This paper presents a new mechanism for producing sanitized statistical summaries that achieve \emph{differential privacy}, called the \emph{K-Norm Gradient} Mechanism, or KNG. This new approach maintains the strong flexibility of the exponential mechanism, while achieving the powerful utility performance of objective …
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48 results for “gradient mechanism”
New method learns population dynamics from snapshots, outperforming existing models.
problem Capturing periodic and other dynamical properties of population dynamics.
method Wasserstein Lagrangian Mechanics (WLM) for learning second-order dynamics from observed marginals.
result WLM outperforms existing methods across various dynamics, including vortex dynamics, embryonic development, and flocking.
The Impact of Local Geometry and Batch Size on Stochastic Gradient Descent for Nonconvex Problemsmath.OC
In several experimental reports on nonconvex optimization problems in machine learning, stochastic gradient descent (SGD) was observed to prefer minimizers with flat basins in comparison to more deterministic methods, yet there is very little rigorous understanding of this phenomenon. In fact, the lack of such work has…
A new privacy-preserving mechanism for shapes on manifolds.
problem Privacy-preserving sanitization of shapes on curved manifolds.
method Developed a K-norm gradient mechanism on Riemannian manifolds.
result The K-norm gradient mechanism offers better control over sensitivity than the Laplace mechanism on positively curved manifolds.
On the role of geometry in statistical mechanics and thermodynamics I: Geometric perspectivecond-mat.stat-mech
The paper provides a geometric framework for understanding non-equilibrium thermodynamics.
problem Unclear geometric structure of GENERIC in non-equilibrium thermodynamics.
method Cotangent lifts of dynamics, splitting into holonomic and vertical representatives, and formulation within contact geometry.
result Physical meaning and explicit formulation of the second law of thermodynamics within evolution equations.
Adaptive model learns from time series data with changing distributions.
problem Predicting time series data under distribution shift.
method Formulates distribution shift as weighted empirical risk minimization. Uses a gradient-based learning method for a forgetting mechanism.
result Proposes an efficient method for adaptive time series prediction.
New algorithm maintains privacy while improving model performance in selective release.
problem Privacy degradation and slow convergence in DPSGD.
method Differentially Private Selective Release based on Clipped Gradients (DPSR-CG).
result Maintains strict privacy guarantees while achieving exceptional model performance.
This paper explains how low-precision arithmetic causes loss spikes in deep learning models.
problem Loss spikes during long-term training of deep neural networks.
method Analyzes the impact of floating-point precision limits on gradient updates and feature means.
result Numerical Feature Inflation (NFI) explains loss spikes and rapid parameter norm growth.
Improved algorithm finds second-order stationary points in non-convex optimization.
problem Minimizing non-convex objectives while preserving training data privacy.
method SpiderBoost framework with two gradient oracles: precise and less precise.
result Improved rates for finding second-order stationary points.
Formulates mechanics for probability distributions on statistical manifold.
problem Formulating mechanics for probability distributions on statistical manifold.
method Information-geometric formulation of Classical Mechanics on statistical manifold, using dually-flat connection and Hilbert bundle structure.
result Provides coherent formalism for Lagrangian and Hamiltonian mechanics on statistical bundle.
New DP mechanisms improve ML privacy-utility-computational tradeoffs.
problem Improving privacy in machine learning with multiple passes over data.
method Formalized DP for adaptive streams, extended matrix factorization techniques, Fourier-transform-based mechanism.
result Substantial improvements in privacy-utility-computational tradeoffs over previous methods.
Gradient Gating improves deep GNNs by modulating message passing updates.
problem Oversmoothing and performance degradation in deep GNNs.
method Gradient gating mechanism for multi-rate message passing.
result G framework alleviates oversmoothing and achieves state-of-the-art performance.
Unified framework for analyzing gradient flows of measures with exponential decay of entropy.
problem Analyzing exponential decay of entropy functionals in gradient flows of measures.
method Characterization of global exponential decay behaviors using Hellinger-Kantorovich geometry, shape-mass decomposition, and Polyak-Łojasiewicz-type inequalities.
result Unified theoretical framework for gradient flows with complete analysis of exponential decay behaviors.
Ghost mechanism explains abrupt learning in RNNs, revealing constraints on optimization landscapes.
problem Understanding abrupt learning in recurrent neural networks (RNNs) trained on working memory tasks.
method Introducing the ghost mechanism, a process driven by saddle-node bifurcations, to analyze and model abrupt learning.
result A critical learning rate scales as an inverse power law with the timescale of computation, leading to vanishing and oscillatory gradients.
Quantum systems learn like machine learning models, influenced by dissipation.
problem Understanding how quantum systems learn and evolve.
method Hydrodynamical formulation of quantum mechanics, gradient descent model, empirical demonstration.
result Quantum systems follow a disrupted gradient descent model, influenced by dissipation.
New framework improves model robustness by focusing on stable relations across environments.
problem Standard supervised learning fails under data distribution shift.
method Gradient-based learning framework derived from the principle of independent causal mechanisms (ICM).
result Models generalize well to unseen scenarios, ignoring unstable relations.
The paper tackles extrapolation in generative models by enforcing independence of mechanisms.
problem How to make generative models extrapolate to new, unseen environments?
method Developed a theoretical framework for independence of mechanisms, demonstrated on toy examples and real-world data.
result Extrapolation capabilities of generative models can be improved by enforcing independence of mechanisms explicitly during training.
Analyzes self-attention in recurrent networks, proving it mitigates vanishing gradients.
problem Vanishing gradients in recurrent networks when capturing long-term dependencies.
method Formal analysis of self-attention's effect on gradient propagation, proposing a relevancy screening mechanism.
result Self-attention mitigates vanishing gradients in recurrent networks, providing guarantees.
A method uses CG to create efficient channels for ideal observers.
problem Computational intractability of ideal observers for high-dimensional image data.
method Conjugate gradient (CG) method for constructing efficient channels.
result CG-based channels approximate IO and HO performance efficiently.
On the Interpretability of Regularisation for Neural Networks Through Model Gradient Similaritystat.ML
New framework monitors neural network training and reveals regularisation mechanisms.
problem Overfitting in neural networks and the need for explicit regularizers.
method Model Gradient Similarity (MGS) framework to measure and monitor regularisation.
result Explicit regularizers increase Model Gradient Similarity (MGS).
EoS selectively shapes learning, affecting some groups more than others.
problem EoS affects learning differently across the data distribution.
method Branching intervention to enter or exit EoS regime, controlled perturbation to isolate mechanisms.
result EoS redistributes learning, amplifying progress on some groups and suppressing others.
Modelling long-term dependencies is a challenge for recurrent neural networks. This is primarily due to the fact that gradients vanish during training, as the sequence length increases. Gradients can be attenuated by transition operators and are attenuated or dropped by activation functions. Canonical architectures lik…
Investigates the benefits of multi-head attention in Transformers, deriving convergence and generalization guarantees.
problem Underexplored dynamics of multi-head attention in Transformer training and generalization.
method Derives convergence and generalization guarantees for gradient-descent training of a multi-head self-attention model.
result Establishes conditions for initialization that ensure multi-head attention's realizability.
Paper identifies how neural networks learn features.
problem Understanding how neural networks automatically select features.
method Deep Neural Feature Ansatz, implementing average gradient outer product.
result Recursive Feature Machines achieve state-of-the-art performance.
New method improves combinatorial optimization by overcoming inefficient sampling.
problem Wandering in contours: sampling similar solutions for long periods.
method Reheated Gradient-based Discrete Sampling with a novel mechanism.
result Superior performance across various combinatorial optimization problems.
This work develops sampling methods for differential privacy using SHK geometry.
problem Approximating sampling for the exponential mechanism in differential privacy.
method Develops perturbation theory for SHK gradient flows and applies to differential privacy.
result Derives time-dependent Pure-DP guarantees and Approximate-DP certificates.
New method for efficient matrix completion with nonignorable missing data.
problem Nonignorable missing data in matrix completion.
method Nuclear norm regularized U-statistic loss function and accelerated proximal gradient algorithm.
result Near minimax optimal statistical convergence rate for nonignorable missing data.
Adaptive sampling method solves constrained and composite optimization problems.
problem Solving constrained optimization problems with stochastic objectives and deterministic constraints.
method Proximal gradient method with adaptive sampling to improve gradient approximation quality.
result Convergence results established for both strongly convex and general convex objectives.
AdaDPIGU improves privacy in deep learning by adaptively clipping and pruning gradients.
problem Privacy in deep learning models, especially in high-dimensional settings.
method Importance-based gradient updates, adaptive clipping, differentially private SGD.
result AdaDPIGU achieves high accuracy while maintaining privacy, outperforming non-private models.
Transformers learn causal structure through gradient descent on self-attention mechanisms.
problem Understanding how transformers learn causal structure during training.
method In-context learning task and simplified two-layer transformer model.
result Gradient descent on a simplified transformer learns to encode latent causal graphs.
Data is continuously generated by modern data sources, and a recent challenge in machine learning has been to develop techniques that perform well in an incremental (streaming) setting. In this paper, we investigate the problem of private machine learning, where as common in practice, the data is not given at once, but…
Deep learning is built on the foundational guarantee that gradient descent on an objective function converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, that exhibit multiple interacting losses. The behavior of gradient-based methods in games is not well under…
New mechanisms from primate vision improve neural network robustness.
problem Demonstrating robust neural networks to small adversarial perturbations.
method Investigated two biologically plausible mechanisms: non-uniform retina sampling and receptive field diversity.
result Non-uniform retina sampling and receptive field diversity improve adversarial robustness.
EXODUS improves training of SNNs by stabilizing gradients and reducing complexity.
problem Training SNNs using BPTT is time-consuming and numerically unstable.
method EXODUS modifies SLAYER to account for neuron reset and uses IFT for correct gradient calculation, eliminating manual scaling.
result EXODUS achieves comparable or better performance than SLAYER, especially in tasks with temporal features.
Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence analysis for a general class of adaptive gradient methods including AMSGrad, RMSPr…
The paper identifies patterns in language model weights used for memorizing paragraphs.
problem Locating the specific mechanisms and weights used by language models to memorize paragraphs.
method Examined gradients and attention patterns in language models to identify memorized paragraphs.
result Gradients of memorized paragraphs have a distinguishable spatial pattern, and localized attention heads are involved in paragraph memorization.
Solving Statistical Mechanics Using Variational Autoregressive Networkscond-mat.stat-mech
We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and exact calculation of normalized probability of configurations. It computes variation…
Modern neural networks are often augmented with an attention mechanism, which tells the network where to focus within the input. We propose in this paper a new framework for sparse and structured attention, building upon a smoothed max operator. We show that the gradient of this operator defines a mapping from real val…
The paper introduces a differentially private method for optimization on Riemannian manifolds.
problem Differential privacy in optimization constrained to Riemannian manifolds.
method Adding Gaussian noise to the Riemannian gradient on the tangent space, with privacy and utility guarantees.
result Privacy and utility guarantees for differentially private Riemannian optimization.
Gradient descent optimization improved by circuit perspective.
problem Efficient training of large AI systems.
method Utilizing circuit perspective for mechanistic interpretability.
result Designing a curriculum for efficient learning.
AGOP mechanism explains deep neural collapse in neural networks.
problem Explaining the rigid structure of data representations in deep neural networks.
method Introducing AGOP and Deep RFM to demonstrate DNC.
result AGOP mechanism causes deep neural collapse in neural networks.
SAD-DPSGD improves model performance on imbalanced medical datasets like HAM10000.
problem Data leakage and imbalanced distribution in medical image classification datasets.
method SAD-DPSGD uses a linear decaying mechanism for noise and clipping thresholds to enhance performance.
result SAD-DPSGD outperforms Auto-DPSGD on HAM10000, improving accuracy by 2.15%.
Paper introduces proof-of-learning to verify ML model training.
problem No mechanism to prove ML model training parameters were obtained through optimization.
method Inspired by proof-of-work and verified computations, introduces proof-of-learning mechanism.
result Proves model training parameters were obtained through optimization with minimal adversary work.
Method identifies root causes of anomalies in causal processes.
problem Identifying root causes of anomalies in causal processes.
method Noisy functional causal model, Bayesian learning, gradient-based attribution.
result Proposes efficient method to compute anomaly attribution scores.
This paper proposes a communication-efficient deep anomaly detection framework for industrial IoT.
problem Accurately detecting anomalies in time-series data from edge devices in industrial IoT.
method A federated learning-based approach with an Attention Mechanism-based Convolutional Neural Network-Long Short Term Memory (AMCNN-LSTM) model and gradient compression.
result The proposed framework accurately and timely detects anomalies with reduced communication overhead.
Global singularities propagate in magnetic mechanical systems on Riemannian manifolds.
problem Propagation of singularities in magnetic mechanical systems.
method Combines reduction from magnetic to Riemannian systems, analysis of reparameterized flows, and regularization techniques.
result Invariant singular set under generalized gradient flow dynamics.
New learned optimizers outperform baselines by incorporating known and novel mechanisms.
problem Understanding how learned optimizers outperform traditional ones.
method Careful analysis and visualization of learned optimizers trained on various tasks.
result Learned optimizers incorporate known techniques like momentum and gradient clipping, as well as new forms of learning rate adaptation.
New method makes reinforcement learning robust to heavy-tailed rewards.
problem Heavy-tailed rewards cause statistical outliers in reinforcement learning.
method Dynamic gradient clipping in TD learning and NAC.
result Provably robust TD and NAC achieve optimal sample complexities.