Likelihood-based generative models are a promising resource to detect out-of-distribution (OOD) inputs which could compromise the robustness or reliability of a machine learning system. However, likelihoods derived from such models have been shown to be problematic for detecting certain types of inputs that significant…
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48 results for “input complexity”
We investigate the complexity of logistic regression models which is defined by counting the number of indistinguishable distributions that the model can represent (Balasubramanian, 1997). We find that the complexity of logistic models with binary inputs does not only depend on the number of parameters but also on the …
Effect of Various Regularizers on Model Complexities of Neural Networks in Presence of Input Noisecs.LG
Deep neural networks are over-parameterized, which implies that the number of parameters are much larger than the number of samples used to train the network. Even in such a regime deep architectures do not overfit. This phenomenon is an active area of research and many theories have been proposed trying to understand …
This thesis investigates unsupervised time series representation learning for sequence prediction problems, i.e. generating nice-looking input samples given a previous history, for high dimensional input sequences by decoupling the static input representation from the recurrent sequence representation. We introduce thr…
This paper studies the generalization error of invariant classifiers. In particular, we consider the common scenario where the classification task is invariant to certain transformations of the input, and that the classifier is constructed (or learned) to be invariant to these transformations. Our approach relies on fa…
Aims to optimize complex multivariate systems with constraints.
problem Optimizing force-field systems in physics with large-scale simulations.
method Combines machine learning and experimental design to find feasible input combinations.
result Locates multiple good regions in the input space.
TOQ-Nets learn to recognize complex temporal events with varying objects and sequences.
problem Recognizing complex relational-temporal events with varying numbers of objects and sequence lengths.
method Neuro-symbolic networks with reasoning layers for finite-domain quantification over objects and time.
result TOQ-Nets can generalize to scenarios with more objects than training data and temporal warpings.
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.
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input variables of the model. When the statistics of the output event are known, these input …
Easy conditions found for simplifying complex systems.
problem Linearizing complex two-input systems.
method Endogenous dynamic feedback with a dimension of at most two.
result Necessary and sufficient conditions for linearizability.
Previous studies have found that an adversary attacker can often infer unintended input information from intermediate-layer features. We study the possibility of preventing such adversarial inference, yet without too much accuracy degradation. We propose a generic method to revise the neural network to boost the challe…
The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M `pseudo-inputs', thereby reducing complexity from N^3 to NM^2. One limitation of th…
Neural networks learn to mimic brain neurons with two-input activation functions, improving performance and robustness.
problem Training neural networks to mimic the complex interactions of brain neurons.
method Developed a network-in-network architecture with two-input activation functions, optimized hyperparameters, and compared to conventional ReLU networks.
result Two-input activation functions can learn soft XOR functions, improving network performance and robustness.
Poor economies not only produce less; they typically produce things that involve fewer inputs and fewer intermediate steps. Yet the supply chains of poor countries face more frequent disruptions---delivery failures, faulty parts, delays, power outages, theft, government failures---that systematically thwart the product…
Diffusion models learn simple statistics before complex ones, revealing a sample complexity exponent.
problem Understanding the learning dynamics of diffusion models.
method Empirical observations and theoretical analysis of diffusion models and denoisers.
result Diffusion models learn simple statistics (pair-wise correlations) at linear sample complexity, while higher-order statistics (e.g., fourth cumulant) require cubic sample complexity.
Lower bounds and upper bounds on sample complexity for identifying linear dynamical systems.
problem Identifying an unknown linear dynamical system with limited data.
method Sample complexity lower and upper bounds, persistent excitation condition, active learning algorithm.
result Lower and upper bounds share the same dependency on key problem parameters.
We consider reinforcement learning in input-driven environments, where an exogenous, stochastic input process affects the dynamics of the system. Input processes arise in many applications, including queuing systems, robotics control with disturbances, and object tracking. Since the state dynamics and rewards depend on…
Transformers show strengths and weaknesses in complexity analysis.
problem Understanding the strengths and limitations of attention layers in transformers.
method Analysis of representation power through complexity parameters and task-specific constructions.
result Transformers can solve sparse averaging tasks with logarithmic complexity, but triple detection tasks require linear complexity.
In practice it is often found that large over-parameterized neural networks generalize better than their smaller counterparts, an observation that appears to conflict with classical notions of function complexity, which typically favor smaller models. In this work, we investigate this tension between complexity and gen…
Study Bernstein-Gelfand-Gelfand complexes on Lipschitz domains, computing cohomology and applying to elasticity models.
problem Cohomology of BGG complexes on bounded Lipschitz domains.
method Computes cohomology of conformal deformation and Hessian complexes in Sobolev spaces, allowing multiple input complexes.
result Establishes conformal Korn inequality and proposes generalizations of continuum models with microstructures.
ASADG improves data generation for accurate surrogate modeling of complex physical problems.
problem Training surrogate models on imbalanced data leads to inaccurate predictions.
method ASADG iteratively adds input data to improve the representation of the response manifold.
result ASADG generates more representative input data compared to LHS for better model accuracy.
New method uses spherical harmonics to simplify learning single-index models.
problem Learning single-index models with unknown one-dimensional projections.
method Proposes using spherical harmonics instead of Hermite polynomials to capture rotational symmetry.
result Characterizes the complexity of learning single-index models under arbitrary spherically symmetric input distributions.
New method distinguishes predictive distribution estimators in high-dimensional inputs.
problem Difficulty in evaluating predictive distributions for high-dimensional inputs.
method Introduces dyadic sampling to focus on predictive distributions associated with pairs of inputs.
result Demonstrates efficient distinction of predictive distribution estimators in high-dimensional examples.
ICA reveals deep learning's feature learning mechanisms from non-Gaussian data.
problem Understanding feature learning from non-Gaussian inputs in deep neural networks.
method Investigates ICA and SGD on synthetic and real data.
result FastICA requires samples for single non-Gaussian direction recovery, while SGD outperforms and optimised SGD reaches .
We consider a set of probabilistic functions of some input variables as a representation of the inputs. We present bounds on how informative a representation is about input data. We extend these bounds to hierarchical representations so that we can quantify the contribution of each layer towards capturing the informati…
Neural networks benefit from intermediate representations, reducing sample complexity.
problem Understanding how neural networks leverage intermediate representations for hierarchical learning.
method Fixed, randomly initialized neural network as a representation function, compared with raw inputs and other trainable networks.
result Neural representations can achieve improved sample complexities compared to raw inputs, especially for low-rank polynomials.
Complex nonlinear models such as deep neural network (DNNs) have become an important tool for image classification, speech recognition, natural language processing, and many other fields of application. These models however lack transparency due to their complex nonlinear structure and to the complex data distributions…
CVNNs improve performance in tasks with complex-valued inputs.
problem Improving performance in tasks with complex-valued inputs.
method Analyze the approximation properties of complex-valued neural networks (CVNNs).
result Quantitative approximation bounds for CVNNs, showing error scales as .
Methods for combining predictions from different models in a supervised learning setting must somehow estimate/predict the quality of a model's predictions at unknown future inputs. Many of these methods (often implicitly) make the assumption that the test inputs are identical to the training inputs, which is seldom re…
We present a novel method for exact hierarchical sparse polynomial regression. Our regressor is that degree polynomial which depends on at most inputs, counting at most monomial terms, which minimizes the sum of the squares of its prediction errors. The previous hierarchical sparse specification aligns w…
Multioutput Gaussian Processes with Functional Data: A Study on Coastal Flood Hazard Assessmentstat.ML
A new model predicts spatially varying inland flooding from time-varying inputs.
problem Ignoring time series and spatial correlations in flood models leads to inaccurate predictions.
method Introduced a multioutput Gaussian process model with separable kernels for functional inputs and spatial locations.
result The model provides accurate predictions of spatially varying inland flooding with minimal computational time.
Deep neural networks with more parameters and FLOPs have higher capacity and generalize better to diverse domains. But to be deployed on edge devices, the model's complexity has to be constrained due to limited compute resource. In this work, we propose a method to improve the model capacity without increasing inferenc…
Sparse-Input Neural Networks for High-dimensional Nonparametric Regression and Classificationstat.ME
Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate functions, they generally require a large number of training observations to obtai…
Centroid Transformers reduce memory and computation by summarizing inputs into centroids.
problem Efficiently summarize inputs with reduced memory and computation.
method Generalizes self-attention to map N inputs to M centroids (M ≤ N), reducing complexity.
result Centroid Transformers reduce memory and computation while preserving key information.
Self-attention prefers sparse functions of input sequences, reducing sample complexity.
problem Understanding the inductive biases of self-attention in modeling long-range dependencies.
method Theoretical analysis and synthetic experiments to probe sample complexity of learning sparse functions with Transformers.
result Bounded-norm Transformer networks can represent sparse functions of the input sequence with logarithmic sample complexity.
When simulating a complex stochastic system, the behavior of output response depends on input parameters estimated from finite real-world data, and the finiteness of data brings input uncertainty into the system. The quantification of the impact of input uncertainty on output response has been extensively studied. Most…
New findings show learning deeper neural networks is hard even with Gaussian inputs and non-degenerate weights.
problem The computational complexity of learning neural networks, especially deeper ones.
method Smoothed analysis framework and local pseudorandom generators.
result Learning depth-3 ReLU networks under Gaussian input distribution is hard even if weight matrices are non-degenerate.
Aux-Net model handles dynamic systems with inconsistent inputs.
problem Inconsistent or unreliable input data in real-world scenarios.
method Aux-Net uses a weighted ensemble of classifiers and online gradient descent.
result Aux-Net provides scalable and agile online learning for dynamic systems.
Algorithm classifies surface homeomorphisms with polynomial time complexity.
problem Classifying surface homeomorphisms with polynomial time complexity.
method Algorithm to compute curve distances and decide Nielsen-Thurston types.
result Polynomial time classification of surface homeomorphisms.
New algorithm adds Hessian regularization to improve neural network robustness.
problem Improving neural network robustness against adversarial attacks.
method Proposes an efficient algorithm to train neural networks with Hessian operator-norm regularization.
result Hessian operator-norm regularization increases neural network robustness over input gradient regularization.
We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor between the output and a non-linear transformation of the input, based on score …
Generative models can approximate high-dimensional data from lower dimensions without needing a latent dimension equal to or greater than the data's intrinsic dimension.
problem Theoretical limitations on the latent dimension required for generative models to approximate high-dimensional data distributions.
method Inspired by space-filling curves, the work demonstrates that generative networks can approximate distributions on -dimensional manifolds from inputs of any arbitrary dimension, even lower than .
result Generative models can approximate high-dimensional data distributions from lower-dimensional inputs without needing a latent dimension equal to or greater than the data's intrinsic dimension.
A new method warps inputs to learn nonstationary kernels efficiently.
problem Learning nonstationary patterns in data with varying smoothness.
method Sparse spectrum Gaussian processes with input warping as conditional Gaussian measures.
result Efficient learning of nonstationary patterns with fewer parameters.
This work investigates how gradient-based learning performs with structured data, revealing issues and improvements.
problem Gradient-based learning under structured data, particularly with a spiked covariance structure.
method Investigates the effect of a spiked covariance structure on gradient-based feature learning and proposes weight normalization.
result Gradient-based dynamics may fail to recover the true direction in anisotropic settings, but weight normalization can improve performance.
For any ReLU network there is a representation in which the sum of the absolute values of the weights into each node is exactly , and the input layer variables are multiplied by a value coinciding with the total variation of the path weights. Implications are given for Gaussian complexity, Rademacher complexity,…
We propose reinforcement learning on simple networks consisting of random connections of spiking neurons (both recurrent and feed-forward) that can learn complex tasks with very little trainable parameters. Such sparse and randomly interconnected recurrent spiking networks exhibit highly non-linear dynamics that transf…
Complex embeddings handle non-metric proximity data better than traditional methods.
problem Proximities not always metric or inner product-based, causing convergence issues.
method Proposes complex-valued embeddings for non-vectorial data.
result Complex embeddings outperform traditional techniques on benchmarks.
In this paper, we present a new explainability formalism designed to shed light on how each input variable of a test set impacts the predictions of machine learning models. Hence, we propose a group explainability formalism for trained machine learning decision rules, based on their response to the variability of the i…