Model predicts composite structures assembly quality with input uncertainty.
problem Accurate prediction of dimensional deviations and residual stress in composite structures assembly.
method Neural Network Gaussian Process considering input uncertainty.
result NNGPIU model outperforms other methods for nonsmooth, nonlinear responses.
Learning theory for linear systems with compositional inputs.
problem Training linear system operators with unknown variables constrained to non-negativity and unity.
method Bayesian inversion method for inferring unknown variable from noisy linear system output.
result Quantified uncertainty in trained operator and convergence rates for various cases.
New framework interprets deep neural networks through input structure.
problem Limited understanding of how input structure, network parameters, and optimization algorithms work together.
method Introducing a novel theoretical framework based on the compositional structure of piecewise linear activation functions.
result Shows that input instances can be grouped based on their similarity in the internal representation of the neural network.
Estimates input from output of nonlinear systems using ANN.
problem Estimating unknown compositional input from system output.
method Artificial Neural Networks (ANNs) for nonlinear system inversion.
result ANNs can compete with optimal bounds for linear systems and demonstrate promising results for nonlinear systems.
Measures compositionality in machine learning representations.
problem Evaluating how compositional structure is reflected in learned representations.
method Measures compositionality by approximating true representation-producing models with composed primitives.
result Characterizes compositional structure in various settings.
New framework infers multiple classes per image for one-shot learning.
problem Inferring multiple classes per image in one-shot learning.
method Compositional embedding framework with joint training of embedding and composition/query functions.
result Compositional embedding models outperform existing methods on various datasets.
A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different datasets through model composition, enhance predictions of quantities of interest thr…
Generative model learns to compose images of objects from different distributions.
problem Capturing complex interactions between objects in scenes.
method Composition-by-Decomposition (CoDe) network.
result Model generates realistic composite images capturing interactions between input objects.
Deep learning can learn compositional functions more efficiently by breaking them into stages.
problem Understanding why deep learning performs better than shallow models in learning compositional functions.
method Analyzed learnability of compositional target functions using a three-layer fitting model trained with layer-wise spectral estimators.
result Learning compositional functions can be simplified by breaking them into stages, reducing the complexity of the learning problem.
IRNet improves material property prediction from composition and crystal structure.
problem Predicting material properties from composition and crystal structure.
method Deep residual regression network with individual residual learning.
result IRNet outperforms state-of-the-art machine learning approaches in predicting material properties.
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion is given by an averaged ordinary differential equation. We then demonstrate that…
New findings show disentangled latent representations are not enough for robust compositional generalization.
problem Deep learning models struggle with compositional generalization, especially in out-of-distribution samples.
method Investigated a 2D Gaussian generation task with fully disentangled inputs, then forced disentangled latent representations into full-dimensional output space.
result Forcing disentangled latent representations into full-dimensional output space enables robust compositional generalization.
Cosmos models scenes using neural encodings and symbolic attributes for compositional generalization.
problem Modeling scenes with high performance on unseen input scenes composed of known visual elements.
method Neurosymbolic grounding with neurosymbolic scene encodings and attention mechanisms.
result Establishes a new state-of-the-art for compositional generalization in world modeling.
Sublinearly structured DNNs achieve feature learning consistency for compositional functions.
problem Achieving feature-learning and prediction consistency in deep neural networks.
method Sublinearly structured DNNs
result Sublinearly structured DNNs match or surpass wide DNNs in prediction.
BoTier optimizes experiments by balancing multiple objectives hierarchically.
problem Balancing multiple competing objectives in scientific experiments.
method Composite objective that flexibly represents a hierarchy of preferences over outcomes and parameters.
result Demonstrates robust applicability across various use cases and seamless integration.
LMGPs extend GPs to handle mixed data, offering better accuracy and interpretability.
problem Handling mixed data types (quantitative and qualitative) in metamodeling.
method Introduce LMGPs that learn a latent manifold for qualitative inputs, using a low-rank linear map.
result LMGPs outperform existing methods in accuracy and versatility.
Adaptive MAB algorithms handle composite, anonymous feedback without reward interval knowledge.
problem Multi-armed bandit with composite and anonymous feedback, especially without reward interval size knowledge.
method Proposed adaptive algorithms for stochastic and adversarial cases, without reward interval knowledge.
result First algorithm for adversarial case handling non-oblivious adversary and unknown reward interval size.
We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map portions of each layer's input-space to the same output. In this way, deep models c…
Generative Neuro-Symbolic model learns from raw data with rich conceptual representations.
problem Learning rich, general-purpose conceptual representations from raw perceptual inputs.
method Generative Neuro-Symbolic (GNS) model combining symbolic and neural network approaches.
result Model learns from raw data and generalizes to 4 unique tasks.
Study shows how transformers learn to combine simple tasks into complex ones.
problem Understanding how transformers learn to perform complex tasks not seen during training.
method Controlled setting involving variable assignment and modular addition; partitioned training data analysis.
result Small transformers can generalize to unseen combinations of variables and numbers.
Study uses AI and ML to predict and optimize corrosion resistance of aluminum alloys.
problem Corrosion resistance of aluminum alloys in marine environments.
method Investigated two ML approaches: direct and inverse, using Random Forest, neural network, and Gaussian Process Regression.
result Gaussian Process Regression with hybrid kernel functions provided superior predictive performance.
Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet diverse examples. Under a probabilistic setting for discrete input spaces, we focus …
Enhances multi-fidelity modeling with DGPs for different input domains.
problem Improving prediction accuracy with multi-fidelity models using different input domains.
method Extends Deep Gaussian Processes (DGPs) to handle different input domains for high and low-fidelity models.
result Demonstrates improved performance on real-world physical problems.
Deep Gaussian Processes model functions on DAGs with partially observed data.
problem Reconstructing and inferring from partially observed functions on DAGs with noisy measurements.
method Place priors over functions on DAGs, theoretically study prior-collapse behavior, and offer a structured variational approximation.
result Almost-sure lower bounds on the preservation of input distinctions and interpretability of simulator hierarchies.
New active learning methods for Gaussian process improve predictive modeling of composite fuselage.
problem Improving predictive modeling of composite fuselage with limited training samples and uncertainties.
method Proposed two new active learning algorithms for Gaussian process considering uncertainties.
result The proposed approach realizes better prediction performance for automatic shape control of composite fuselage.
Transformer improves pop piano composition by incorporating beat-based structure.
problem Generating expressive pop piano compositions with coherent rhythmic structure.
method Improved data representation for Transformers, incorporating beat-bar-phrase structure.
result Composes pop piano music with better rhythmic structure than existing models.
This study ranks feature-block importance in multiblock neural networks.
problem Understanding feature contributions in multiblock neural networks.
method Three methods: composite, knock-in, and knock-out strategies.
result Each strategy has its merits for specific application scenarios.
Discover governing equations from data without specifying terms.
problem Discovering differential equations from data without predefined terms.
method Data-driven approach using genetic programming and automatic differentiation.
result Calibrated differential equations from various solutions of a differential equation.
Deep neural networks achieve optimal classification rates in high dimensions.
problem Binary classification on high-dimensional data with specific smoothness and composition properties.
method Proved optimal convergence rate for ReLU DNNs trained with hinge loss.
result ReLU DNNs achieve optimal classification rates up to a logarithmic factor.
Proposes TDNs for learning complex video structures.
problem Complex temporal dependencies in sequential data, especially videos.
method Temporal Dependency Networks (TDNs) using graph representations and graph convolutions.
result Efficiently learns complex semantic structures of video data.
CB-GLNs learn video data's complex dependencies via graph representation.
problem Capturing complex dependency structures in sequential data like videos.
method Represent video data as a graph, find compositional dependencies via graph-cut and message passing.
result CB-GLNs efficiently learn video data's semantic compositional structure.
CPVs enable efficient learning and generalization of complex tasks.
problem Learning and generalizing complex tasks efficiently.
method Compositional plan vectors (CPVs) for efficient task composition and generalization.
result CPVs enable efficient learning and generalization of complex tasks without additional supervision.
Kernel models learn low-dimensional predictive subspaces from input data.
problem Learning effective feature transformations in kernel models.
method Study of a compositional kernel ridge regression model.
result Global minimizers of the objective function identify the subspace with high probability.
Transformers learn to generalize unseen tasks by composing self-attention layers.
problem How Transformers generalize to unseen, out-of-distribution tasks.
method Examined synthetic examples and pretrained LLMs, focusing on induction heads and latent subspace.
result Transformers can learn hidden rules for unseen tasks by composing self-attention layers, achieving OOD generalization.
Framework generates pop song melodies and piano accompaniment.
problem Creating high-quality pop songs with automated systems.
method Unified strategy using three models: harmony alternation, melody generation, and melody integration.
result Generated melodies rated significantly higher than those from LSTM, and accompaniment comparable to Band in a Box.
Adversarial weight perturbations can inject backdoors into trained neural models.
problem Security risk of using publicly available trained models due to backdoors.
method Extended adversarial perturbations to model weights, using a composite loss and projected gradient descent.
result Adversarial weight perturbations can be successfully injected with very small changes, exposing security risks across various tasks.
SNNs can represent complex functions efficiently.
problem Understanding the representational power of SNNs.
method Viewed as sequence-to-sequence processors, analyzed using spike train functions.
result SNNs have the universal representation property for certain functions.
Proposes a method for clearer counterfactual explanations of deep networks.
problem Unclear explanations from current counterfactual methods.
method Gradual construction of explanations through masking and composition steps.
result Produces human-friendly, interpretable explanations with fewer modifications.
Study develops efficient algorithm for probabilistic penetration response of composite plates.
problem Probabilistic modeling of discrete structural response, focusing on binary events like buckling.
method Adaptive domain-based decomposition, sparse grid sampling, assumption of monotonic behavior.
result Efficient computational framework for probabilistic penetration response of composite plates.
Deep-HGP uses Bayesian nonparametric approach for complex data regression.
problem Complex data regression with compositional structures.
method Deep Gaussian processes with a squared-exponential kernel, data-driven lengthscale parameters.
result Posterior distribution optimally recovers unknown true regression curve in terms of quadratic loss.
Large language models can't efficiently reason conditionally in a distribution-free setting.
problem Impossibility of conditional PAC-efficient reasoning in large language models.
method Proof of impossibility in a distribution-free setting for non-atomic input spaces.
result Any algorithm achieving conditional PAC efficiency must defer to the expert model with high probability.
Slot Attention extracts object-centric representations from images.
problem Learning distributed representations that don't capture natural scene composition.
method Slot Attention module interfaces with CNN outputs to produce task-dependent abstract slots.
result Slot Attention enables generalization to unseen compositions.
PNNs model aleatoric uncertainty in scientific machine learning with high accuracy.
problem Aleatoric uncertainty in scientific systems with unequal variance.
method Developed a probabilistic distance metric to optimize PNN architecture and used it in material science applications.
result PNNs yield remarkably accurate output mean estimates and high correlation in predicted intervals.
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched t…
Deep networks partition input space into regions with complex affine mappings.
problem Understanding the geometry and complexity of deep neural networks.
method Analyzed deep networks as max-affine spline operators and power diagrams.
result Composition of deep networks results in a progressively subdivided power diagram.
Simplifies efficient estimation via automatic differentiation and probabilistic programming.
problem Constructing efficient estimators for complex statistical models.
method Automatic differentiation applied to statistical functionals, avoiding the need to derive efficient influence functions.
result Users can generate efficient estimators with minimal code, simplifying the process for non-experts.
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function …
The paper develops a neural network method for estimating drift functions of diffusion processes from discrete observations.
problem Nonparametric estimation of drift function for diffusion processes from high-frequency discrete observations.
method Neural network-based estimator for drift function estimation.
result Derives a non-asymptotic convergence rate for the neural network estimator.