Last-layer approximation improves UQ performance without sacrificing computational efficiency.
problem Epistemic uncertainty quantification for deep neural networks.
method Comparison of full-network and last-layer linearization using theoretical and empirical approaches.
result Last-layer approximation yields comparable UQ performance with improved computational efficiency.
Bayesian approach learns invariances from data alone, but last layer approximation is not always sufficient.
problem Learning invariances in neural networks using only training data.
method Bayesian marginal likelihood for last layer, custom optimisation routine, new lower bound.
result Partial success on standard benchmarks and medical imaging dataset, failure on CIFAR10.
Proposes DAK model for improved GP computations.
problem Challenges in high-dimensional GP layers in DKL.
method Additive structure and induced prior approximation for GP units.
result Outperforms state-of-the-art DKL methods in regression and classification.
New method improves BLL models for complex datasets.
problem Limited expressive capacity of Gaussian priors in BLL models.
method Combines diffusion techniques and implicit priors for variational learning.
result Enhanced predictive accuracy and uncertainty quantification.
New conditions ensure deep neural networks can approximate any function on non-Euclidean spaces.
problem Understanding how to modify neural network architectures to approximate functions on non-Euclidean spaces.
method Developed conditions for feature and readout maps that preserve universal approximation capabilities.
result Modified architectures can deterministically approximate any classifier on non-Euclidean spaces.
CLAPS improves conformal regression by adaptively scaling interval widths based on last-layer Laplace uncertainty.
problem Lack of adaptive interval width scaling in conformal regression for heterogeneous inputs.
method CLAPS uses heteroscedastic last-layer Laplace uncertainty to adaptively scale interval widths, combining aleatoric and epistemic uncertainties.
result CLAPS provides competitive interval efficiency with nominal-level coverage, reducing to aleatoric scaling as epistemic uncertainty decreases.
Data augmentation methods improve worst-case model performance.
problem Ensuring fair predictions across subpopulations in large models.
method Linear last layer retraining with data augmentation techniques.
result Optimal worst-group accuracy achieved for Gaussian latent representation distribution.
Last layer retraining improves robustness to spurious correlations without high computational costs.
problem Neural networks can rely on spurious features like backgrounds for predictions.
method Simple last layer retraining on large models.
result Last layer retraining matches or outperforms state-of-the-art approaches on spurious correlation benchmarks.
Optimizes neural networks' last layer with closed-form solutions.
problem Optimizing neural networks' last layer with stochastic gradient descent.
method Adapting closed-form last layer optimization for stochastic gradient descent, alternating between backbone and last layer updates.
result The method converges to optimal solutions and outperforms standard SGD and Adam in regression tasks.
Improved uncertainty estimation in neural networks with VBLL.
problem Improving uncertainty estimation in neural networks.
method Deterministic variational formulation for training Bayesian last layer neural networks.
result Improves predictive accuracy, calibration, and out-of-distribution detection.
The paper provides approximation guarantees for neural networks trained with gradient flow.
problem Approximating neural networks trained with gradient flow in continuous L 2 ( S d − 1 ) L_2(\mathbb{S}^{d-1}) L 2 ( S d − 1 ) -norm. method NTK argument for non-convex second but last layer, under-parametrized regime.
result Gradient flow convergence guarantees for neural networks under Sobolev smoothness assumptions.
Freezing intermediate layers reduces DNN inference latency.
problem High latency in deep learning inference due to computationally expensive models.
method Introduce approximate caching at each intermediate layer to avoid running all layers for many inference requests.
result Reduces the number of effective layers by half for 91.58% of CIFAR-10 requests.
This research shows loss weighting remains effective in last layer retraining despite model overparameterization.
problem Overcoming biases in machine learning models at scale.
method Theoretical and practical exploration of last layer retraining in an overparameterized setting.
result Loss weighting is still effective in last layer retraining, but weights must account for model overparameterization.
For any positive integer k k k , there exist neural networks with Θ ( k 3 ) Θ(k^3) Θ ( k 3 ) layers, Θ ( 1 ) Θ(1) Θ ( 1 ) nodes per layer, and Θ ( 1 ) Θ(1) Θ ( 1 ) distinct parameters which can not be approximated by networks with O ( k ) \mathcal{O}(k) O ( k ) layers unless they are exponentially large --- they must possess Ω ( 2 k ) Ω(2^k) Ω ( 2 k ) nodes. This result is proved here for a class o…
Neural networks can approximate any continuous function with a single hidden layer.
problem Approximating any continuous function using neural networks.
method Direct algebraic proof and explicit quantification of hidden units required.
result Explicit bounds on the number of hidden units needed for approximation.
New method calibrates LLMs for safety-critical tasks with scalable Bayesian inference.
problem Overconfidence in LLMs after fine-tuning for specific tasks.
method Orthogonalized Low-Rank Adapters (PoLAR) with variational Bayesian inference.
result Scalable and well-calibrated uncertainty estimation for LLMs.
Our paper explains deep neural collapse in multiple layers.
problem Understanding deep neural collapse in multi-layered neural networks.
method Generalized unconstrained features model for deep networks.
result Deep unconstrained features model exhibits deep neural collapse.
A novel gradient boosting method trains neural networks sequentially for improved performance.
problem Training neural networks efficiently and adapting to different classification speeds.
method Sequential training of neural networks with gradient boosting, where the network is trained in T steps, and a portion of the network is trained at each step to approximate pseudo-residuals.
result The proposed method achieves competitive generalization performance and allows for dynamic adaptation of the model's complexity.
Wide neural networks' last hidden layers split into groups of redundant neurons.
problem Understanding why wide neural networks generalize well despite overfitting.
method Analyzed the last hidden layer representations of various convolutional neural networks.
result Wide hidden layers split into groups of redundant neurons, which help generalize.
Deep neural networks converge to Gaussian mixtures as layer width increases.
problem Understanding the distribution of outputs from deep neural networks.
method Proof and experiments with a simple model showing the convergence of neural network outputs to Gaussian mixtures.
result Neural networks converge to Gaussian mixtures as the width of the last hidden layer increases.
We analyze neural collapse in neural networks, showing that features collapse to vertices of a Simplex ETF.
problem Understanding and optimizing the features learned in the last layer of neural networks during training.
method Simplified unconstrained feature model, studying the global optimization landscape of cross-entropy loss with weight decay.
result The global minimizers of the loss are Simplex ETFs, and other critical points are strict saddles with negative curvature.
Bayesian neural network models improve uncertainty quantification in multivariate regression.
problem Uncertainty quantification in multivariate regression models with heteroscedastic noise.
method Proposes Bayesian Last Layer neural network models and EM algorithms for parameter learning.
result Capable of disentangling aleatoric and epistemic uncertainty.
One of the main challenges of deep learning methods is the choice of an appropriate training strategy. In particular, additional steps, such as unsupervised pre-training, have been shown to greatly improve the performances of deep structures. In this article, we propose an extra training step, called post-training, whi…
Bayesian optimization improved with variational last layer training.
problem Bayesian optimization performance on complex input correlations.
method Connecting variational Bayesian last layer training to exact conditioning in Gaussian processes, developing an efficient online training algorithm.
result VBLL networks significantly outperform GPs and match well-tuned GPs on benchmark tasks.
A new algorithm learns from raw feature vectors using deep neural networks and UCB for exploration.
problem Learning from raw feature vectors with unknown reward functions.
method Deep representation learning followed by UCB exploration in the last layer.
result Achieves i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) finite-time regret. RAD improves robustness to domain annotation noise without explicit domain annotations.
problem Robustness to domain annotation noise in training data.
method Regularized Annotation of Domains (RAD) for last layer retraining.
result RAD outperforms state-of-the-art methods even with 5% noise in training data.
NESTA accelerates neural networks by compressing Hamming weights.
problem Efficiently computing convolution layers in deep neural networks.
method NESTA reformats convolutions into 3 i m e s 3 3 imes 3 3 im es 3 batches and uses Hamming Weight Compressors to process each batch, approximating partial sums and adding residuals. result Significantly speeds up convolution computations with reduced energy consumption.
Posterior refinement improves sample efficiency in Bayesian neural networks.
problem Bayesian neural networks suffer from poor predictive performance due to inaccurate posterior approximations.
method Propose refining Gaussian approximate posteriors with normalizing flows to improve predictive distributions.
result Posterior refinement yields competitive predictive performance with minimal computational overhead.
Deep random feature models are analyzed for their performance with exact asymptotic expressions.
problem Understanding the performance of deep random feature models.
method Established a novel universality result and used the convex Gaussian Min-Max theorem.
result Exact asymptotic expressions for the performance of deep random feature models are derived.
ELF simplifies normalizing flows, making them more efficient and universal.
problem Computational inefficiency of normalizing flows.
method ELF introduces a simple, one-layer network with closed-form Lipschitz constants, combining the ease of residual flows with the performance of autoregressive flows.
result ELF is a provably universal density approximator, more efficient computationally and parameter-wise.
Bayesian neural networks approximate Student-t processes in the infinite-width limit.
problem Modeling uncertainty in neural networks with greater flexibility.
method Extending asymptotic properties of Gaussian processes to Student-t processes in the infinite-width limit of BNNs.
result Posterior BNNs converge to Student-t processes in the infinite-width limit.
New method isolates epistemic uncertainty in diffusion models, improving plausibility scores.
problem Uncertainty quantification in diffusion models, especially epistemic uncertainty.
method Fisher information based approach using FLARE (Fisher-Laplace Randomized Estimator).
result FLARE improves uncertainty estimation in synthetic time-series generation tasks.
Study on SGD for overparameterized neural networks, focusing on convergence rates.
problem Understanding convergence rates of SGD in overparameterized two-layer neural networks.
method Combines NTK approximation with RKHS analysis to explore SGD dynamics.
result Established sharp convergence rates for SGD in overparameterized two-layer neural networks.
Deep reinforcement learning (DRL) methods such as the Deep Q-Network (DQN) have achieved state-of-the-art results in a variety of challenging, high-dimensional domains. This success is mainly attributed to the power of deep neural networks to learn rich domain representations for approximating the value function or pol…
Normalization methods play an important role in enhancing the performance of deep learning while their theoretical understandings have been limited. To theoretically elucidate the effectiveness of normalization, we quantify the geometry of the parameter space determined by the Fisher information matrix (FIM), which als…
Randomized neural networks improve optimal stopping problems efficiently.
problem Approximating solutions to optimal stopping problems in high dimensions.
method Randomly generated neural networks with only the last layer trained.
result Our methods outperform state-of-the-art approaches in computation time and accuracy.
Study clarifies Bayesian generalization error in CBM for 3-layered linear neural networks.
problem Understanding the generalization error in concept bottleneck models.
method Mathematical analysis of Bayesian generalization error and free energy in CBM for 3-layered linear neural networks.
result CBM significantly alters the parameter region and Bayesian generalization error compared to standard models.
LLEB uses a learned prior to quantify neural network uncertainty.
problem Quantifying uncertainty in neural network predictions.
method LLEB uses a learnable prior as a normalizing flow to maximize the evidence lower bound.
result LLEB performs on par with existing approaches in uncertainty quantification.
The monotonic linear interpolation in deep networks often leads to plateaus, revealing biases in optimization.
problem Plateaus in the optimization landscape of deep networks during monotonic linear interpolation.
method Investigated monotonic linear interpolation on deep neural networks, focusing on biases in weights and biases.
result Interpolating weights and biases differently can lead to significant differences in loss and accuracy, revealing biases in optimization.
Deep linear networks exhibit collapsing features and classifiers across datasets.
problem Understanding the collapse of features and classifiers in deep linear networks.
method Theoretical and empirical analysis of deep linear networks with MSE and CE losses.
result Deep linear networks exhibit NC properties, collapsing features and classifiers to orthogonal vectors.
Bayesian approach fixes overconfidence in ReLU networks, even slightly.
problem Overconfidence in ReLU networks far from training data.
method Theoretical analysis of approximate Gaussian distributions on ReLU weights, and empirical validation.
result Even a simplistic Bayesian approximation fixes overconfidence issues.
Researchers analyze the geometric and statistical properties of transformer model representations.
problem Understanding the semantic structure of large transformer models across various data types.
method Characterization of geometric and statistical properties through analysis of intrinsic dimension and neighbor composition.
result The semantic information of the dataset is better expressed at the end of the first peak in transformer models.
This paper establishes risk convergence and asymptotic weight matrix alignment --- a form of implicit regularization --- of gradient flow and gradient descent when applied to deep linear networks on linearly separable data. In more detail, for gradient flow applied to strictly decreasing loss functions (with similar re…
This review tackles long horizon forecasting in time series analysis using deep learning.
problem Long horizon forecasting in time series analysis.
method Incorporates deep learning techniques such as trend, seasonality, Fourier and wavelet transforms, and various model architectures.
result LHF is an error propagation problem, with models like xLSTM and Triformer showing better performance.
Binary representation is desirable for its memory efficiency, computation speed and robustness. In this paper, we propose adjustable bounded rectifiers to learn binary representations for deep neural networks. While hard constraining representations across layers to be binary makes training unreasonably difficult, we s…
STRIC detects anomalies in time series by analyzing residual signals.
problem Anomaly detection in multivariate time series data.
method End-to-end differentiable neural network architecture with Sequential Probability Ratio Test on residuals.
result STRIC outperforms state-of-the-art methods on multiple benchmarks.
This paper extends neural collapse to regression problems, revealing key features and structures.
problem Understanding the structure learned by deep neural networks in regression tasks.
method Established Neural Regression Collapse (NRC) across different models, analyzing feature and weight alignments.
result Deep neural regression models exhibit a collapsed feature space, aligning with target dimensions and covariances.
This work justifies neural collapse under MSE loss and analyzes the optimization landscape.
problem Understanding neural collapse in deep neural networks under MSE loss.
method Global landscape analysis of vanilla nonconvex MSE loss.
result The only global minimizers are neural collapse solutions.