Bias Mitigation

Spectral bias, the tendency of neural networks to learn low-frequency features first, is a well-known issue with many training algorithms for physics-informed neural networks (PINNs). To overcome this issue, we propose IFeF-PINN, an algorithm for iterative training of PINNs with Fourier-enhanced features. The key idea is to enrich the latent space using high-frequency components through Random Fourier Features. This creates a two-stage training problem: (i) estimate a basis in the feature space, and (ii) perform regression to determine the coefficients of the enhanced basis functions. For an underlying linear model, it is shown that the latter problem is convex, and we prove that the iterative training scheme converges. Furthermore, we empirically establish that Random Fourier Features enhance the expressive capacity of the network, enabling accurate approximation of high-frequency PDEs. Through extensive numerical evaluation on classical benchmark problems, the superior performance of our method over state-of-the-art algorithms is shown, and the improved approximation across the frequency domain is illustrated.

Vision-Language models (VLMs), including CLIP, are known to encode biases such as learning spurious correlations that falsely associate background attributes with particular labels. Debiasing approaches typically aim to isolate and remove subspaces corresponding to a target concept via projecting its embedding away from the concept. This strategy succeeds in debiasing VLM embeddings with respect to the concepts considered but can amplify biased shortcuts in unconsidered concepts. In practice, it is impossible to enumerate all possible biases, meaning that an increase in bias can go unobserved during evaluation. We propose a debiasing approach for a set of known concepts such that the relation to the remaining, unconsidered, concepts is minimally changed. We achieve this by rotating the VLM’s embeddings within only a relevant subspace, rather than removing these subspaces, which mitigates unintended bias amplification.

Scaling laws in deep learning -- empirical power-law relationships linking model performance to resource growth -- have emerged as simple yet striking regularities across architectures, datasets, and tasks. These laws are particularly impactful in guiding the design of state-of-the-art models, since they quantify the benefits of increasing data or model size, and hint at the foundations of interpretability in machine learning. However, most studies focus on asymptotic behavior at the end of training. In this work, we describe a richer picture by analyzing the entire training dynamics: we identify two novel \textit{dynamical} scaling laws that govern how performance evolves as function of different norm-based complexity measures. Combined, our new laws recover the well-known scaling for test error at convergence. Our findings are consistent across CNNs, ResNets, and Vision Transformers trained on MNIST, CIFAR-10 and CIFAR-100. Furthermore, we provide analytical support using a single-layer perceptron trained with logistic loss, where we derive the new dynamical scaling laws, and we explain them through the implicit bias induced by gradient-based training.

Parameter-efficient fine-tuning (PEFT) has become a de facto standard for adapting Large Language Models (LLMs). However, we identify a critical vulnerability within popular low-rank adaptation methods like LoRA: they can exacerbate "Catastrophic Inheritance"—the unchecked propagation of biases, noise, and data imbalances from pre-training. This phenomenon can degrade model robustness and fairness, undermining the benefits of efficient adaptation. To address this, we introduce Bias-Alleviating Low-Rank Adaptation (BA-LoRA). Our approach is founded on a principled decomposition of Catastrophic Inheritance into three core challenges: Knowledge Drift, Representation Collapse, and Overfitting to Noise. BA-LoRA systematically mitigates these issues by incorporating a trio of targeted regularizers—consistency, diversity, and SVD—designed to preserve core knowledge, enforce representational richness, and stabilize the low-rank updates. We conduct comprehensive evaluations on a suite of natural language understanding (NLU) and generation (NLG) tasks using diverse, prominent open-source language models (e.g., LLaMA-2-7B and DeBERTa-v3-base). Our results show that BA-LoRA not only outperforms state-of-the-art LoRA variants in terms of performance and stability, but also demonstrates quantitatively superior robustness and bias mitigation on targeted evaluations. This confirms its ability to counteract the adverse effects of Catastrophic Inheritance. The code is available at https://anonymous.4open.science/r/p5q9a1z8.

Noise is ubiquitous in data used to train large language models, but it is not well understood whether these models are able to correctly generalize to inputs generated without noise. Here, we study noise-robust learning: are transformers trained on data with noisy features able to find a target function that correctly predicts labels for noiseless features? We show that transformers succeed at noise-robust learning for a selection of $k$-sparse parity and majority functions, compared to LSTMs which fail at this task for even modest feature noise. However, we find that transformers typically fail at noise-robust learning of random $k$-juntas, especially when the boolean sensitivity of the optimal solution is smaller than that of the target function. We argue that this failure is due to a combination of two factors: transformers' bias toward simpler functions, combined with an observation that the empirically optimal function for noise-robust learning has lower sensitivity than the target function. We test this hypothesis by exploiting transformers' simplicity bias to trap them in an incorrect solution, but show that transformers can escape this trap by training with an additional loss term penalizing high-sensitivity solutions. Overall, we find that transformers are particularly ineffective for learning boolean functions in the presence of feature noise.

Large language models (LLMs) have demonstrated impressive capabilities across a wide range of natural language processing tasks. However, their outputs often exhibit social biases, raising fairness concerns. Existing debiasing methods, such as fine-tuning on additional datasets or prompt engineering, face scalability issues or compromise user experience in multi-turn interactions. To address these challenges, we propose a framework for detecting stereotype-inducing words and attributing neuron-level bias in LLMs, without the need for fine-tuning or prompt modification. Our framework first identifies stereotype-inducing adjectives and nouns via comparative analysis across demographic groups. We then attribute biased behavior to specific neurons using two attribution strategies based on integrated gradients. Finally, we mitigate bias by directly intervening on their activations at the projection layer. Experiments on three widely used LLMs demonstrate that our method effectively reduces bias while preserving overall model performance.

In-context learning (ICL) enables pre-trained transformers (TFs) to perform few-shot learning across diverse tasks, fostering growing research into its underlying mechanisms. However, existing studies typically assume a causally-sufficient regime, overlooking spurious correlations and prediction bias introduced by hidden confounders (HCs). As HC commonly exists in real-world cases, current ICL understandings may not align with actual data structures. To fill this gap, we contribute the pioneer theoretical analysis towards a novel problem setup termed as ICL-HC, which offers understanding the effect of HC on the pre-training of TFs and the following ICL prediction. Our theoretical results entail that pre-trained TFs exhibits certain prediction bias with proportional to the confounding strength. To migrate such prediction bias, we further propose a gradient-free debiasing method named Double-Debiasing (DDbias) by collecting and prompting with extremely few unconfounded examples, correcting pre-trained TFs with unbiased ICL predictions. Extensive experiments on regression tasks across diverse designs of the TF architectures and data generation protocols verify both our theoretical results and the effectiveness of the proposed DDbias method.

Data pruning (DP), as an oft-stated strategy to alleviate heavy training burdens, reduces the volume of training samples according to a well-defined pruning method while striving for near-lossless performance. However, existing approaches, which commonly select highly informative samples, can lead to biased gradient estimation compared to full-dataset training. Furthermore, the analysis of this bias and its impact on final performance remains ambiguous. To address these challenges, we propose OrderDP, a plug-and-play framework that aims to obtain stable, unbiased, and near-lossless training acceleration with theoretical guarantees. Specifically, OrderDP first randomly selects a subset and then chooses the top-$q$ samples, where unbiasedness is established with respect to a surrogate loss. This ensures that OrderDP conducts unbiased training in terms of the surrogate objective. We further establish convergence and generalization analyses, elucidating how OrderDP affects optimal performance and enables well-controlled acceleration while ensuring guaranteed final performance. Empirically, we evaluate OrderDP against comprehensive baselines on CIFAR-10, CIFAR-100, and ImageNet-1K, demonstrating competitive accuracy, stable convergence, and exact control---all with a simpler design and faster runtime, while reducing training cost by over 40\%. Delivering both strong performance and computational efficiency, our method serves as a robust and easily adaptable tool for data-efficient learning.

How does the choice of optimization algorithm shape a model’s ability to learn features? To address this question for steepest descent methods—including sign descent, which is closely related to Adam—we introduce steepest mirror flows as a unifying theoretical framework. This framework reveals how optimization geometry governs learning dynamics, implicit bias, and sparsity and it provides two explanations for why Adam and AdamW often outperform SGD in fine-tuning. Focusing on diagonal linear networks and deep diagonal linear reparameterizations (a simplified proxy for attention), we show that steeper descent facilitates both saddle-point escape and feature learning. In contrast, gradient descent requires unrealistically large learning rates to escape saddles, an uncommon regime in fine-tuning. Empirically, we confirm that saddle-point escape is a central challenge in fine-tuning. Furthermore, we demonstrate that decoupled weight decay, as in AdamW, stabilizes feature learning by enforcing novel balance equations. Together, these results highlight two mechanisms how steepest descent can aid modern optimization.

Understanding the implicit bias of optimization algorithms is key to explaining and improving the generalization of deep models. The hyperbolic implicit bias induced by pointwise overparameterization promotes sparsity, but also yields a small inverse Riemannian metric near zero, slowing down parameter movement and impeding meaningful parameter sign flips. To overcome this obstacle, we propose Hyperbolic Aware Minimization (HAM), which alternates a standard optimizer step with a lightweight hyperbolic mirror step. The mirror step incurs less compute and memory than pointwise overparameterization, reproduces its beneficial hyperbolic geometry for feature learning, and mitigates the small–inverse-metric bottleneck. Our characterization of the implicit bias in the context of underdetermined linear regression provides insights into the mechanism how HAM consistently increases performance --even in the case of dense training, as we demonstrate in experiments with standard vision benchmarks. HAM is especially effective in combination with different sparsification methods, advancing the state of the art.

Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of architecture, hyperparameters and optimization procedure. However, deep neural networks can be surprisingly non-robust, resulting in overconfident predictions and poor out-of-distribution generalization. Bayesian deep learning addresses this via model averaging, but typically requires significant computational resources as well as carefully elicited priors to avoid overriding the benefits of implicit regularization. Instead, in this work, we propose to regularize variational neural networks solely by relying on the implicit bias of (stochastic) gradient descent. We theoretically characterize this inductive bias in overparametrized linear models as generalized variational inference and demonstrate the importance of the choice of parametrization. Empirically, our approach demonstrates strong in- and out-of-distribution performance without additional hyperparameter tuning and with minimal computational overhead.

Neural networks trained with gradient descent often learn solutions of increasing complexity over time, a phenomenon known as simplicity bias. Despite being widely observed across architectures, existing theoretical treatments lack a unifying framework. We present a theoretical framework that explains a simplicity bias arising from saddle-to-saddle learning dynamics for a general class of neural networks, incorporating fully-connected, convolutional, and attention-based architectures. Here, simple means expressible with few hidden units, i.e., hidden neurons, convolutional kernels, or attention heads. Specifically, we show that linear networks learn solutions of increasing rank, ReLU networks learn solutions with an increasing number of kinks, convolutional networks learn solutions with an increasing number of convolutional kernels, and self-attention models learn solutions with an increasing number of attention heads. By analyzing fixed points, invariant manifolds, and dynamics of gradient descent learning, we show that saddle-to-saddle dynamics operates by iteratively evolving near an invariant manifold, approaching a saddle, and switching to another invariant manifold. Our analysis also illuminates the effects of data distribution and initialization on the duration and number of plateaus in learning, dissociating previously confounding factors. Overall, our theory offers a framework for understanding when and why gradient descent progressively learns increasingly complex solutions.

Understanding simplicity biases in deep learning offers a promising path toward developing reliable AI. A common metric for this, inspired by Boolean function analysis, is average sensitivity, which captures a model's robustness to single-token perturbations. We argue that average sensitivity has two key limitations: it lacks a natural generalization to real-valued domains and fails to explain the "junta-like" input dependence we empirically observe in modern LLMs. To address these limitations, we propose *noise stability* as a more comprehensive simplicity metric. Noise stability expresses a model's robustness to correlated noise applied to *all* input coordinates simultaneously. We provide a theoretical analysis of noise stability for single-layer attention and ReLU MLP layers and tackle the multi-layer propagation problem with a covariance interval propagation approach. Building on this theory, we develop a practical *noise stability regularization* method. Experiments on algorithmic and next-token-prediction tasks show that our regularizer consistently catalyzes grokking and accelerates training by approximately $35$\% and $75$\% respectively. Our results establish noise stability as a powerful tool for understanding and improving modern Transformers.

In this paper, we provide sufficient conditions of benign overfitting of fixed width leaky ReLU two-layer neural network classifiers trained on mixture data via gradient descent. Our results are derived by establishing directional convergence of the network parameters and classification error bound of the convergent direction. Our classification error bound also lead to the discovery of a newly identified phase transition. Previously, directional convergence in (leaky) ReLU neural networks was established only for gradient flow. Due to the lack of directional convergence, previous results on benign overfitting were limited to those trained on nearly orthogonal data. All of our results hold on mixture data, which is a broader data setting than the nearly orthogonal data setting in prior work. We demonstrate our findings by showing that benign overfitting occurs with high probability in a much wider range of scenarios than previously known. Our results also allow us to characterize cases when benign overfitting provably fails even if directional convergence occurs. Our work thus provides a more complete picture of benign overfitting in leaky ReLU two-layer neural networks.

Model merging methods combine models with different capabilities into a single one while maintaining the same inference cost. Two popular approaches are lin- ear interpolation, which linearly interpolates between model weights, and task arithmetic, which combines task vectors obtained by the difference between fine- tuned and base models. While useful in practice, what properties make merging effective are poorly understood. This paper explores how the optimization pro- cess affects the loss landscape geometry and its impact on merging success. We show that a single quantity – the effective noise scale – unifies the impact of opti- mizer and data choices on model merging. Across architectures and datasets, the effectiveness of merging success is a non-monotonic function of effective noise, with a distinct optimum. Decomposing this quantity, we find that larger learning rates, stronger weight decay, smaller batch sizes, and data augmentation all inde- pendently modulate the effective noise scale, exhibiting the same qualitative trend. Unlike prior work that connects optimizer noise to the flatness or generalization of individual minima, we show that it also affects the global loss landscape, predict- ing when independently trained solutions can be merged. Our findings broaden the understanding of how optimization shapes the loss landscape geometry and its downstream consequences for model merging, suggesting the possibility of fur- ther manipulating the training dynamics to improve mergeability.

Existing studies on bias mitigation methods for large language models (LLMs) use diverse baselines and metrics to evaluate debiasing performance, leading to inconsistent comparisons among them. Moreover, their evaluations are mostly based on the comparison between LLMs' probabilities of biased and unbiased contexts, which ignores the gap between such evaluations and real-world use cases where users interact with LLMs by reading model responses and expect fair and safe outputs rather than LLMs' probabilities. To enable consistent evaluation across debiasing methods and bridge this gap, we introduce **BiasFreeBench**, an empirical benchmark that comprehensively compares eight mainstream bias mitigation techniques (covering four prompting-based and four training-based methods) on two test scenarios (multi-choice QA and open-ended multi-turn QA) by reorganizing existing datasets into a unified query-response setting. We further introduce a response-level metric, **Bias-Free Score**, to measure the extent to which LLM responses are fair, safe, and anti-stereotypical. Debiasing performances are systematically compared and analyzed across key dimensions: the prompting vs. training paradigm, model size, and generalization of different training strategies to unseen bias types. We release our benchmark, aiming to establish a unified testbed for bias mitigation research [https://github.com/xxupiano/BiasFreeBench](https://github.com/xxupiano/BiasFreeBench).

Adam [Kingma & Ba, 2015] is the de facto optimizer in deep learning, yet its theoretical understanding remains limited. Prior analyses show that Adam favors solutions aligned with $\ell_\infty$-geometry, but these results are restricted to the full-batch regime. In this work, we study the implicit bias of incremental Adam (using one sample per step) for logistic regression on linearly separable data, and show that its bias can deviate from the full-batch behavior. As an extreme example, we construct datasets on which incremental Adam provably converges to the $\ell_2$-max-margin classifier, in contrast to the $\ell_\infty$-max-margin bias of full-batch Adam. For general datasets, we characterize its bias using a proxy algorithm for the $\beta_2 \to 1$ limit. This proxy maximizes a data-adaptive Mahalanobis-norm margin, whose associated covariance matrix is determined by a data-dependent dual fixed-point formulation. We further present concrete datasets where this bias reduces to the standard $\ell_2$- and $\ell_\infty$-max-margin classifiers. As a counterpoint, we prove that Signum [Bernstein et al., 2018] converges to the $\ell_\infty$-max-margin classifier for any batch size. Overall, our results highlight that the implicit bias of Adam crucially depends on both the batching scheme and the dataset, while Signum remains invariant.

Machine learning models trained on real-world data often inherit and amplify biases against certain social groups, raising urgent concerns about their deployment at scale. While numerous bias mitigation methods have been proposed, comparing the effectiveness of bias mitigation methods remains difficult due to heterogeneous datasets, inconsistent fairness metrics, isolated evaluation of vision versus multi-modal models, and insufficient hyperparameter tuning that undermines fair comparisons. We introduce NH-Fair, a unified benchmark for fairness without harm that spans both vision models and large vision–language models (LVLMs) under standardized data, metrics, and training protocols, covering supervised and zero-shot regimes. Our key contributions are: (1) a systematic ERM tuning study that identifies training choices with large influence on both utility and disparities, yielding empirically grounded guidelines to help practitioners reduce expensive hyperparameter tuning space in achieving strong fairness and accuracy; (2) evidence that many debiasing methods do not reliably outperform a well-tuned ERM baseline, whereas a composite data-augmentation method consistently delivers parity gains without sacrificing utility, emerging as a promising practical strategy. (3) an analysis showing that while LVLMs achieve higher average accuracy, they still exhibit subgroup disparities, and gains from scaling are typically smaller than those from architectural or training-protocol choices. NH-Fair provides a reproducible, tuning-aware pipeline for rigorous, harm-aware fairness evaluation.

We study the implicit bias of sharpness-aware minimization (SAM) when training $L$-layer linear diagonal networks on linearly separable binary classification. For linear models ($L=1$), both $\ell_\infty$- and $\ell_2$-SAM recover the $\ell_2$ max-margin classifier, matching gradient descent (GD). However, for depth $L = 2$, the behavior changes drastically—even on a single-example dataset where we can analyze the dynamics. For $\ell_\infty$-SAM, the limit direction depends critically on initialization and can converge to $0$ or to any standard basis vector; this is in stark contrast to GD, whose limit aligns with the basis vector of the dominant coordinate in the data. For $\ell_2$-SAM, we uncover a phenomenon we call *sequential feature discovery*, in which the predictor initially relies on minor coordinates and gradually shifts to larger ones as training proceeds or initialization grows. Our theoretical analysis attributes this phenomenon to $\ell_2$-SAM’s gradient normalization factor applied in its perturbation, which amplifies minor coordinates early and allows major ones to dominate later. Synthetic and real-data experiments corroborate our findings.

Agents backed by large language models (LLMs) often rely on external tools drawn from marketplaces where multiple providers offer functionally equivalent options. This raises a critical point concerning fairness: if selection is systematically biased, it can degrade user experience and distort competition by privileging some providers over others. We introduce a benchmark of diverse tool categories, each containing multiple functionally equivalent tools, to evaluate tool-selection bias. Using this benchmark, we test seven models and show that unfairness exists with models either fixating on a single provider or disproportionately preferring earlier-listed tools in context. To investigate the origins of this bias, we conduct controlled experiments examining tool features, metadata (name, description, parameters), and pre-training exposure. We find that: (1) semantic alignment between queries and metadata is the strongest predictor of choice; (2) perturbing descriptions significantly shifts selections; and (3) repeated pre-training exposure to a single endpoint amplifies bias. Finally, we propose a lightweight mitigation that first filters the candidate tools to a relevant subset and then samples uniformly, reducing bias while preserving good task coverage. Our findings highlight tool-selection bias as a key obstacle for the fair deployment of tool-augmented LLMs.