patient-specific risk-mitigating interventions in the predefined subsets of accessible control variables.
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising from parametric modelling and computational uncertainty quantification. It is common to use Monte Carlo sampling in such applications, so as not to succumb to the curse of dimensionality. However, it is well known that such a strategy is theoretically suboptimal. Specifically, there are many polynomial spaces of dimension $n$ for which the sample complexity scales log-quadratically, i.e., like $c \cdot n^2 \cdot \log(n)$ as $n \rightarrow \infty$. This well-documented phenomenon has led to a concerted effort over the last decade to design improved, and moreover, near-optimal strategies, whose sample complexities scale log-linearly, or even linearly in $n$. In this work we demonstrate that Monte Carlo is actually a perfectly good strategy in high dimensions, despite its apparent suboptimality. We first document this phenomenon empirically via a systematic set of numerical experiments. Next, we present a theoretical analysis that rigorously justifies this fact in the case of holomorphic functions of infinitely-many variables. We show that there is a least-squares approximation based on $m$ Monte Carlo samples whose error decays algebraically fast in $m/\log(m)$, with a rate that is the same as that of the best $n$-term polynomial approximation. This result is non-constructive, since it assumes knowledge of a suitable polynomial subspace in which to perform the approximation. We next present a compressed sensing-based scheme that achieves the same rate, except for a larger polylogarithmic factor. This scheme is practical, and numerically it performs as well as or better than well-known adaptive least-squares schemes.
We survey recent contributions to finite element exterior calculus over manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differential equations over manifolds. Our primary focus is on uniformly bounded commuting projections over manifolds: these projections map from Sobolev de Rham complexes onto finite element de Rham complexes, commute with the differential operators, and satisfy uniform bounds in Lebesgue norms. They enable the Galerkin theory of Hilbert complexes for a large range of intrinsic finite element methods over manifolds. However, these intrinsic finite element methods are generally not computable and thus primarily of theoretical interest. This leads to our second point: estimating the geometric variational crime incurred by transitioning to computable approximate problems. Lastly, our third point addresses how to estimate the approximation error of the intrinsic finite element method in terms of the mesh size. If the solution is not continuous, then such an estimate is achieved via modified Cl\'ement or Scott-Zhang interpolants that facilitate a broken Bramble--Hilbert lemma.
Previous audio-visual speech separation methods use the synchronization of the speaker's facial movement and speech in the video to supervise the speech separation in a self-supervised way. In this paper, we propose a model to solve the speech separation problem assisted by both face and sign language, which we call the extended speech separation problem. We design a general deep learning network for learning the combination of three modalities, audio, face, and sign language information, for better solving the speech separation problem. To train the model, we introduce a large-scale dataset named the Chinese Sign Language News Speech (CSLNSpeech) dataset, in which three modalities of audio, face, and sign language coexist. Experiment results show that the proposed model has better performance and robustness than the usual audio-visual system. Besides, sign language modality can also be used alone to supervise speech separation tasks, and the introduction of sign language is helpful for hearing-impaired people to learn and communicate. Last, our model is a general speech separation framework and can achieve very competitive separation performance on two open-source audio-visual datasets. The code is available at //github.com/iveveive/SLNSpeech
Clinical texts, such as admission notes, discharge summaries, and progress notes, contain rich and valuable information that can be used for various clinical outcome prediction tasks. However, applying large language models, such as BERT-based models, to clinical texts poses two major challenges: the limitation of input length and the diversity of data sources. This paper proposes a novel method to preserve the knowledge of long clinical texts using aggregated ensembles of large language models. Unlike previous studies which use model ensembling or text aggregation methods separately, we combine ensemble learning with text aggregation and train multiple large language models on two clinical outcome tasks: mortality prediction and length of stay prediction. We show that our method can achieve better results than baselines, ensembling, and aggregation individually, and can improve the performance of large language models while handling long inputs and diverse datasets. We conduct extensive experiments on the admission notes from the MIMIC-III clinical database by combining multiple unstructured and high-dimensional datasets, demonstrating our method's effectiveness and superiority over existing approaches. We also provide a comprehensive analysis and discussion of our results, highlighting our method's applications and limitations for future research in the domain of clinical healthcare. The results and analysis of this study is supportive of our method assisting in clinical healthcare systems by enabling clinical decision-making with robust performance overcoming the challenges of long text inputs and varied datasets.
Large-sample Bayesian analogs exist for many frequentist methods, but are less well-known for the widely-used 'sandwich' or 'robust' variance estimates. We review existing approaches to Bayesian analogs of sandwich variance estimates and propose a new analog, as the Bayes rule under a form of balanced loss function, that combines elements of standard parametric inference with fidelity of the data to the model. Our development is general, for essentially any regression setting with independent outcomes. Being the large-sample equivalent of its frequentist counterpart, we show by simulation that Bayesian robust standard error estimates can faithfully quantify the variability of parameter estimates even under model misspecification -- thus retaining the major attraction of the original frequentist version. We demonstrate our Bayesian analog of standard error estimates when studying the association between age and systolic blood pressure in NHANES.
Pre-trained language models can be surprisingly adept at tasks they were not explicitly trained on, but how they implement these capabilities is poorly understood. In this paper, we investigate the basic mathematical abilities often acquired by pre-trained language models. Concretely, we use mechanistic interpretability techniques to explain the (limited) mathematical abilities of GPT-2 small. As a case study, we examine its ability to take in sentences such as "The war lasted from the year 1732 to the year 17", and predict valid two-digit end years (years > 32). We first identify a circuit, a small subset of GPT-2 small's computational graph that computes this task's output. Then, we explain the role of each circuit component, showing that GPT-2 small's final multi-layer perceptrons boost the probability of end years greater than the start year. Finally, we find related tasks that activate our circuit. Our results suggest that GPT-2 small computes greater-than using a complex but general mechanism that activates across diverse contexts.
This paper presents the workspace optimization of one-translational two-rotational (1T2R) parallel manipulators using a dimensionally homogeneous constraint-embedded Jacobian. The mixed degrees of freedom of 1T2R parallel manipulators, which cause dimensional inconsistency, make it difficult to optimize their architectural parameters. To solve this problem, a point-based approach with a shifting property, selection matrix, and constraint-embedded inverse Jacobian is proposed. A simplified formulation is provided, eliminating the complex partial differentiation required in previous approaches. The dimensional homogeneity of the proposed method was analytically proven, and its validity was confirmed by comparing it with the conventional point-based method using a 3-PRS manipulator. Furthermore, the approach was applied to an asymmetric 2-RRS/RRRU manipulator with no parasitic motion. This mechanism has a T-shape combination of limbs with different kinematic parameters, making it challenging to derive a dimensionally homogeneous Jacobian using the conventional method. Finally, optimization was performed, and the results show that the proposed method is more efficient than the conventional approach. The efficiency and simplicity of the proposed method were verified using two distinct parallel manipulators.
Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.
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