To improve detection robustness in adverse conditions (e.g., haze and low light), image restoration is commonly applied as a pre-processing step to enhance image quality for the detector. However, the functional mismatch between restoration and detection networks can introduce instability and hinder effective integration--an issue that remains underexplored. We revisit this limitation through the lens of Lipschitz continuity, analyzing the functional differences between restoration and detection networks in both the input space and the parameter space. Our analysis shows that restoration networks perform smooth, continuous transformations, while object detectors operate with discontinuous decision boundaries, making them highly sensitive to minor perturbations. This mismatch introduces instability in traditional cascade frameworks, where even imperceptible noise from restoration is amplified during detection, disrupting gradient flow and hindering optimization. To address this, we propose Lipschitz-regularized object detection (LROD), a simple yet effective framework that integrates image restoration directly into the detector's feature learning, harmonizing the Lipschitz continuity of both tasks during training. We implement this framework as Lipschitz-regularized YOLO (LR-YOLO), extending seamlessly to existing YOLO detectors. Extensive experiments on haze and low-light benchmarks demonstrate that LR-YOLO consistently improves detection stability, optimization smoothness, and overall accuracy.

Learning instability is a long-standing problem across machine learning, but it is especially acute in the overparameterized regime that defines modern deep learning: large models fine-tuned or trained on limited data traverse flat loss landscapes with many nearly-equivalent minima, and stochastic factors (initialization, data order, dropout, hardware non-determinism) can route optimization to very different solutions. The rise of large pretrained models (LPMs) makes the problem more urgent: training cost is high, downstream data is often small, and repeated runs for variance reduction are prohibitive. We introduce \textbf{GRAIN} (\textbf{G}roup \textbf{A}ggregation via m\textbf{IN}-norm objective), a lightweight training algorithm that replaces the mean aggregation used in mini-batch optimization (both across mini-batches and within a mini-batch) with a min-norm convex combination of group-wise gradients. \mName guarantees a non-negative inner product between the aggregated update and every group gradient, resolving intra- and inner-batch gradient conflict, and retains an $\mathcal{O}(1/T)$ convergence rate comparable to SGD. Under mild smoothness and absolute-continuity assumptions, the min-norm solution differs almost surely from the arithmetic mean, which yields a uniform-stability bound for \mName strictly tighter than the standard bound for SGD. Empirically across generation, classification, and regression at LPM scale, \mName delivers consistent improvements in mean performance and reductions in run-to-run variance over a broad suite of tasks, with no extra training-time or storage cost beyond a single backward pass.

State-of-the-art membership inference attacks (MIAs) typically require training many reference models, making it difficult to scale these attacks to large pre-trained language models (LLMs). As a result, prior research has either relied on weaker attacks that avoid training references (e.g., fine-tuning attacks), or on stronger attacks applied to small models and datasets. However, weaker attacks have been shown to be brittle and insights from strong attacks in simplified settings do not translate to today's LLMs. These challenges prompt an important question: are the limitations observed in prior work due to attack design choices, or are MIAs fundamentally ineffective on LLMs? We address this question by scaling LiRA--one of the strongest MIAs--to GPT-2 architectures ranging from 10M to 1B parameters, training references on over 20B tokens from the C4 dataset. Our results advance the understanding of MIAs on LLMs in four key ways. While (1) strong MIAs can succeed on pretrained LLMs, (2) their effectiveness, remains limited (e.g., AUC<0.7) in practical settings.

Although today's pretrained discriminative vision-language models (e.g., CLIP) have demonstrated strong perception abilities, such as zero-shot image classification, they also suffer from the bag-of-words problem and spurious bias. To mitigate these problems, some pioneering studies leverage powerful generative models (e.g., pretrained diffusion models) to realize generalizable image classification, dubbed Diffusion Classifier (DC). Specifically, by randomly sampling a Gaussian noise, DC utilizes the differences of denoising effects with different category conditions to classify categories. Unfortunately, an inherent and notorious weakness of existing DCs is noise instability: different random sampled noises lead to significant performance changes. To achieve stable classification performance, existing DCs always ensemble the results of hundreds of sampled noises, which significantly reduces the classification speed.

Brain-computer interfaces have shown great potential in motor and speech rehabilitation, but still suffer from low performance stability across days, mostly due to the instabilities in neural signals. These instabilities, partially caused by neuron deaths and electrode shifts, leading to channel-level variabilities among different recording days. Previous studies mostly focused on aligning multi-day neural signals of onto a low-dimensional latent manifold to reduce the variabilities, while faced with difficulties when neural signals exhibit significant drift. Here, we propose to learn a channel-level invariant neural representation to address the variabilities in channels across days. It contains a channel-rearrangement module to learn stable representations against electrode shifts, and a channel reconstruction module to handle the missing neurons. The proposed method achieved the state-of-the-art performance with cross-day decoding tasks over two months, on multiple benchmark BCI datasets. The proposed approach showed good generalization ability that can be incorporated to different neural networks.

Deep neural networks exhibit periodic loss spikes during unregularized long-term training, a phenomenon known as the "Slingshot Mechanism." Existing work usually attributes this to intrinsic optimization dynamics, but its triggering mechanism remains unclear. This paper proves that this phenomenon is a result of floating-point arithmetic precision limits. As training enters a high-confidence stage, the difference between the correct-class logit and the other logits may exceed the absorption-error threshold. Then during backpropagation, the gradient of the correct class is rounded exactly to zero, while the gradients of the incorrect classes remain nonzero. This breaks the zero-sum constraint of gradients across classes and introduces a systematic drift in the parameter update of the classifier layer. We prove that this drift forms a positive feedback loop with the feature, causing the global classifier mean and the global feature mean to grow exponentially. We call this mechanism Numerical Feature Inflation (NFI). This mechanism explains the rapid norm growth before a Slingshot spike, the subsequent reappearance of gradients, and the resulting loss spike. We further show that NFI is not equivalent to an observed loss spike: in more practical tasks, partial absorption may not produce visible spikes, but it can still break the zero-sum constraint and drive rapid growth of parameter norms. Our results reinterpret Slingshot as a numerical dynamic of finite-precision training, and provide a testable explanation for abnormal parameter growth and logit divergence in late-stage training.

No feature ranking can be simultaneously faithful, stable, and complete when features are collinear. For collinear pairs, ranking reduces to a coin flip. We prove this impossibility, quantify it for four model classes, resolve it via ensemble averaging (DASH), and machine-verify it with 305 Lean 4 theorems. We characterize the complete attribution design space: exactly two families of methods exist -- faithful-complete methods (unstable, with rankings that flip up to 50% of the time) and ensemble methods like DASH (stable, reporting ties for symmetric features) -- and no method lies outside this dichotomy. The impossibility is quantitative: the attribution ratio diverges as 1/(1-rho^2) for gradient boosting, is infinite for Lasso, and converges for random forests. DASH (Diversified Aggregation of SHAP) is provably Pareto-optimal among unbiased aggregations, achieving the Cramer-Rao variance bound with a tight ensemble size formula. In a survey of 77 public datasets, 68% exhibit attribution instability. Switching to conditional SHAP does not escape the impossibility when features have equal causal effects. The framework includes practical diagnostics -- a Z-test workflow and single-model screening tool -- and has direct consequences for fairness auditing: SHAP-based proxy discrimination audits are provably unreliable under collinearity. The design space theorem, diagnostics, and impossibility are mechanically verified in Lean 4 (305 theorems from 16 axioms, 0 sorry) -- to our knowledge, the first formally verified impossibility in explainable AI.

Gradient-flow analyses show that simplified linear transformers can learn the in-context linear-regression algorithm, but they do not explain the finite-step behavior of gradient descent at large learning rates. Motivated by empirical work on high-learning-rate transformer instabilities and by the cubic-map phase diagram for quadratic regression, we study an exactly reducible one-prompt linear-transformer training problem. After normalization, the dynamics reduce to a two-factor product map with an effective step-size parameter \(μ\). On the balanced slice, this map recovers the known scalar cubic transition from monotone convergence to catapult convergence, periodic and chaotic bounded nonconvergence, and divergence. We then analyze the full two-dimensional system and show that, for \(0<μ<2\), it has an explicit invariant Chebyshev ellipse separating forward-invariant regions; this ellipse carries off-balanced chaotic dynamics but is transversely repelling, while balanced scalar attractors can be transversely attracting. These results show that large constant learning rates can change the training attractor of the learned transformer rather than merely accelerating convergence: beyond sharp stability thresholds, finite-step training may settle into cycles, bounded chaos, or divergence instead of a single in-context linear-regression solution. We also discuss the consequences for mini-batch gradient descent based training methods.

Hyperparameter transfer allows extrapolating optimal optimization hyperparameters from small to large scales, making it critical for training large language models (LLMs). This is done either by fitting a scaling law to the hyperparameters or by a judicious choice of parameterization, such as Maximal Update ($μ$P), that renders optimal hyperparameters approximately scale invariant. In this paper, we first develop a framework to quantify hyperparameter transfer through three metrics: (1) the quality of the scaling law fit, (2) the robustness to extrapolation errors, and (3) the asymptotic loss penalty due to choice of parameterization. Next, we investigate through a comprehensive series of ablations why $μ$P appears to offer high-quality learning rate transfer relative to standard parameterization (SP), as existing theory is inadequate. We find that the overwhelming benefit of $μ$P relative to SP when training with AdamW arises simply from maximizing the learning rate of the embedding layer. In SP, the embedding layer learning rate acts as a bottleneck that induces training instabilities; increasing it by a factor of width to match $μ$P dramatically smooths out training while improving hyperparameter transfer. We also find that weight decay improves the scaling law fits, while, in the fixed token-per-parameter setting, it hurts the robustness of the extrapolation.

Dense Associative Memory (DenseAM) is a promising family of AI architectures that is represented by a neural network performing temporal dynamics on an energy landscape. While hyperparameter transfer methods are well-studied for feed-forward networks, these methods have not been developed for settings in which weights are shared across layers and within the layer, which is common in DenseAMs. Additionally, DenseAMs utilize rapidly peaking activation functions that are rarely used in feed-forward architectures. The confluence of these aspects makes DenseAM a challenging framework for using existing methods for hyperparameter transfer. Our work initiates the development of hyperparameter transfer methods for this class of models. We derive explicit prescriptions for how the hyperparameters tuned on small models can be transferred to models trained at scale. We demonstrate excellent agreement between these theoretical findings and empirical results.