Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We describe and study in these models a decomposition of predictive uncertainty into its epistemic and aleatoric components. First, we show how such a decomposition ar…
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48 results for “activation decomposition”
Depth uncertainty networks don't improve with bias correction, contrary to expectations.
problem Improving performance in active learning with overparameterised models like NNs.
method Depth uncertainty networks, compared to underparameterised models, show no improvement in performance with bias correction.
result Depth uncertainty networks do not improve with bias correction, unlike underparameterised models.
The paper examines topological features of ReLU networks and their relation to decision boundaries and training loss.
problem Understanding the topological structure of ReLU neural network activation patterns.
method Polytope decomposition of feature space, Fiedler partition of dual graph, homology computation of cellular decomposition.
result The Fiedler partition of the dual graph correlates with decision boundaries in binary classification tasks, and similar patterns in training loss and polyhedral cell-count emerge in regression tasks.
The paper explores tensor decompositions in deep learning models.
problem Compressing parameter space and creating richer representations.
method Tensor decompositions applied to deep learning models.
result Tensor methods can yield richer adaptive representations of complex data.
The measurement and analysis of Electrodermal Activity (EDA) offers applications in diverse areas ranging from market research, to seizure detection, to human stress analysis. Unfortunately, the analysis of EDA signals is made difficult by the superposition of numerous components which can obscure the signal informatio…
Study on identifiability of deep polynomial neural networks.
problem Understanding when polynomial neural networks can be uniquely identified.
method Comprehensive analysis including various architectures, using tensor decompositions and Kruskal-type theorems.
result Identifiability conditions for deep PNNs, including layer width and activation degree constraints.
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in practice, and no extensive comparisons have been made between available methods. Previo…
Extends Alòs' formula to Barndorff-Nielsen and Shephard model.
problem Modeling call option prices in a stochastic volatility model.
method Uses Alòs' decomposition formula and Ito's formula for an Ornstein-Uhlenbeck model with infinite jumps.
result First Alòs type decomposition formula for Barndorff-Nielsen and Shephard model.
MSD removes dequantization bottleneck in LLM inference by approximating high-precision activations.
problem Dequantization bottleneck in LLM inference on modern AI accelerators.
method MSD decomposes high-precision activations into multiple low-precision components for direct multiplication with quantized weights.
result MSD avoids INT8-to-BF16 weight conversion, reducing dequantization cycles and HBM traffic.
This work is devoted to elaboration on the idea to use block term decomposition for group data analysis and to raise the possibility of modelling group activity with (Lr, 1) and Tucker blocks. A new generalization of block tensor decomposition was considered in application to group data analysis. Suggested approach was…
A new mutual information lower bound for multimodal regression active learning.
problem Lack of effective acquisition functions for multimodal regression active learning.
method Introduces a Two-Index framework for separating epistemic and aleatoric sources of uncertainty, deriving MI-LB as a closed-form approximation.
result MI-LB consistently outperforms baselines on multimodal regression tasks.
The digital revolution of the banking system with evolving European regulations have pushed the major banking actors to innovate by a newly use of their clients' digital information. Given highly sparse client activities, we propose CPOPT-Net, an algorithm that combines the CP canonical tensor decomposition, a multidim…
In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a sm…
Polynomial time algorithm learns depth-2 neural networks with ReLU activations.
problem Learning depth-2 neural networks with non-zero bias terms and general ReLU activations.
method Robust tensor decomposition of Hermite expansions.
result Polynomial time and sample efficient learning of depth-2 networks with ReLU activations.
Improved neural network verification using Lagrangian decomposition and parallel algorithms.
problem Formally proving input-output properties of neural networks efficiently.
method Novel bounding and branching algorithms based on Lagrangian Decomposition and activation-based heuristics.
result Significant reduction in verification times, up to 50x faster on adversarial robustness properties.
We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors , hidden units with weights and output , i.e., $y=\sum_{i=1}^r σ( \boldsymbol w_i…
Study examines money flow network among firms' accounts in a Japanese region.
problem Understanding the relationship between money flow and economic activities of firms.
method Employed exhaustive bank transfer data, network statistics, Hodge decomposition, and non-negative matrix factorization.
result Identified a 'walnut' structure with core and upstream/downstream components, correlated with economic activities.
We propose a variable decomposition algorithm -greedy block coordinate descent (GBCD)- in order to make dense Gaussian process regression practical for large scale problems. GBCD breaks a large scale optimization into a series of small sub-problems. The challenge in variable decomposition algorithms is the identificati…
Unified model explains volatility memory in stocks and forex.
problem Understanding the components of volatility memory in financial markets.
method Developed a three-dimensional decomposition of volatility memory into level, shape, and tempo.
result Unified model shows that volatility memory is state-dependent, with different gates prevailing in equities and forex.
Improved SSD for faster and more accurate goodness-of-fit tests and model learning.
problem Optimal slicing directions for SSD are computationally expensive and sub-optimal.
method Relaxed optimal slicing requirement, active sub-space construction, spectral decomposition.
result 14-80x speed-up in goodness-of-fit tests compared to gradient-based alternatives.
BayPOD-AL learns reduced-order models from high-fidelity data efficiently.
problem Capturing dynamics of complex systems with large training datasets.
method Bayesian active learning based on uncertainty-aware POD.
result BayPOD-AL reduces computational cost and improves model accuracy.
Study shows trained neural networks can overfit without bias or variance issues.
problem Understanding overfitting in trained two-layer ReLU networks.
method Analysis of gradient flow in the neural tangent kernel regime, decomposition of excess risk.
result Trained networks can overfit benignly without bias or variance issues.
Optimized DMD for fast atmospheric chemistry forecasting.
problem Forecasting global atmospheric chemistry dynamics efficiently.
method Optimized Dynamic Mode Decomposition (DMD) for reduced order modeling.
result Significant improvement in computational speed and interpretability.
Decomposition of Uncertainty in Bayesian Deep Learning for Efficient and Risk-sensitive Learningstat.ML
Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns in the data. We show how to extract and decompose uncertainty into epistemic and…
A new method tackles Bayesian inverse problems with complex PDEs.
problem Bayesian inverse problems with expensive forward model evaluations and high-dimensional priors.
method Domain-decomposed variational auto-encoder Markov chain Monte Carlo (DD-VAE-MCMC) method.
result The method efficiently solves Bayesian inverse problems in parallel and low-dimensional latent spaces.
New dynamic allocation methods for multi-armed bandit models.
problem Dynamic allocation problems in multi-armed bandit models.
method New types of dynamic allocation problems and proofs for Gittins index decomposition.
result New proofs for Gittins index decomposition and related results.
New CSC model extracts EEG signals with low noise sensitivity.
problem Analyzing noisy EEG signals during anesthesia.
method Kruskal CSC model using Kruskal decomposition for low-rank tensor activations.
result TC-FISTA efficiently extracts robust, sparse, and interpretable EEG encodings.
This paper introduces a new measure to identify model redundancy in compressed CNNs.
problem Identifying remaining model redundancy in compressed CNNs.
method Developed a statistical formulation of CNNs and compressed CNNs via tensor decomposition, revealing discrepancies in sample complexity and model redundancy.
result Introduced a new model redundancy measure, the ratio, for compressed CNNs.
S2KAN integrates symbolic primitives into neural network activations for improved interpretability.
problem Training activations in KANs often lack symbolic fidelity, leading to unintelligible models.
method Softly Symbolified Kolmogorov-Arnold Networks (S2KAN) integrates symbolic primitives into training with learnable gates and a Minimum Description Length objective.
result S2KAN discovers interpretable forms when symbolic terms suffice, gracefully degrading to dense splines when necessary.
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the resid…
A new protocol corrects confounding effects to measure alignment-induced activation shifts accurately.
problem Confounding effects in measuring alignment-induced activation shifts using naive methods.
method Introduces a four-variant decomposition to separate alignment shift from template effects.
result Correctly measures alignment-induced activation shifts, recovering behaviorally active subspace.
SAP: Corrective Machine Unlearning with Scaled Activation Projection for Label Noise Robustnesscs.LG
SAP corrects model for label noise by identifying and removing noisy samples.
problem Label corruption degrades model performance; acquiring perfect labels is costly.
method SAP uses SVD to identify and project model weights onto a clean activation space.
result SAP improves model generalization by up to 6% on CIFAR dataset with 25% synthetic corruption.
New algorithms accelerate solving nonlinear matrix decomposition with ReLU.
problem Nonlinear matrix decomposition with ReLU function.
method Two new algorithms: A-NMD and 3B-NMD, with adaptive extrapolation and block parametrization.
result Effective algorithms accelerate solving ReLU-NMD problems.
ADMM algorithm solves nonlinear matrix decompositions efficiently.
problem Nonlinear matrix decompositions for various applications.
method Alternating Direction Method of Multipliers (ADMM) for nonlinear matrix factorization.
result The method efficiently solves diverse nonlinear matrix decompositions.
Wide neural networks learn features under P, identifying weights and decomposing support.
problem Feature learning in wide neural networks under P.
method Proving mean-field limit, characterizing identifiability, sparse-dictionary decomposition, and feature-learning-error decomposition.
result The triple identifies the natural learning cell of the architecture-data pair .
The paper analyzes deep ReLU CNNs' approximation properties in 2D space.
problem Establishing approximation properties for deep ReLU CNNs.
method Analysis based on decomposition theorem for convolutional kernels, properties of ReLU activation, and connections with one-hidden-layer ReLU NNs.
result Universal approximation theorem for deep ReLU CNNs with classic structure.
We study deep neural networks with polynomial activations, particularly their expressive power. For a fixed architecture and activation degree, a polynomial neural network defines an algebraic map from weights to polynomials. The image of this map is the functional space associated to the network, and it is an irreduci…
Paper reconstructs training data from a single gradient query.
problem Privacy threats in federated learning due to model gradients.
method Provable attack using tensor decomposition.
result Training samples can be fully reconstructed from a single gradient query.
A Structural Matrix Autoregressive Model for the Joint Dynamics of Volume, Volatility, and Returnsecon.EM
Proposes a Structural Matrix Autoregressive model for joint analysis of asset returns, realized volatility, and trading volume.
problem Joint analysis of asset returns, realized volatility, and trading volume
method Structural Matrix Autoregressive model
result Volatility is primary driver of trading activity, with informational shocks incorporated through price variability.
Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of the observed higher order input moments. However, in many domains, additional inv…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many solutions. However, it may be shown that sufficiently sparse solutions may be identi…
New method estimates covariance in multi-view data with better accuracy and uncertainty.
problem Estimating covariance in multi-view data with shared and view-specific latent factors.
method Spectral decompositions and conditional conjugate priors for factor loadings and residual variances.
result Proves favorable asymptotic properties and excellent performance in simulations and real data.
Efficient Bitwidth Search optimizes neural network quantization for better performance.
problem Finding optimal bitwidth for weights and activations of each layer efficiently.
method EBS algorithm reusing meta weights and binary decomposition for efficient mixed precision convolution.
result Mixed precision QNN outperforms uniform bitwidth and other techniques on CIFAR10 and ImageNet.
Hierarchical Spatio-Channel Clustering for Efficient Model Compression in Medical Image Analysiscs.CV
This paper proposes a new method to compress CNNs for medical image analysis, improving efficiency and accuracy.
problem Large memory and computational requirements of CNNs in resource-constrained environments.
method Hierarchical spatio-channel low-rank compression framework that partitions feature maps into spatial regions and groups channels according to co-activation patterns within each region.
result The proposed method achieves significant FLOP reduction, inference speed-up, and improved classification accuracy compared to existing methods.
FeDXL tackles federated learning for X-risk optimization.
problem Optimizing a family of X-risks with federated learning, where existing algorithms are not applicable.
method Active-passive decomposition framework, federated averaging and merging, novel theoretical analysis.
result FeDXL algorithms for linear and nonlinear are developed, with established complexities and improved performance.
IGSD separates task-specific content channels in transformer components by comparing activation replacement with zero ablation.
problem Mechanistic interpretability of transformer components
method IGSD: paired-intervention framework for comparing activation replacement with zero ablation
result IGSD identifies an early-layer content channel in transformer components that standard importance methods underestimate.
Efficient algorithms for monophonic halfspaces in graphs simplify learning and compression.
problem Learning and compressing monophonic halfspaces in graphs.
method 2-satisfiability based decomposition theorem, efficient algorithms for various learning problems.
result Achieved efficient and nearly optimal algorithms for various learning problems.
Methods based on vector embeddings of knowledge graphs have been actively pursued as a promising approach to knowledge graph completion.However, embedding models generate storage-inefficient representations, particularly when the number of entities and relations, and the dimensionality of the real-valued embedding vect…