We study alignment in linear neural networks and its relation to gradient descent.
problem Understanding alignment in linear neural networks and its impact on training.
method Defined alignment for fully connected networks, analyzed alignment under gradient descent, and compared gradient descent to projected gradient descent for layer-constrained networks.
result Gradient descent can converge linearly to a global minimum when alignment is invariant, and alignment is impossible with large datasets in layer-constrained networks.
PGD-trained models have a preferential direction in their gradients, which improves robustness.
problem Mathematical lack of clarity in the direction of preferential gradient alignment after adversarial training.
method Proposed a novel definition of preferential direction and evaluated it using a metric based on GANs.
result PGD-trained models have higher alignment with the proposed preferential direction than baseline models.
A function that optimally aligns a timelike vector field with its gradients
problem Finding a time function that aligns a timelike vector field with its gradients
method Introducing a functional that penalizes null gradients and minimizes misalignment
result Proving the existence of a unique alignment time function under suitable conditions
SGD's training dynamics align with Hessian and gradient spectra in high-dimensional classification tasks.
problem Understanding the spectra of Hessian and gradient matrices in high-dimensional classification tasks.
method Rigorous analysis of SGD dynamics and spectra of Hessian and gradient matrices.
result SGD trajectory and emergent outlier eigenspaces align with a common low-dimensional subspace in multi-class high-dimensional mixtures and neural networks.
Multi-subject fMRI data analysis is an interesting and challenging problem in human brain decoding studies. The inherent anatomical and functional variability across subjects make it necessary to do both anatomical and functional alignment before classification analysis. Besides, when it comes to big data, time complex…
GENIE balances domain-invariant feature learning and gradient alignment for improved DG performance.
problem Domain Generalization (DG) overfitting to domain-specific features
method GENIE (Generalization-ENhancing Iterative Equalizer) optimizer
result Prevents a small subset of parameters from dominating optimization, promoting domain-invariant feature learning
GALA adapts learning rates online by aligning gradients, improving deep learning model performance.
problem Fine-tuning learning rates for deep learning models requires extensive grid search.
method GALA dynamically adjusts learning rates by tracking gradient alignment and local curvature.
result GALA produces a flexible, adaptive learning rate schedule that increases when gradients align.
DFA trains deep networks by aligning weights then memorizing data.
problem Understanding why DFA works for some networks but not others.
method Two-step learning process: alignment followed by memorization.
result DFA aligns weights to maximize gradient alignment, breaking degeneracy.
For a standard convolutional neural network, optimizing over the input pixels to maximize the score of some target class will generally produce a grainy-looking version of the original image. However, Santurkar et al. (2019) demonstrated that for adversarially-trained neural networks, this optimization produces images …
LoRA-One uses one-step full gradient to align adapters for efficient large model fine-tuning.
problem Fine-tuning large language models efficiently and accurately.
method Properly initializing LoRA adapters using the one-step full gradient and incorporating preconditioners.
result LoRA-One achieves significant empirical improvements over existing methods.
Unified approach to domain generalization by aligning gradients and Hessians.
problem Developing models that generalize well across unseen domains.
method Moment Alignment, extending transfer measure to DG, aligning derivatives across domains.
result Moment Alignment unifies gradient and Hessian matching approaches, improving generalizability.
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…
We present label gradient alignment, a novel algorithm for semi-supervised learning which imputes labels for the unlabeled data and trains on the imputed labels. We define a semantically meaningful distance metric on the input space by mapping a point (x, y) to the gradient of the model at (x, y). We then formulate an …
New research shows input-gradients can be manipulated without changing model's core function, challenging their use for model interpretation.
problem Current methods for model interpretability using input-gradients are flawed due to their arbitrary manipulability.
method Investigated by reinterpreting logits as unnormalized log-densities, proposing novel approximations for score-matching.
result Improving alignment between implicit density model and data distribution enhances gradient structure and explanatory power.
This work shows how exploiting gradient alignment can improve distributed and federated learning performance.
problem Misalignment of gradients across clients in distributed and federated learning.
method Utilizing implicit regularization through a novel GradAlign algorithm that induces gradient alignment with large mini-batches.
result Improvements in test accuracies and generalization performance.
Early alignment in neural networks leads to sparse representations but hinders convergence.
problem The implicit bias of gradient descent during early training phases.
method Quantitative description of early alignment phase in small initialisation, one hidden layer networks.
result Early alignment induces a sparse representation but also hinders convergence to global minima.
Hessian alignment improves OOD generalization in deep learning.
problem Improving deep learning models' ability to generalize to out-of-distribution data.
method Analyzed Hessian and gradient alignment for domain generalization using recent OOD theory.
result Hessian alignment methods achieve promising performance on various OOD benchmarks.
Training avoids edge of stability by aligning Jacobian matrices.
problem Training neural networks on the edge of stability causes inaccuracies.
method Used an exponential Euler solver to prevent entering the edge of stability.
result Alignment of Jacobian matrices causes sharpness increase in Hessian.
New metric m-coherence measures gradient alignment during training, revealing surprising memorization patterns.
problem Measuring and understanding the alignment of per-example gradients during training.
method Introducing m-coherence as a metric to study gradient alignment, showing its advantages over existing metrics. result Training with random labels leads to high m-coherence, indicating common patterns even when generalization is not possible. Proposes a new method for better explaining neural network decisions.
problem Challenges in explaining neural network decisions due to base-point choice.
method Introduces tangentially aligned integrated gradients to maximize explanation tangential alignment.
result Optimal base-point maximizes explanation tangential alignment, leading to more accurate interpretations.
Transformer models align words through attention weights, closely approximating Optimal Transport.
problem Understanding the internal mechanism of transformer models in language processing.
method Empirical evidence and theoretical analysis of attention weights and their relation to Optimal Transport.
result Transformer models can simulate gradient descent on the dual of entropy-regularized OT problem, providing a theoretical foundation for token alignment.
The paper addresses rigid alignment of noisy patches, providing a polynomial time algorithm and convergence conditions.
problem Finding a rigid alignment of overlapping local views (patches) that minimizes alignment error in a noisy setting.
method Characterizes non-degeneracy based on kernel and positivity of a matrix, provides polynomial time algorithm for testing non-degeneracy, and uses Riemannian gradient descent for alignment.
result The algorithm converges locally linearly to a non-degenerate perfect alignment under certain conditions.
Unsupervised domain adaptation aims to transfer and adapt knowledge learned from a labeled source domain to an unlabeled target domain. Key components of unsupervised domain adaptation include: (a) maximizing performance on the target, and (b) aligning the source and target domains. Traditionally, these tasks have eith…
Cohen et al. (2021) show GD trajectories align on a bifurcation diagram.
problem Understanding the Edge of Stability (EoS) phenomenon in gradient descent.
method Empirical studies and rigorous mathematical proofs for two-layer networks and single-neuron networks.
result GD trajectories align on a specific bifurcation diagram independent of initialization.
Gradient descent aligns neural feature matrices with pre-activation tangent features.
problem Understanding neural feature learning mechanisms.
method Analytical proof of alignment between weight matrices and pre-activation tangent features.
result Derivative alignment occurs almost surely in high-dimensional settings.
New algorithm shows neural networks can learn without full backpropagation.
problem Stochastic gradient descent with backpropagation is non-biologically plausible.
method Random and fixed backpropagation weights in a feedback alignment algorithm.
result Error converges to zero exponentially fast in overparameterized networks.
New framework aligns latent representations over-the-air using intelligent metasurfaces.
problem Heterogeneous transmitter-receiver models produce misaligned latent representations in semantic communication.
method Intelligent metasurfaces (SIM) emulate supervised and zero-shot semantic aligners directly in the wave domain.
result SIMs achieve up to 90% task accuracy in high SNR regimes, robust to low SNR.
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.
The backpropagation algorithm has long been the canonical training method for neural networks. Modern paradigms are implicitly optimized for it, and numerous guidelines exist to ensure its proper use. Recently, synthetic gradients methods -where the error gradient is only roughly approximated - have garnered interest. …
New method aligns diffusion models for inference-time properties without retraining.
problem Aligning pre-trained diffusion models for desired inference-time properties.
method Variationally stable Doob's matching for provable guidance estimation.
result Consistent estimator of guidance with non-asymptotic convergence guarantees.
EAGC boosts GCD by regulating gradient entanglement, improving known and novel category separability.
problem Gradient entanglement distorts supervised gradients and overlaps known and novel class representations.
method EAGC uses AGA and EEP to align and project gradients, reducing entanglement and overlap.
result EAGC consistently boosts GCD performance, setting new state-of-the-art results.
New method prevents RLHF alignment collapse by accounting for policy's influence on reward model updates.
problem Iterative RLHF leads to alignment collapse where policies exploit RM's blind spots.
method Foresighted policy optimization (FPO) restores missing steering term via regularization.
result FPO prevents alignment collapse on LLM alignment pipelines using Llama-3.2-1B.
Study improves understanding and performance of FA learning rules in neural networks.
problem Lack of theoretical understanding and limited applications of Feedback Alignment (FA) methods.
method Introduces a unified framework linking synaptic weight changes to implicit regularization, providing convergence conditions and empirical evidence.
result Better alignment can enhance FA performance on complex multi-class tasks.
A new principle for optimizer selection improves training speed and performance.
problem Finding the best optimizer hyperparameters for faster training.
method Formulate optimizer selection as maximizing the expected drop rate in loss, treating gradients and updates as signals and an optimizer as a causal filter.
result Greedy optimizer selection yields stable and effective momentum rules.
The paper analyzes how noise geometry influences the performance of SGD in machine learning.
problem Understanding how noise geometry affects the performance of stochastic gradient descent.
method Developed two metrics to quantify noise alignment strength and analyzed their effects on loss and subspace projection dynamics.
result Noise geometry can be used to guarantee alignment under certain conditions, aiding SGD's ability to escape from sharp minima.
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two kernels, data kernel and class indicator kernel. The problem is to find a subspace to …
FRA-Attack improves adversarial transferability for closed-source MLLMs by aligning visual focus across models.
problem Improving adversarial transferability for closed-source MLLMs, especially with high accuracy.
method Unified frequency-domain regularization approach: high-pass DCT objective for feature alignment and Frequency-domain Gradient Regularization (FGR) for gradient optimization.
result FRA-Attack achieves superior cross-model transferability, especially on GPT-5.4, Claude-Opus-4.6, and Gemini-3-flash.
Hölder-DPO aligns models robustly with noisy human feedback.
problem No existing alignment methods can handle severe label noise.
method Proposes Hölder-DPO, a principled alignment loss with provable redescending property.
result Hölder-DPO enables scalable human feedback valuation and improves model alignment.
Paper proposes MDAT to stabilize domain alignment in label-scarce settings.
problem Stable and comprehensive domain alignment in label-scarce settings.
method Max-margin Domain-Adversarial Training (MDAT) with Adversarial Reconstruction Network (ARN).
result MDAT stabilizes gradient reversing and achieves strong robustness to hyper-parameters.
Geometric approach for unsupervised word embedding alignment.
problem Learning alignment between word embeddings of source and target languages.
method Formulates alignment as domain adaptation on the manifold of doubly stochastic matrices, employing Riemannian conjugate gradient algorithm.
result Empirically outperforms state-of-the-art methods on bilingual lexicon induction tasks.
SGD updates align with a low-rank subspace but do not lead to further loss reduction.
problem Understanding the training dynamics of deep neural networks, particularly the role of the dominant subspace.
method Exploring whether neural networks can be trained within the dominant subspace of the loss Hessian.
result SGD updates, when projected onto the dominant subspace, do not decrease the training loss further, suggesting spurious alignment.
SpecGD mitigates misalignment in phase retrieval models with anisotropic inputs.
problem Misalignment during gradient descent in phase retrieval models with anisotropic inputs.
method Spectral gradient descent modifies gradient updates to preserve directional information and remove spike amplification.
result SpecGD removes spike amplification, leading to stable alignment and accelerated noise contraction.
New learning rules for wide neural networks without backpropagation.
problem Training wide neural networks efficiently and without backpropagation.
method Input-weight alignment driven by gradient descent in the NTK regime.
result Biologically-motivated learning rules equivalent to backpropagation in wide networks.
Let (MN,g,e−fdv) be a complete smooth metric measure space with ∞-Bakry-Émery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation \begin{align*} \displaystyle \Big(Δ_f - \frac{\partial}{\partial t}\Big) u(x,t) +q(x,t)u^α…
Gradient descent reshapes the function space of neural networks.
problem Understanding how feature learning affects the function space of neural networks.
method Characterized the evolution of the feature space during training using a two-layer neural network.
result Gradient descent induces a data-adaptive deformation that selectively enhances signal-aligned directions.
Gradient descent trains both layers of a ReLU network to fit a linear model.
problem Training dynamics of a ReLU network to fit a linear target function.
method Jointly training both layers of a one-hidden-layer ReLU network in a realizable setting with Gaussian inputs and labels.
result Gradient descent from a small random initialization converges to a global minimizer at a linear rate with optimal sample complexity.
The paper explores how symmetries and noise in SGD influence parameter dynamics.
problem Understanding the dynamics of parameter updates in SGD with symmetries.
method Proved the existence of noise equilibria and showed their role in balancing gradient noise.
result Gradient noise creates a systematic motion of parameters to a unique fixed point, called noise equilibria.
Feedback alignment methods need to be evaluated for accuracy and gradient cosine similarity.
problem Evaluating feedback alignment methods
method Proposed diagnostic evaluation protocol
result Identified silent failures in standard reporting pair