OpenRaiser/Intern-Atlas huggingface dataset:
A Minimalist Example of Edge-of-Stability and Progressive Sharpening
Venue: Conference NeurIPS 2025
Year: 2025

Recent advances in deep learning optimization have unveiled two intriguing phenomena under large learning rates: Edge of Stability (EoS) and Progressive Sharpening (PS), challenging classical Gradient Descent (GD) analyses. Current research approaches, using either generalist frameworks or minimalist examples, face significant limitations in explaining these phenomena. This paper advances the minimalist approach by introducing a two-layer network with a two-dimensional input, where one dimension is relevant to the response and the other is irrelevant. Through this model, we rigorously prove the existence of progressive sharpening and self-stabilization under large learning rates, and establish non-asymptotic analysis of the training dynamics and sharpness along the entire GD trajectory. Besides, we connect our minimalist example to existing works by reconciling the existence of a well-behaved ``stable set" between minimalist and generalist analyses, and extending the analysis of Gradient Flow Solution sharpness to our two-dimensional input scenario. These findings provide new insights into the EoS phenomenon from both parameter and input data distribution perspectives, potentially informing more effective optimization strategies in deep learning practice.
Large Language Models as Model Organisms for Human Associative Learning
Venue: Conference NeurIPS 2025
Year: 2025

Associative learning--forming links between co-occurring items--is fundamental to human cognition, reshaping internal representations in complex ways. Testing hypotheses on how representational changes occur in biological systems is challenging, but large language models (LLMs) offer a scalable alternative. Building on LLMs' in-context learning, we adapt a cognitive neuroscience associative learning paradigm and investigate how representations evolve across six models. Our initial findings reveal a non-monotonic pattern consistent with the Non-Monotonic Plasticity Hypothesis, with moderately similar items differentiating after learning. Leveraging the controllability of LLMs, we further show that this differentiation is modulated by the overlap of associated items with the broader vocabulary--a factor we term vocabulary interference, capturing how new associations compete with prior knowledge. We find that higher vocabulary interference amplifies differentiation, suggesting that representational change is influenced by both item similarity and global competition. Our findings position LLMs not only as powerful tools for studying representational dynamics in human-like learning systems, but also as accessible and general computational models for generating new hypotheses about the principles underlying memory reorganization in the brain.
DEFT: Decompositional Efficient Fine-Tuning for Text-to-Image Models
Venue: Conference NeurIPS 2025
Year: 2025

Efficient fine-tuning of pre-trained Text-to-Image (T2I) models involves adjusting the model to suit a particular task or dataset while minimizing computational resources and limiting the number of trainable parameters. However, it often faces challenges in striking a trade-off between aligning with the target distribution: learning a novel concept from a limited image for personalization and retaining the instruction ability needed for unifying multiple tasks, all while maintaining editability (aligning with a variety of prompts or in-context generation). In this work, we introduce DEFT, Decompositional Efficient Fine-Tuning, an efficient fine-tuning framework that adapts a pre-trained weight matrix by decomposing its update into two components with two trainable matrices: (1) a projection onto the complement of a low-rank subspace spanned by a low-rank matrix, and (2) a low-rank update. The single trainable low-rank matrix defines the subspace, while the other trainable low-rank matrix enables flexible parameter adaptation within that subspace. We conducted extensive experiments on the Dreambooth and Dreambench Plus datasets for personalization, the InsDet dataset for object and scene adaptation, and the VisualCloze dataset for a universal image generation framework through visual in-context learning with both Stable Diffusion and a unified model. Our results demonstrated state-of-the-art performance, highlighting the emergent properties of efficient fine-tuning. Our code is available on \href{https://github.com/MAXNORM8650/DEFT}{DEFTBase}.
Gradient Descent as Loss Landscape Navigation: a Normative Framework for Deriving Learning Rules
Venue: Conference NeurIPS 2025
Year: 2025

Learning rules -- prescriptions for updating model parameters to improve performance -- are typically assumed rather than derived. Why do some learning rules work better than others, and under what assumptions can a given rule be considered optimal? We propose a theoretical framework that casts learning rules as policies for navigating (partially observable) loss landscapes, and identifies optimal rules as solutions to an associated optimal control problem. A range of well-known rules emerge naturally within this framework under different assumptions: gradient descent from short-horizon optimization, momentum from longer-horizon planning, natural gradients from accounting for parameter space geometry, non-gradient rules from partial controllability, and adaptive optimizers like Adam from online Bayesian inference of loss landscape shape. We further show that continual learning strategies like weight resetting can be understood as optimal responses to task uncertainty. By unifying these phenomena under a single objective, our framework clarifies the computational structure of learning and offers a principled foundation for designing adaptive algorithms.
Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modeling
Venue: Conference NeurIPS 2025
Year: 2025

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result, they are fundamentally ill-suited for applications involving inherently discrete quantities-such as particle counts or material units-that are constrained by strict conservation laws like mass conservation, limiting their applicability in scientific workflows. To address this limitation, we propose Discrete Spatial Diffusion (DSD), a framework based on a continuous-time, discrete-state jump stochastic process that operates directly in discrete spatial domains while strictly preserving particle counts in both forward and reverse diffusion processes. By using spatial diffusion to achieve particle conservation, we introduce stochasticity naturally through a discrete formulation. We demonstrate the expressive flexibility of DSD by performing image synthesis, class conditioning, and image inpainting across standard image benchmarks, while exactly conditioning total image intensity. We validate DSD on two challenging scientific applications: porous rock microstructures and lithium-ion battery electrodes, demonstrating its ability to generate structurally realistic samples under strict mass conservation constraints, with quantitative evaluation using state-of-the-art metrics for transport and electrochemical performance.
CTRL-ALT-DECEIT Sabotage Evaluations for Automated AI R&D
Venue: Conference NeurIPS 2025
Year: 2025

AI systems are increasingly able to autonomously conduct realistic software engineering tasks, and may soon be deployed to automate machine learning (ML) R&D itself. Frontier AI systems may be deployed in safety-critical settings, including to help ensure the safety of future systems. Unfortunately, frontier and future systems may not be sufficiently trustworthy, and there is evidence that these systems may even be misaligned with their developers or users. Therefore, we investigate the capabilities of AI agents to act against the interests of their users when conducting ML engineering, by sabotaging ML models, sandbagging their performance, and subverting oversight mechanisms. First, we extend MLE-Bench, a benchmark for realistic ML tasks, with code-sabotage tasks such as implanting backdoors and purposefully causing generalisation failures. Frontier agents make meaningful progress on our sabotage tasks. In addition, we study agent capabilities to sandbag on MLE-Bench. Agents can calibrate their performance to specified target levels below their actual capability. To mitigate sabotage, we use LM monitors to detect suspicious agent behaviour, and we measure model capability to sabotage and sandbag without being detected by these monitors. Overall, monitors are capable at detecting code-sabotage attempts but our results suggest that detecting sandbagging is more difficult. Additionally, aggregating multiple monitor predictions works well, but monitoring may not be sufficiently reliable to mitigate sabotage in high-stakes domains. Our benchmark is implemented in the UK AISI's Inspect framework and we make our code publicly available at https://github.com/TeunvdWeij/ctrl-alt-deceit
Differentiation Through Black-Box Quadratic Programming Solvers
Venue: Conference NeurIPS 2025
Year: 2025

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on specific integrated solvers. This integration limits their applicability, including their use in neural network architectures and bi-level optimization tasks, restricting users to a narrow selection of solver choices. To address this limitation, we introduce dQP, a modular and solver-agnostic framework for plug-and-play differentiation of virtually any QP solver. A key insight we leverage to achieve modularity is that, once the active set of inequality constraints is known, both the solution and its derivative can be expressed using simplified linear systems that share the same matrix. This formulation fully decouples the computation of the QP solution from its differentiation. Building on this result, we provide a minimal-overhead, open-source implementation ( https://github.com/cwmagoon/dQP ) that seamlessly integrates with over 15 state-of-the-art solvers. Comprehensive benchmark experiments demonstrate dQP's robustness and scalability, particularly highlighting its advantages in large-scale sparse problems.
An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models
Venue: Conference NeurIPS 2025
Year: 2025

We develop an analytical framework for understanding how the generated distribution evolves during diffusion model training. Leveraging a Gaussian-equivalence principle, we solve the full-batch gradient-flow dynamics of linear and convolutional denoisers and integrate the resulting probability-flow ODE, yielding analytic expressions for the generated distribution. The theory exposes a universal inverse-variance spectral law: the time for an eigen- or Fourier mode to match its target variance scales as $τ\proptoλ^{-1}$, so high-variance (coarse) structure is mastered orders of magnitude sooner than low-variance (fine) detail. Extending the analysis to deep linear networks and circulant full-width convolutions shows that weight sharing merely multiplies learning rates accelerating but not eliminating the bias whereas local convolution introduces a qualitatively different bias. Experiments on Gaussian and natural-image datasets confirm the spectral law persists in deep MLP-based UNet. Convolutional U-Nets, however, display rapid near-simultaneous emergence of many modes, implicating local convolution in reshaping learning dynamics. These results underscore how data covariance governs the order and speed with which diffusion models learn, and they call for deeper investigation of the unique inductive biases introduced by local convolution.
Low Precision Streaming PCA
Venue: Conference NeurIPS 2025
Year: 2025

Low-precision streaming PCA estimates the top principal component in a streaming setting under limited precision. We establish an information-theoretic lower bound on the quantization resolution required to achieve a target accuracy for the leading eigenvector. We study Oja's algorithm for streaming PCA under linear and nonlinear stochastic quantization. The quantized variants use unbiased stochastic quantization of the weight vector and the updates. Under mild moment and spectral-gap assumptions on the data distribution, we show that a batched version achieves the lower bound up to logarithmic factors under both schemes. This leads to a nearly dimension-free quantization error in the nonlinear quantization setting. Empirical evaluations on synthetic streams validate our theoretical findings and demonstrate that our low-precision methods closely track the performance of standard Oja's algorithm.
Conformal Prediction Beyond the Seen: A Missing Mass Perspective for Uncertainty Quantification in Generative Models
Venue: Conference NeurIPS 2025
Year: 2025

Uncertainty quantification (UQ) is essential for safe deployment of generative AI models such as large language models (LLMs), especially in high stakes applications. Conformal prediction (CP) offers a principled uncertainty quantification framework, but classical methods focus on regression and classification, relying on geometric distances or softmax scores: tools that presuppose structured outputs. We depart from this paradigm by studying CP in a query only setting, where prediction sets must be constructed solely from finite queries to a black box generative model, introducing a new trade off between coverage, test time query budget, and informativeness. We introduce Conformal Prediction with Query Oracle (CPQ), a framework characterizing the optimal interplay between these objectives. Our finite sample algorithm is built on two core principles: one governs the optimal query policy, and the other defines the optimal mapping from queried samples to prediction sets. Remarkably, both are rooted in the classical missing mass problem in statistics. Specifically, the optimal query policy depends on the rate of decay, or the derivative, of the missing mass, for which we develop a novel estimator. Meanwhile, the optimal mapping hinges on the missing mass itself, which we estimate using Good Turing estimators. We then turn our focus to implementing our method for language models, where outputs are vast, variable, and often under specified. Fine grained experiments on three real world open ended tasks and two LLMs, show CPQ applicability to any black box LLM and highlight: (1) individual contribution of each principle to CPQ performance, and (2) CPQ ability to yield significantly more informative prediction sets than existing conformal methods for language uncertainty quantification.
Towards Resilient Safety-driven Unlearning for Diffusion Models against Downstream Fine-tuning
Venue: Conference NeurIPS 2025
Year: 2025

Text-to-image (T2I) diffusion models have achieved impressive image generation quality and are increasingly fine-tuned for personalized applications. However, these models often inherit unsafe behaviors from toxic pretraining data, raising growing safety concerns. While recent safety-driven unlearning methods have made promising progress in suppressing model toxicity, they are found to be fragile to downstream fine-tuning, as we reveal that state-of-the-art methods largely fail to retain their effectiveness even when fine-tuned on entirely benign datasets. To mitigate this problem, in this paper, we propose ResAlign, a safety-driven unlearning framework with enhanced resilience against downstream fine-tuning. By modeling downstream fine-tuning as an implicit optimization problem with a Moreau envelope-based reformulation, ResAlign enables efficient gradient estimation to minimize the recovery of harmful behaviors. Additionally, a meta-learning strategy is proposed to simulate a diverse distribution of fine-tuning scenarios to improve generalization. Extensive experiments across a wide range of datasets, fine-tuning methods, and configurations demonstrate that ResAlign consistently outperforms prior unlearning approaches in retaining safety, while effectively preserving benign generation capability. Our code and pretrained models are publicly available at https://github.com/AntigoneRandy/ResAlign.
Benign Overfitting in Single-Head Attention
Venue: Conference NeurIPS 2025
Year: 2025

The phenomenon of benign overfitting, where a trained neural network perfectly fits noisy training data but still achieves near-optimal test performance, has been extensively studied in recent years for linear models and fully-connected/convolutional networks. In this work, we study benign overfitting in a single-head softmax attention model, which is the fundamental building block of Transformers. We prove that under appropriate conditions, the model exhibits benign overfitting in a classification setting already after two steps of gradient descent. Moreover, we show conditions where a minimum-norm/maximum-margin interpolator exhibits benign overfitting. We study how the overfitting behavior depends on the signal-to-noise ratio (SNR) of the data distribution, namely, the ratio between norms of signal and noise tokens, and prove that a sufficiently large SNR is both necessary and sufficient for benign overfitting.
Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions
Venue: Conference NeurIPS 2025
Year: 2025

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs $(\mathbf{y}, g \cdot \mathbf{y})$, where $g$ is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group $G:= (R_m \times \mathbb{Z}_n \times \mathbb{Z}_n)$, combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group $O(n)$ and the general linear group $GL(n)$. We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.
LoMix: Learnable Weighted Multi-Scale Logits Mixing for Medical Image Segmentation
Venue: Conference NeurIPS 2025
Year: 2025

U-shaped networks output logits at multiple spatial scales, each capturing a different blend of coarse context and fine detail. Yet, training still treats these logits in isolation - either supervising only the final, highest-resolution logits or applying deep supervision with identical loss weights at every scale - without exploring mixed-scale combinations. Consequently, the decoder output misses the complementary cues that arise only when coarse and fine predictions are fused. To address this issue, we introduce LoMix (Logits Mixing), a NAS-inspired, differentiable plug-and-play module that generates new mixed-scale outputs and learns how exactly each of them should guide the training process. More precisely, LoMix mixes the multi-scale decoder logits with four lightweight fusion operators: addition, multiplication, concatenation, and attention-based weighted fusion, yielding a rich set of synthetic mutant maps. Every original or mutant map is given a softplus loss weight that is co-optimized with network parameters, mimicking a one-step architecture search that automatically discovers the most useful scales, mixtures, and operators. Plugging LoMix into recent U-shaped architectures (i.e., PVT-V2-B2 backbone with EMCAD decoder) on Synapse 8-organ dataset improves DICE by +4.2% over single-output supervision, +2.2% over deep supervision, and +1.5% over equally weighted additive fusion, all with zero inference overhead. When training data are scarce (e.g., one or two labeled scans), the advantage grows to +9.23%, underscoring LoMix's data efficiency. Across four benchmarks and diverse U-shaped networks, LoMiX improves DICE by up to +13.5% over single-output supervision, confirming that learnable weighted mixed-scale fusion generalizes broadly while remaining data efficient, fully interpretable, and overhead-free at inference. Our code is available at https://github.com/SLDGroup/LoMix.
Robust and Computation-Aware Gaussian Processes
Venue: Conference NeurIPS 2025
Year: 2025

Gaussian processes (GPs) are widely used for regression and optimization tasks such as Bayesian optimization (BO) due to their expressiveness and principled uncertainty estimates. However, in settings with large datasets corrupted by outliers, standard GPs and their sparse approximations struggle with computational tractability and robustness. We introduce Robust Computation-aware Gaussian Process (RCaGP), a novel GP model that jointly addresses these challenges by combining a principled treatment of approximation-induced uncertainty with robust generalized Bayesian updating. The key insight is that robustness and approximation-awareness are not orthogonal but intertwined: approximations can exacerbate the impact of outliers, and mitigating one without the other is insufficient. Unlike previous work that focuses narrowly on either robustness or approximation quality, RCaGP combines both in a principled and scalable framework, thus effectively managing both outliers and computational uncertainties introduced by approximations such as low-rank matrix multiplications. Our model ensures more conservative and reliable uncertainty estimates, a property we rigorously demonstrate. Additionally, we establish a robustness property and show that the mean function is key to preserving it, motivating a tailored model selection scheme for robust mean functions. Empirical results confirm that solving these challenges jointly leads to superior performance across both clean and outlier-contaminated settings, both on regression and high-throughput Bayesian optimization benchmarks.
Low Rank Gradients and Where to Find Them
Venue: Conference NeurIPS 2025
Year: 2025

This paper investigates low-rank structure in the gradients of the training loss for two-layer neural networks while relaxing the usual isotropy assumptions on the training data and parameters. We consider a spiked data model in which the bulk can be anisotropic and ill-conditioned, we do not require independent data and weight matrices and we also analyze both the mean-field and neural-tangent-kernel scalings. We show that the gradient with respect to the input weights is approximately low rank and is dominated by two rank-one terms: one aligned with the bulk data-residue , and another aligned with the rank one spike in the input data. We characterize how properties of the training data, the scaling regime and the activation function govern the balance between these two components. Additionally, we also demonstrate that standard regularizers, such as weight decay, input noise and Jacobian penalties, also selectively modulate these components. Experiments on synthetic and real data corroborate our theoretical predictions.