Score Function
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Related Articles from SNS
On the Robustness of Langevin Dynamics to Score Function Error
Announce Type: replace Abstract: We consider the robustness of score-based generative modeling to errors in the estimate of the score function. In particular, we show that Langevin dynamics is not robust to the $L^2$ errors (more generally $L^p$ errors) in the estimate of the score function. It is well-established that with small $L^2$ errors in the estimate of the score function, diffusion models can sample faithfully from the target distribution under fairly mild regularity assumptions in...
Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning
arXiv:2307.05213v3 Announce Type: replace Abstract: Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is to estimate said parameters via machine learning (ML) models trained to minimize the prediction error, which however is not necessarily aligned with the downstream task-level error. The decision-focused...
ScoreStop: Gradient-based early stopping using functional score tests
Announce Type: cross Abstract: Gradient boosted decision trees require a stopping rule to avoid overfitting. The standard rule monitors a validation loss and stops if the loss fails to improve for a fixed patience period. However, the patience parameter has no interpretable scale and validation losses can be noisy or implicitly defined by a user-specified gradient.
Generalizing Fair Top-$k$ Selection: An Integrative Approach
arXiv:2603.04689v3 Announce Type: replace Abstract: Fair top-$k$ selection, which ensures appropriate proportional representation of members from minority or historically disadvantaged groups among the top-$k$ selected candidates, has drawn significant attention. We study the problem of finding a fair (linear) scoring function with multiple protected groups while also minimizing the disparity from a reference scoring function. This generalizes the prior setup, which was restricted to the...
Customizing the Inductive Biases of Softmax Attention using Structured Matrices
arXiv:2509.07963v2 Announce Type: replace Abstract: The core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys and takes the dot product of each pair. While the low-dimensional projection improves efficiency, it causes information loss for certain tasks that have intrinsically high-dimensional inputs. Additionally, attention uses the same scoring function for all input pairs, without imposing a distance-dependent compute bias...
Multi-level, multi-body atomic interaction graphs for machine learning-based prediction of protein-ligand binding energies
Accurate prediction of binding affinity is crucial for rational drug design and discovery. Traditional computational methods often rely on complex scoring functions that incorporate a multitude of physical and chemical descriptors, leading to high computational demands and sometimes limited generalizability. In this work, we propose a novel scoring function that models multi-level, multi-body atomic interactions using graph-based representations.
Mitigating Diffusion Model Hallucinations with Dynamic Guidance
arXiv:2510.05356v2 Announce Type: replace Abstract: Hallucinations in diffusion models are samples with structural inconsistencies that can emerge due to the excessive smoothing of the learned score function, which in turn leads to interpolations between modes of the data distribution. Since semantic interpolations are often desirable and contribute to sample diversity, we believe that a nuanced and targeted solution is required to address diffusion model hallucinations. In this work, we...
Diffusion Image Generation with Explicit Modeling of Data Manifold Geometry
Announce Type: replace Abstract: Image generative models aim to sample data points from the underlying data manifold, a task that requires learning and decoding a dense, low-dimensional, and compact parameterization space. To achieve this, we propose the Data Manifold-aware Image diffusioN moDel (MIND), a novel framework that explicitly models manifold geometry by integrating discrete patch tokenization into the score function of a continuous diffusion model. This approach successfully...
A Theoretical Analysis of Memory and Overfitting Phenomena in Stochastic Interpolation Models
new Abstract: This paper provides a theoretical account of memorization in stochastic interpolation models. By leveraging closed-form expressions for the optimal velocity field and the associated score function, we show that, in the continuous-time oracle setting, both deterministic and stochastic generation processes recover training samples. Under Euler discretization, generated samples remain centered around training samples, with deviations controlled by the step size.
Generation Properties of Stochastic Interpolation under Finite Training Set
arXiv:2509.21925v2 Announce Type: replace Abstract: This paper investigates the theoretical behavior of generative models under finite training populations. Within the stochastic interpolation generative framework, we derive closed-form expressions for the optimal velocity field and score function when only a finite number of training samples are available. We demonstrate that, under some regularity conditions, the deterministic generative process exactly recovers the training samples, while...