Continuous Representation Research Articles

Notes from the field: Practical considerations for agent‐based and continuous representations of system dynamics

Notes from the field: Practical considerations for agent‐based and continuous representations of system dynamics

A renormalization scheme for semi-regular continued fractions

AbstractIn this article we study a renormalization scheme with which we find all semi-regular continued fractions of a number in a natural way. We define two maps, $$\hat{T}_{slow}$$ T ^ slow and $$\hat{T}_{fast}$$ T ^ fast : these maps are defined for $$(x,y)\in [0,1]$$ ( x , y ) ∈ [ 0 , 1 ] , where x is the number for which a semi- regular continued fraction representation is developed by $$\hat{T}_{slow}$$ T ^ slow according to the parameter y. The set of all possible semi-regular continued fraction representations of x are bijectively constructed as the parameter y varies. The map $$\hat{T}_{fast}$$ T ^ fast is a “sped up" version of the map $$\hat{T}_{slow}$$ T ^ slow , and we show that $$\hat{T}_{fast}$$ T ^ fast is ergodic with respect to a probability measure which is mutually absolutely continuous with Lebesgue measure. In contrast, $$\hat{T}_{slow}$$ T ^ slow preserves no such measure, but does preserve an infinite, $$\sigma $$ σ -finite measure mutually absolutely continuous with Lebesgue measure. Furthermore, we generate a sequence of substitutions which generate a symbolic coding of the orbit of y under rotation by x modulo one. In the last section we highlight how our scheme can be used to generate semi-regular continued fractions explicitly for specific continued fraction algorithms such as Nakada’s $$\alpha $$ α -continued fractions.

Cognitive Representations of Social Relationships and their Developmental Origins.

In the human mind, what is a social relationship, and what are the developmental origins of this representation? I consider findings from infant psychology and propose that our representations of social relationships are intuitive theories built on core knowledge. I propose three central components of this intuitive theory. The purpose of the first component is to recognize whether a relationship exists, the purpose of the second is to characterize the relationship by categorizing it into a model and to compute its strength (i.e., intensity, pull, or thickness), and the purpose of the third is to understand how to change relationships through explicit or implicit communication. I propose that infants possess core knowledge on which this intuitive theory is built. This paper focuses on the second component and considers evidence that infants characterize relationships. Following Relational Models Theory (A. P. Fiske, 1992, 2004) I propose that from infancy humans recognize relationships that belong to three models: communal sharing (where people are 'one'), authority ranking (where people are ranked), and equality matching (where people are separate, but evenly balanced). I further propose that humans, and potentially infants, recognize a relationship's strength which can be thought of as a continuous representation of obligations (the extent to which certain actions are expected), and commitment (the likelihood that people will continue the relationship). These representations and the assumption that others share them allow us to form, maintain, and change social relationships throughout our lives by informing how we interpret and evaluate the actions of others and plan our own.

Spatiotemporal implicit neural representation as a generalized traffic data learner

Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. Existing methods aim to reconstruct STTD using low-dimensional models. However, they are limited to data-specific dimensions or source-dependent patterns, restricting them from unifying representations. Here, we present a novel paradigm to address the STTD learning problem by parameterizing STTD as an implicit neural representation. To discern the underlying dynamics in low-dimensional regimes, coordinate-based neural networks that can encode high-frequency structures are employed to directly map coordinates to traffic variables. To unravel the entangled spatial–temporal interactions, the variability is decomposed into separate processes. We further enable modeling in irregular spaces such as sensor graphs using spectral embedding. Through continuous representations, our approach enables the modeling of a variety of STTD with a unified input, thereby serving as a generalized learner of the underlying traffic dynamics. It is also shown that it can learn implicit low-rank priors and smoothness regularization from the data, making it versatile for learning different dominating data patterns. We validate its effectiveness through extensive experiments in real-world scenarios, showcasing applications from corridor to network scales. Empirical results not only indicate that our model has significant superiority over conventional low-rank models, but also highlight that the versatility of the approach extends to different data domains, output resolutions, and network topologies. Comprehensive model analyses provide further insight into the inductive bias of STTD. We anticipate that this pioneering modeling perspective could lay the foundation for universal representation of STTD in various real-world tasks. PyTorch implementations of this project is publicly available at:https://github.com/tongnie/traffic_dynamics.

A New Computer-Aided Diagnosis System for Breast Cancer Detection from Thermograms Using Metaheuristic Algorithms and Explainable AI

Advances in the early detection of breast cancer and treatment improvements have significantly increased survival rates. Traditional screening methods, including mammography, MRI, ultrasound, and biopsies, while effective, often come with high costs and risks. Recently, thermal imaging has gained attention due to its minimal risks compared to mammography, although it is not widely adopted as a primary detection tool since it depends on identifying skin temperature changes and lesions. The advent of machine learning (ML) and deep learning (DL) has enhanced the effectiveness of breast cancer detection and diagnosis using this technology. In this study, a novel interpretable computer aided diagnosis (CAD) system for breast cancer detection is proposed, leveraging Explainable Artificial Intelligence (XAI) throughout its various phases. To achieve these goals, we proposed a new multi-objective optimization approach named the Hybrid Particle Swarm Optimization algorithm (HPSO) and Hybrid Spider Monkey Optimization algorithm (HSMO). These algorithms simultaneously combined the continuous and binary representations of PSO and SMO to effectively manage trade-offs between accuracy, feature selection, and hyperparameter tuning. We evaluated several CAD models and investigated the impact of handcrafted methods such as Local Binary Patterns (LBP), Histogram of Oriented Gradients (HOG), Gabor Filters, and Edge Detection. We further shed light on the effect of feature selection and optimization on feature attribution and model decision-making processes using the SHapley Additive exPlanations (SHAP) framework, with a particular emphasis on cancer classification using the DMR-IR dataset. The results of our experiments demonstrate in all trials that the performance of the model is improved. With HSMO, our models achieved an accuracy of 98.27% and F1-score of 98.15% while selecting only 25.78% of the HOG features. This approach not only boosts the performance of CAD models but also ensures comprehensive interpretability. This method emerges as a promising and transparent tool for early breast cancer diagnosis.

A Cluster-Based Deep Learning Model Perceiving Series Correlation for Accurate Prediction of Phonon Spectrum.

The spectral properties are the most prevalent continuous representation for characterizing transport phenomena and excitation responses, yet their accurate predictions remain a challenge due to the inability to perceive series correlations by existing machine learning (ML) models. Herein, a ML model named cluster-based series graph networks (CSGN) is developed based on the dynamical theory of crystal lattices to predict phonon density of states (PDOS) spectrum for crystal materials. The multiple atomic cluster representation is constructed to capture the diverse vibration modes, while the mixture Gaussian process and dynamic time warping mechanism are compiled to project from clusters to PDOS spectrum. Accurate predictions of complicated spectra with multiple or overlapping peaks are achieved. The high performance of CSGN model can be attributed to the pertinent feature extraction and the appropriate similarity evaluation, which enable the natural perception of structure-property relation and intrinsic series correlations as confirmed in the predictive results. The transferable and interpretable CSGN model advances ML predictions of spectral properties and reveals the potential of designing ML methods based on physical mechanisms.

Sustainable Personalized E-Learning through Integrated Cross-Course Learning Path Planning

This study addresses the growing need for sustainable and personalized learning solutions in online education by optimizing cross-course learning paths. With the increasing volume of e-learning resources, students often struggle to select appropriate courses and learning paths that align with their individual abilities and goals. A novel cross-course learning path planning model is proposed, which integrates resources from multiple courses using modified matching functions based on Item Response Theory (IRT) and a knowledge graph. This model effectively matches learner attributes, such as abilities, learning styles, and goals, with material attributes like difficulty, types, and prerequisites. An innovative variable-length continuous representation (VLCR) and an improved differential evolution algorithm are employed to optimize the multi-attribute matching (MAM) model, enhancing learning personalization. Results from numerical experiments indicate that cross-course learning paths significantly enhance learning outcomes for a wide range of learners, with over 45% benefiting from improved matches compared to single-course paths. Additionally, 70% of learners experienced similar or better results with cross-course learning. This approach not only promotes efficient learning but also supports sustainable educational practices, preparing educators and learners to meet the challenges of a rapidly changing world.

A Deep Learning Framework for Satellite-Derived Surface PM2.5 Estimation: Enhancing Spatial Analysis in the United States

Abstract Monitoring fine particulate matter (PM2.5) is crucial for evaluating air quality and its effects on public health. However, the limited distribution of monitoring stations presents a challenge in accurately assessing air pollution, especially in areas distant from these stations. To address this challenge, our study introduces a two-step deep learning approach for estimating daily gap-free surface PM2.5 concentrations across the contiguous United States (CONUS) from 2018 to 2022, with a spatial resolution of 4 km. In the first phase, we employ a Depthwise-Partial Convolutional Neural Network (DW-PCNN) to fill gaps between surface PM2.5 stations, utilizing Aerosol Optical Depth (AOD) data from the Moderate Resolution Imaging Spectroradiometer (MODIS). In the second phase, we integrate the PM2.5 grids imputed by the DW-PCNN with meteorological and anthropogenic variables into a Deep Convolutional Neural Network (Deep-CNN) to further enhance the accuracy of our estimation. This enables us to estimate gap-free surface PM2.5 concentrations accurately, evidenced by a Pearson’s correlation coefficient (R) of 0.92 and an Index of Agreement (IOA) of 0.96 in ten-fold cross-validation. We also introduce a grid-based method for calculating PM2.5 Design Values (DV), providing a continuous spatial representation of PM2.5 DV that enhances the traditional station-based approach. Our grid-based DV representations offer a comprehensive perspective on air quality, facilitating more detailed analysis. Furthermore, our model's ability to provide spatiotemporally consistent, gap-free PM2.5 data addresses the issue of missing values, supporting health impact research, policy formulation, and the accuracy of environmental assessments.

Maintaining and updating accurate internal representations of continuous variables with a handful of neurons.

Many animals rely on persistent internal representations of continuous variables for working memory, navigation, and motor control. Existing theories typically assume that large networks of neurons are required to maintain such representations accurately; networks with few neurons are thought to generate discrete representations. However, analysis of two-photon calcium imaging data from tethered flies walking in darkness suggests that their small head-direction system can maintain a surprisingly continuous and accurate representation. We thus ask whether it is possible for a small network to generate a continuous, rather than discrete, representation of such a variable. We show analytically that even very small networks can be tuned to maintain continuous internal representations, but this comes at the cost of sensitivity to noise and variations in tuning. This work expands the computational repertoire of small networks, and raises the possibility that larger networks could represent more and higher-dimensional variables than previously thought.

CIRG-SL: Commonsense Inductive Relation Graph framework with Soft Labels for Empathetic Response Generation

Empathy, the ability to understand and respond to others’ emotions, is critical in dialogue systems, particularly for applications such as psychological counselling and casual conversation. However, existing approaches often struggle to accurately capture emotional transitions in user utterances and dialogue contexts across multiple levels of granularity. Additionally, the orthogonality of one-hot emotion representations overlooks the subtle relationships between emotion categories. To overcome these limitations, we propose a novel framework: the commonsense inductive relation graph with fine emotional soft labels for empathetic response generation. This framework refines the representation of user utterances by incorporating commonsense knowledge to derive external emotional cues, which are integrated into an adaptive inductive relation graph. This graph explicitly captures and models dynamic emotional trajectories throughout the dialogue. Additionally, we propose a fine-grained soft label construction method that more accurately reflects the nuanced distribution of emotions, replacing the rigid one-hot encoding with a continuous representation that better captures inter-emotion relationships. Our approach achieves strong performance on the benchmark EmpatheticDialogues dataset, with a perplexity score of 27.85, Dist-1 of 1.81, Dist-2 of 6.58, and a dialogue emotion accuracy of 55.65%. These results highlight the effectiveness of our framework in capturing subtle emotions and generating contextually rich, empathetic responses.

Exploring the categorical nature of colour perception: Insights from artificial networks

The electromagnetic spectrum of light from a rainbow is a continuous signal, yet we perceive it vividly in several distinct colour categories. The origins and underlying mechanisms of this phenomenon remain partly unexplained. We investigate categorical colour perception in artificial neural networks (ANNs) using the odd-one-out paradigm. In the first experiment, we compared unimodal vision networks (e.g., ImageNet object recognition) to multimodal vision-language models (e.g., CLIP text-image matching). Our results show that vision networks predict a significant portion of human data (approximately 80%), while vision-language models account for the remaining unexplained data, even in non-linguistic experiments. These findings suggest that categorical colour perception is a language-independent representation, though it is partly shaped by linguistic colour terms during its development. In the second experiment, we explored how the visual task influences the colour categories of an ANN by examining twenty-four Taskonomy networks. Our results indicate that human-like colour categories are task-dependent, predominantly emerging in semantic and 3D tasks, with a notable absence in low-level tasks. To explain this difference, we analysed kernel responses before the winner-takes-all stage, observing that networks with mismatching colour categories may still align in underlying continuous representations. Our findings quantify the dual influence of visual signals and linguistic factors in categorical colour perception and demonstrate the task-dependent nature of this phenomenon, suggesting that categorical colour perception emerges to facilitate certain visual tasks.

Empowering Graph Neural Network-Based Computational Drug Repositioning with Large Language Model-Inferred Knowledge Representation.

Computational drug repositioning, through predicting drug-disease associations (DDA), offers significant potential for discovering new drug indications. Current methods incorporate graph neural networks (GNN) on drug-disease heterogeneous networks to predict DDAs, achieving notable performances compared to traditional machine learning and matrix factorization approaches. However, these methods depend heavily on network topology, hampered by incomplete and noisy network data, and overlook the wealth of biomedical knowledge available. Correspondingly, large language models (LLMs) excel in graph search and relational reasoning, which can possibly enhance the integration of comprehensive biomedical knowledge into drug and disease profiles. In this study, we first investigate the contribution of LLM-inferred knowledge representation in drug repositioning and DDA prediction. A zero-shot prompting template was designed for LLM to extract high-quality knowledge descriptions for drug and disease entities, followed by embedding generation from language models to transform the discrete text to continual numerical representation. Then, we proposed LLM-DDA with three different model architectures (LLM-DDANode Feat, LLM-DDADual GNN, LLM-DDAGNN-AE) to investigate the best fusion mode for LLM-based embeddings. Extensive experiments on four DDA benchmarks show that, LLM-DDAGNN-AE achieved the optimal performance compared to 11 baselines with the overall relative improvement in AUPR of 23.22%, F1-Score of 17.20%, and precision of 25.35%. Meanwhile, selected case studies of involving Prednisone and Allergic Rhinitis highlighted the model's capability to identify reliable DDAs and knowledge descriptions, supported by existing literature. This study showcases the utility of LLMs in drug repositioning with its generality and applicability in other biomedical relation prediction tasks.

Tradeoff relations in open quantum dynamics via Robertson, Maccone–Pati, and Robertson–Schrödinger uncertainty relations

Abstract The Heisenberg uncertainty relation, together with Robertson’s generalisation, serves as a fundamental concept in quantum mechanics, showing that noncommutative pairs of observables cannot be measured precisely. In this study, we explore the Robertson-type uncertainty relations to demonstrate their effectiveness in establishing a series of thermodynamic uncertainty relations and quantum speed limits in open quantum dynamics. The derivation utilises a scaled continuous matrix product state representation that maps the time evolution of the quantum continuous measurement to the time evolution of the system and field. Specifically, we consider the Maccone–Pati uncertainty relation, a refinement of the Robertson uncertainty relation, to derive thermodynamic uncertainty relations and quantum speed limits. These newly derived relations, which use a state orthogonal to the initial state, yield bounds that are tighter than previously known bounds. Moreover, we consider the Robertson–Schrödinger uncertainty, which extends the Robertson uncertainty relation. Our findings not only reinforce the significance of the Robertson-type uncertainty relations, but also expand its applicability in identifying uncertainty relations in open quantum dynamics.

NeRF-OR: neural radiance fields for operating room scene reconstruction from sparse-view RGB-D videos.

RGB-D cameras in the operating room (OR) provide synchronized views of complex surgical scenes. Assimilation of this multi-view data into a unified representation allows for downstream tasks such as object detection and tracking, pose estimation, and action recognition. Neural radiance fields (NeRFs) can provide continuous representations of complex scenes with limited memory footprint. However, existing NeRF methods perform poorly in real-world OR settings, where a small set of cameras capture the room from entirely different vantage points. In this work, we propose NeRF-OR, a method for 3D reconstruction of dynamic surgical scenes in the OR. Where other methods for sparse-view datasets use either time-of-flight sensor depth or dense depth estimated from color images, NeRF-OR uses a combination of both. The depth estimations mitigate the missing values that occur in sensor depth images due to reflective materials and object boundaries. We propose to supervise with surface normals calculated from the estimated depths, because these are largely scale invariant. We fit NeRF-OR to static surgical scenes in the 4D-OR dataset and show that its representations are geometrically accurate, where state of the art collapses to sub-optimal solutions. Compared to earlier work, NeRF-OR grasps fine scene details while training 30 faster. Additionally, NeRF-OR can capture whole-surgery videos while synthesizing views at intermediate time values with an average PSNR of 24.86dB. Last, we find that our approach has merit in sparse-view settings beyond those in the OR, by benchmarking on the NVS-RGBD dataset that contains as few as three training views. NeRF-OR synthesizes images with a PSNR of 26.72dB, a 1.7% improvement over state of the art. Our results show that NeRF-OR allows for novel view synthesis with videos captured by a small number of cameras with entirely different vantage points, which is the typical camera setting in the OR. Code is available via: github.com/Beerend/NeRF-OR .

Data-Driven Radial Compressor Design Space Mapping

Abstract Estimates of turbomachinery performance trends inform system-level compromises during preliminary design. Existing empirical correlations for efficiency use limited experimental data, while analytical loss models require calibration to yield predictive results. From a set of 3708 radial compressor computations, this paper maps efficiency as a function of mean-line aerodynamics, and determines the governing loss mechanisms. An open-source turbomachinery design code creates annulus and blade geometry, then runs a Reynolds-averaged Navier–Stokes simulation for compressors sampled from the mean-line design space. Polynomial surface fits yield a continuous eight-dimensional representation of the design space for analysis, predicting efficiency with a root-mean-square error of 1.2% points. The results show a balance between surface dissipation in boundary layers and mixing loss due to casing separations sets optimum values for inlet Mach number, hub-to-tip ratio, de Haller number, and backsweep angle. Surface dissipation drives the effect of flow coefficient, with high surface areas at low values, and high velocities at high values. Compact compressor designs are achieved by increasing inlet Mach number, reducing hub-to-tip ratio, and minimizing the radial loading coefficient—all of which reduce efficiency approaching design space boundaries. An interactive web-based tool makes the results available to practising engineers, demonstrating large ensembles of automated designs and simulations as a higher-fidelity replacement for legacy empirical correlations in preliminary design.

Bridging auditory perception and natural language processing with semantically informed deep neural networks

Sound recognition is effortless for humans but poses a significant challenge for artificial hearing systems. Deep neural networks (DNNs), especially convolutional neural networks (CNNs), have recently surpassed traditional machine learning in sound classification. However, current DNNs map sounds to labels using binary categorical variables, neglecting the semantic relations between labels. Cognitive neuroscience research suggests that human listeners exploit such semantic information besides acoustic cues. Hence, our hypothesis is that incorporating semantic information improves DNN’s sound recognition performance, emulating human behaviour. In our approach, sound recognition is framed as a regression problem, with CNNs trained to map spectrograms to continuous semantic representations from NLP models (Word2Vec, BERT, and CLAP text encoder). Two DNN types were trained: semDNN with continuous embeddings and catDNN with categorical labels, both with a dataset extracted from a collection of 388,211 sounds enriched with semantic descriptions. Evaluations across four external datasets, confirmed the superiority of semantic labeling from semDNN compared to catDNN, preserving higher-level relations. Importantly, an analysis of human similarity ratings for natural sounds, showed that semDNN approximated human listener behaviour better than catDNN, other DNNs, and NLP models. Our work contributes to understanding the role of semantics in sound recognition, bridging the gap between artificial systems and human auditory perception.

A feature extension and reconstruction method with incremental learning capabilities under limited samples for intelligent diagnosis

Existing data-driven Intelligent Fault Diagnosis (IFD) methods often struggle with continuous learning and integrating new diagnostic knowledge. These methods necessitate a complete retraining process when new fault data emerges. Furthermore, collecting sufficient data for model training is impractical in real-world applications. This study proposes a Feature Extension and Reconstruction (FER) method for model incremental updating with limited samples. FER employs scalable and modular feature extractors for continuous representation learning of new fault modes. In addition, a domain mapping algorithm based on optimal transport is devised to leverage old classification nodes in aiding new nodes’ training, enhancing models’ generalization performance under limited samples. A feature reconstruction technique is also developed to compress the expanded multi-backbone model, eliminating redundant parameters and dimensions for adaptability in subsequent incremental tasks. Validated on simulated transmission systems and real planetary gearboxes, FER demonstrates a better stability-plasticity trade-off in incremental tasks with limited training samples, offering a novel solution for adaptive IFD model updates in sample-constrained scenarios.

Dynamic Graph Representation Learning via Coupling-Process Model.

Representation learning based on dynamic graphs has received a lot of attention in recent years due to its wide range of application scenarios. Although many discrete or continuous dynamic graph representation learning methods have been proposed, many of them ignore the role of edge types. Through the observation of dynamic graphs in the real world, it is found that the types of various edges are very different in nature. They are roughly divided into two categories according to the frequency of occurrence: evolutive edges that appear infrequently and interactive edges that appear frequently. For both types of edges, we propose a coupling-process model (DyCPM) to capture the dynamic mechanisms of them. The model not only generates low-dimensional embedding vectors of nodes, but also aggregates the structural information and temporal information of two kinds of edges. In particular, we design a neural network parameterized discrete process to depict the change law of the topology of evolutive edges and a neural network parameterized temporal point process (TPP) to characterize the temporal dynamic rule of interactive edges. More importantly, we propose a coupling mechanism to transfer the information of the two processes through a shared embedding matrix and finally generate an embedding matrix that aggregates the topology information and temporal information of the two kinds of edges for the dynamic link prediction task. We evaluate our model and several baselines on real datasets. The experimental results show that our model can better aggregate the topology information and temporal information of the two kinds of edges according to their properties and outperforms several state-of-the-art baselines in the performance of dynamic link prediction.

VQ-NeRF: Neural Reflectance Decomposition and Editing With Vector Quantization.

We propose VQ-NeRF, a two-branch neural network model that incorporates Vector Quantization (VQ) to decompose and edit reflectance fields in 3D scenes. Conventional neural reflectance fields use only continuous representations to model 3D scenes, despite the fact that objects are typically composed of discrete materials in reality. This lack of discretization can result in noisy material decomposition and complicated material editing. To address these limitations, our model consists of a continuous branch and a discrete branch. The continuous branch follows the conventional pipeline to predict decomposed materials, while the discrete branch uses the VQ mechanism to quantize continuous materials into individual ones. By discretizing the materials, our model can reduce noise in the decomposition process and generate a segmentation map of discrete materials. Specific materials can be easily selected for further editing by clicking on the corresponding area of the segmentation outcomes. Additionally, we propose a dropout-based VQ codeword ranking strategy to predict the number of materials in a scene, which reduces redundancy in the material segmentation process. To improve usability, we also develop an interactive interface to further assist material editing. We evaluate our model on both computer-generated and real-world scenes, demonstrating its superior performance. To the best of our knowledge, our model is the first to enable discrete material editing in 3D scenes.

In-Clinic and Natural Gait Observations master protocol (I-CAN-GO) to validate gait using a lumbar accelerometer

Traditional measurements of gait are typically performed in clinical or laboratory settings where functional assessments are used to collect episodic data, which may not reflect naturalistic gait and activity patterns. The emergence of digital health technologies has enabled reliable and continuous representation of gait and activity in free-living environments. To provide further evidence for naturalistic gait characterization, we designed a master protocol to validate and evaluate the performance of a method for measuring gait derived from a single lumbar-worn accelerometer with respect to reference methods. This evaluation included distinguishing between participants’ self-perceived different gait speed levels, and effects of different floor surfaces such as carpet and tile on walking performance, and performance under different bouts, speed, and duration of walking during a wide range of simulated daily activities. Using data from 20 healthy adult participants, we found different self-paced walking speeds and floor surface effects can be accurately characterized. Furthermore, we showed accurate representation of gait and activity during simulated daily living activities and longer bouts of outside walking. Participants in general found that the devices were comfortable. These results extend our previous validation of the method to more naturalistic setting and increases confidence of implementation at-home.