Distribution shifts in multi-dimensional data, caused by one or more "corrupted" dimensions, are

Eq. (6) suggests that the SDE drift corresponding to the score may be broken down into 3 steps: 1. However, in practice this modification creates a "discontinuity" between the constrained and unconstrained components, leading to erroneous correlations between them in the generated samples. "learning rate" that is determined empirically such that the loss value reduces adequately close to zero Thus it needs to be tuned empirically. The correction in Eq. (16) is equivalent to imposing a Gaussian likelihood on Remark 2. The post-processing presented in this section is similar to [ In this section, we present the most relevant components for completeness and better reproducibility. B.2 Sampling The reverse SDE in Eq. (5) used for sampling may be rewritten in terms of denoiser D As stated in 4.1 of the main text, for this The energy-based metrics are already defined in Eq. (12) and Eq.

Molecular generation (Stokes et al., 2020) has

We study online transfer reinforcement learning (RL) in episodic Markov decision processes, where experience from related source tasks is available during learning on a target task. A fundamental difficulty is that task similarity is typically defined in terms of rewards or transitions, whereas online RL algorithms operate on Bellman regression targets. As a result, naively reusing source Bellman updates introduces systematic bias and invalidates regret guarantees. We identify one-step Bellman alignment as the correct abstraction for transfer in online RL and propose re-weighted targeting (RWT), an operator-level correction that retargets continuation values and compensates for transition mismatch via a change of measure. RWT reduces task mismatch to a fixed one-step correction and enables statistically sound reuse of source data. This alignment yields a two-stage RWT $Q$-learning framework that separates variance reduction from bias correction. Under RKHS function approximation, we establish regret bounds that scale with the complexity of the task shift rather than the target MDP. Empirical results in both tabular and neural network settings demonstrate consistent improvements over single-task learning and naïve pooling, highlighting Bellman alignment as a model-agnostic transfer principle for online RL.

A new wave of work on covariance cleaning and nonlinear shrinkage has delivered asymptotically optimal analytical solutions for large covariance matrices. The same framework has been generalized to empirical cross-covariance matrices, whose singular value decomposition identifies canonical comovement modes between two asset sets, with singular values quantifying the strength of each mode and providing natural targets for shrinkage. Existing analytical cross-covariance cleaners are derived under strong stationarity and large-sample assumptions, and they typically rely on mesoscopic regularity conditions such as bounded spectra; macroscopic common modes (e.g., a global market factor) violate these conditions. When applied to real equity returns, where dependence structures drift over time and global modes are prominent, we find that these theoretically optimal formulas do not translate into robust out-of-sample performance. We address this gap by designing a random-matrix-inspired neural architecture that operates in the empirical singular-vector basis and learns a nonlinear mapping from empirical singular values to their corresponding cleaned values. By construction, the network can recover the analytical solution as a special case, yet it remains flexible enough to adapt to non-stationary dynamics and mode-driven distortions. Trained on a long history of equity returns, the proposed method achieves a more favorable bias-variance trade-off than purely analytical cleaners and delivers systematically lower out-of-sample cross-covariance prediction errors. Our results demonstrate that combining random-matrix theory with machine learning makes asymptotic theories practically effective in realistic time-varying markets.

A central problem in machine learning theory is to characterize how learning dynamics select particular solutions among the many compatible with the training objective, a phenomenon, called implicit bias, which remains only partially characterized. In the present work, we identify a general mechanism, in terms of an explicit geometric correction of the learning dynamics, for the emergence of implicit biases, arising from the interaction between continuous symmetries in the model's parametrization and stochasticity in the optimization process. Our viewpoint is constructive in two complementary directions: given model symmetries, one can derive the implicit bias they induce; conversely, one can inverse-design a wide class of different implicit biases by computing specific redundant parameterizations. More precisely, we show that, when the dynamics is expressed in the quotient space obtained by factoring out the symmetry group of the parameterization, the resulting stochastic differential equation gains a closed form geometric correction in the stationary distribution of the optimizer dynamics favoring orbits with small local volume. We compute the resulting symmetry induced bias for a range of architectures, showing how several well known results fit into a single unified framework. The approach also provides a practical methodology for deriving implicit biases in new settings, and it yields concrete, testable predictions that we confirm by numerical simulations on toy models trained on synthetic data, leaving more complex scenarios for future work. Finally, we test the implicit bias inverse-design procedure in notable cases, including biases toward sparsity in linear features or in spectral properties of the model parameters.

While modern multivariate forecasters such as Transformers and GNNs achieve strong benchmark performance, they often suffer from systematic errors at specific variables or horizons and, critically, lack guarantees against performance degradation in deployment. Existing post-hoc residual correction methods attempt to fix these errors, but are inherently greedy: although they may improve average accuracy, they can also "help in the wrong way" by overcorrecting reliable predictions and causing local failures in unseen scenarios. To address this critical "safety gap," we propose CRC (Causality-inspired Safe Residual Correction), a plug-and-play framework explicitly designed to ensure non-degradation. CRC follows a divide-and-conquer philosophy: it employs a causality-inspired encoder to expose direction-aware structure by decoupling self- and cross-variable dynamics, and a hybrid corrector to model residual errors. Crucially, the correction process is governed by a strict four-fold safety mechanism that prevents harmful updates. Experiments across multiple datasets and forecasting backbones show that CRC consistently improves accuracy, while an in-depth ablation study confirms that its core safety mechanisms ensure exceptionally high non-degradation rates (NDR), making CRC a correction framework suited for safe and reliable deployment.

We present a new algorithm to generate minimal, stable, and symbolic corrections to an input that will cause a neural network with ReLU activations to change its output. We argue that such a correction is a useful way to provide feedback to a user when the network's output is different from a desired output. Our algorithm generates such a correction by solving a series of linear constraint satisfaction problems. The technique is evaluated on three neural network models: one predicting whether an applicant will pay a mortgage, one predicting whether a first-order theorem can be proved efficiently by a solver using certain heuristics, and the final one judging whether a drawing is an accurate rendition of a canonical drawing of a cat.

Logistic regression remains one of the most widely used tools in applied statistics, machine learning and data science. However, in moderately high-dimensional problems, where the number of features $d$ is a non-negligible fraction of the sample size $n$, the logistic regression maximum likelihood estimator (MLE), and statistical procedures based the large-sample approximation of its distribution, behave poorly. Recently, Sur and Candès (2019) showed that these issues can be corrected by applying a new approximation of the MLE's sampling distribution in this high-dimensional regime. Unfortunately, these corrections are difficult to implement in practice, because they require an estimate of the \emph{signal strength}, which is a function of the underlying parameters $\beta$ of the logistic regression. To address this issue, we propose SLOE, a fast and straightforward approach to estimate the signal strength in logistic regression. The key insight of SLOE is that the Sur and Candès (2019) correction can be reparameterized in terms of the corrupted signal strength, which is only a function of the estimated parameters $\widehat \beta$. We propose an estimator for this quantity, prove that it is consistent in the relevant high-dimensional regime, and show that dimensionality correction using SLOE is accurate in finite samples. Compared to the existing ProbeFrontier heuristic, SLOE is conceptually simpler and orders of magnitude faster, making it suitable for routine use. We demonstrate the importance of routine dimensionality correction in the Heart Disease dataset from the UCI repository, and a genomics application using data from the UK Biobank.

Recently, image-text matching has attracted more and more attention from academia and industry, which is fundamental to understanding the latent correspondence across visual and textual modalities. However, most existing methods implicitly assume the training pairs are well-aligned while ignoring the ubiquitous annotation noise, a.k.a noisy correspondence (NC), thereby inevitably leading to a performance drop. Although some methods attempt to address such noise, they still face two challenging problems: excessive memorizing/overfitting and unreliable correction for NC, especially under high noise. To address the two problems, we propose a generalized Cross-modal Robust Complementary Learning framework (CRCL), which benefits from a novel Active Complementary Loss (ACL) and an efficient Self-refining Correspondence Correction (SCC) to improve the robustness of existing methods. Specifically, ACL exploits active and complementary learning losses to reduce the risk of providing erroneous supervision, leading to theoretically and experimentally demonstrated robustness against NC. SCC utilizes multiple self-refining processes with momentum correction to enlarge the receptive field for correcting correspondences, thereby alleviating error accumulation and achieving accurate and stable corrections. We carry out extensive experiments on three image-text benchmarks, i.e., Flickr30K, MS-COCO, and CC152K, to verify the superior robustness of our CRCL against synthetic and real-world noisy correspondences.