Daily Papers

The quality with which language models follow instructions falls as the load grows, yet there is still no quantity that expresses the limit of a model in units of load with an uncertainty. We propose an instrument in which the load consists of rules that replace single-token words in a text without meaning: such an instruction is atomic, the rules are independent by the construction of the task, and the outcome of every application of a rule is determined by a computable reference answer. Every occurrence of a word to be replaced becomes a Bernoulli trial with a known position in the answer and a known rule number. The statistical model first measures the shape of the dependence of the probability of a right replacement on the text length, the word position, the replacement density, the number of rules and the rule number, then describes it by smooth laws and restores a reference level that does not depend on the choice of the coding. The model yields the instruction capacity - the number of rules held at a given share of right replacements - with an uncertainty. A measurement of GPT-4o mini (2958 requests, 642,430 trials) gave regular laws for every load factor and for the collapse of the answer; the instruction capacity was about 37-38 rules at a share of right replacements of 0.95, and about 18-19 rules at the full replacement density. The code of the instrument, the measurement data and the passport are open, and every number of the passport is recomputed from the published points. The passport of a model serves as the calibration of a future meter of the instruction load of prompts.

The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack of a reliable bandwidth selector; practitioners currently rely on iterative optimization methods that are computationally expensive and prone to instability. We derive the ``Beta Reference Rule,'' a fast, closed-form bandwidth selector based on the unweighted Asymptotic Mean Integrated Squared Error (AMISE) of a beta reference distribution. To address boundary integrability issues, we introduce a principled heuristic for U-shaped and J-shaped distributions. By employing a method-of-moments approximation, we reduce the bandwidth selection complexity from iterative optimization to O(1). Extensive Monte Carlo simulations demonstrate that our rule matches the accuracy of numerical optimization while delivering a speedup of over 35,000 times. Real-world validation on socioeconomic data shows that it avoids the ``vanishing boundary'' and ``shoulder'' artifacts common to Gaussian-based methods. We provide a comprehensive, open-source Python package to facilitate the immediate adoption of the Beta kernel as a drop-in replacement for standard density estimation tools.

Feature preprocessing continues to play a critical role when applying machine learning and statistical methods to tabular data. In this paper, we propose the use of the kernel density integral transformation as a feature preprocessing step. Our approach subsumes the two leading feature preprocessing methods as limiting cases: linear min-max scaling and quantile transformation. We demonstrate that, without hyperparameter tuning, the kernel density integral transformation can be used as a simple drop-in replacement for either method, offering protection from the weaknesses of each. Alternatively, with tuning of a single continuous hyperparameter, we frequently outperform both of these methods. Finally, we show that the kernel density transformation can be profitably applied to statistical data analysis, particularly in correlation analysis and univariate clustering.

We present OrbNet Denali, a machine learning model for electronic structure that is designed as a drop-in replacement for ground-state density functional theory (DFT) energy calculations. The model is a message-passing neural network that uses symmetry-adapted atomic orbital features from a low-cost quantum calculation to predict the energy of a molecule. OrbNet Denali is trained on a vast dataset of 2.3 million DFT calculations on molecules and geometries. This dataset covers the most common elements in bio- and organic chemistry (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, I) as well as charged molecules. OrbNet Denali is demonstrated on several well-established benchmark datasets, and we find that it provides accuracy that is on par with modern DFT methods while offering a speedup of up to three orders of magnitude. For the GMTKN55 benchmark set, OrbNet Denali achieves WTMAD-1 and WTMAD-2 scores of 7.19 and 9.84, on par with modern DFT functionals. For several GMTKN55 subsets, which contain chemical problems that are not present in the training set, OrbNet Denali produces a mean absolute error comparable to those of DFT methods. For the Hutchison conformers benchmark set, OrbNet Denali has a median correlation coefficient of R^2=0.90 compared to the reference DLPNO-CCSD(T) calculation, and R^2=0.97 compared to the method used to generate the training data (wB97X-D3/def2-TZVP), exceeding the performance of any other method with a similar cost. Similarly, the model reaches chemical accuracy for non-covalent interactions in the S66x10 dataset. For torsional profiles, OrbNet Denali reproduces the torsion profiles of wB97X-D3/def2-TZVP with an average MAE of 0.12 kcal/mol for the potential energy surfaces of the diverse fragments in the TorsionNet500 dataset.

The theories of offline and online reinforcement learning, despite having evolved in parallel, have begun to show signs of the possibility for a unification, with algorithms and analysis techniques for one setting often having natural counterparts in the other. However, the notion of density ratio modeling, an emerging paradigm in offline RL, has been largely absent from online RL, perhaps for good reason: the very existence and boundedness of density ratios relies on access to an exploratory dataset with good coverage, but the core challenge in online RL is to collect such a dataset without having one to start. In this work we show -- perhaps surprisingly -- that density ratio-based algorithms have online counterparts. Assuming only the existence of an exploratory distribution with good coverage, a structural condition known as coverability (Xie et al., 2023), we give a new algorithm (GLOW) that uses density ratio realizability and value function realizability to perform sample-efficient online exploration. GLOW addresses unbounded density ratios via careful use of truncation, and combines this with optimism to guide exploration. GLOW is computationally inefficient; we complement it with a more efficient counterpart, HyGLOW, for the Hybrid RL setting (Song et al., 2022) wherein online RL is augmented with additional offline data. HyGLOW is derived as a special case of a more general meta-algorithm that provides a provable black-box reduction from hybrid RL to offline RL, which may be of independent interest.

Material replacement is a common interior-design operation: changing the material of a selected surface while preserving its geometry, surroundings, and illumination. Despite its commercial relevance, no public benchmark isolates this task, and evaluating it is challenging. Reference-based metrics penalize valid outputs in this inherently one-to-many setting, favor the style of the reference generator, and cannot fairly compare editors that receive different forms of guidance. We introduce MatReplace, a reference-free benchmark that evaluates edits along four verifiable dimensions: local material correctness, global lighting harmony, outside preservation, and inside structure. It defines three tracks that vary one conditioning signal at a time: (A) instruction only, (B) instruction plus region mask, and (C) material reference image instead of instruction. Our results reveal a clear divide between naming and visually grounding materials. In Track A, leading closed-source editors achieve exemplar-level material rendering and surpass the exemplar anchor under our primary aggregate. In Track B, masks help only mask-compatible models with weak scene preservation, with task-paired, single-seed effects ranging from +0.137 to -0.090 across aligned model families. In Track C, reference-image conditioning degrades every family under both aggregates, by -0.031 to -0.508; in the worst cases, models repaint the reference image itself and perform worse than returning the input unchanged. Thus, named-material rendering is largely solved by the strongest closed editors on this distribution, but grounding materials from pixels remains an open challenge. Expert ratings validate our ranking (Kendall's tau = 0.68) and align with our aggregates more closely than GT-referenced or CLIP-based baselines.

The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities, for example the normal, while not losing much in precision when the true density is far from the parametric class. The idea is to multiply an initial parametric density estimate with a kernel type estimate of the necessary correction factor. This works well in cases where the correction factor function is less rough than the original density itself. Extensive comparisons with the kernel estimator are carried out, including exact analysis for the class of all normal mixtures. The new method, with a normal start, wins quite often, even in many cases where the true density is far from normal. Procedures for choosing the smoothing parameter of the estimator are also discussed. The new estimator should be particularly useful in higher dimensions, where the usual nonparametric methods have problems. The idea is also spelled out for nonparametric regression.

Explicit density learners are becoming an increasingly popular technique for generative models because of their ability to better model probability distributions. They have advantages over Generative Adversarial Networks due to their ability to perform density estimation and having exact latent-variable inference. This has many advantages, including: being able to simply interpolate, calculate sample likelihood, and analyze the probability distribution. The downside of these models is that they are often more difficult to train and have lower sampling quality. Normalizing flows are explicit density models, that use composable bijective functions to turn an intractable probability function into a tractable one. In this work, we present novel knowledge distillation techniques to increase sampling quality and density estimation of smaller student normalizing flows. We seek to study the capacity of knowledge distillation in Compositional Normalizing Flows to understand the benefits and weaknesses provided by these architectures. Normalizing flows have unique properties that allow for a non-traditional forms of knowledge transfer, where we can transfer that knowledge within intermediate layers. We find that through this distillation, we can make students significantly smaller while making substantial performance gains over a non-distilled student. With smaller models there is a proportionally increased throughput as this is dependent upon the number of bijectors, and thus parameters, in the network.

Devising indicative evaluation metrics for the image generation task remains an open problem. The most widely used metric for measuring the similarity between real and generated images has been the Fr\'echet Inception Distance (FID) score. Because it does not differentiate the fidelity and diversity aspects of the generated images, recent papers have introduced variants of precision and recall metrics to diagnose those properties separately. In this paper, we show that even the latest version of the precision and recall metrics are not reliable yet. For example, they fail to detect the match between two identical distributions, they are not robust against outliers, and the evaluation hyperparameters are selected arbitrarily. We propose density and coverage metrics that solve the above issues. We analytically and experimentally show that density and coverage provide more interpretable and reliable signals for practitioners than the existing metrics. Code: https://github.com/clovaai/generative-evaluation-prdc.

Identifying Out-of-distribution (OOD) data is becoming increasingly critical as the real-world applications of deep learning methods expand. Post-hoc methods modify softmax scores fine-tuned on outlier data or leverage intermediate feature layers to identify distinctive patterns between In-Distribution (ID) and OOD samples. Other methods focus on employing diverse OOD samples to learn discrepancies between ID and OOD. These techniques, however, are typically dependent on the quality of the outlier samples assumed. Density-based methods explicitly model class-conditioned distributions but this requires long training time or retraining the classifier. To tackle these issues, we introduce FlowCon, a new density-based OOD detection technique. Our main innovation lies in efficiently combining the properties of normalizing flow with supervised contrastive learning, ensuring robust representation learning with tractable density estimation. Empirical evaluation shows the enhanced performance of our method across common vision datasets such as CIFAR-10 and CIFAR-100 pretrained on ResNet18 and WideResNet classifiers. We also perform quantitative analysis using likelihood plots and qualitative visualization using UMAP embeddings and demonstrate the robustness of the proposed method under various OOD contexts. Code will be open-sourced post decision.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

Large Language Models (LLMs) have emerged as a milestone in artificial intelligence, and their performance can improve as the model size increases. However, this scaling brings great challenges to training and inference efficiency, particularly for deploying LLMs in resource-constrained environments, and the scaling trend is becoming increasingly unsustainable. This paper introduces the concept of ``capacity density'' as a new metric to evaluate the quality of the LLMs across different scales and describes the trend of LLMs in terms of both effectiveness and efficiency. To calculate the capacity density of a given target LLM, we first introduce a set of reference models and develop a scaling law to predict the downstream performance of these reference models based on their parameter sizes. We then define the effective parameter size of the target LLM as the parameter size required by a reference model to achieve equivalent performance, and formalize the capacity density as the ratio of the effective parameter size to the actual parameter size of the target LLM. Capacity density provides a unified framework for assessing both model effectiveness and efficiency. Our further analysis of recent open-source base LLMs reveals an empirical law (the densing law)that the capacity density of LLMs grows exponentially over time. More specifically, using some widely used benchmarks for evaluation, the capacity density of LLMs doubles approximately every three months. The law provides new perspectives to guide future LLM development, emphasizing the importance of improving capacity density to achieve optimal results with minimal computational overhead.

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality images by mapping noise to a data distribution. However, recent findings suggest that image likelihood does not align with perceptual quality: high-likelihood samples tend to be smooth, while lower-likelihood ones are more detailed. Controlling sample density is thus crucial for balancing realism and detail. In this paper, we analyze an existing technique, Prior Guidance, which scales the latent code to influence image detail. We introduce score alignment, a condition that explains why this method works and show that it can be tractably checked for any continuous normalizing flow model. We then propose Density Guidance, a principled modification of the generative ODE that enables exact log-density control during sampling. Finally, we extend Density Guidance to stochastic sampling, ensuring precise log-density control while allowing controlled variation in structure or fine details. Our experiments demonstrate that these techniques provide fine-grained control over image detail without compromising sample quality.

Neural volume rendering became increasingly popular recently due to its success in synthesizing novel views of a scene from a sparse set of input images. So far, the geometry learned by neural volume rendering techniques was modeled using a generic density function. Furthermore, the geometry itself was extracted using an arbitrary level set of the density function leading to a noisy, often low fidelity reconstruction. The goal of this paper is to improve geometry representation and reconstruction in neural volume rendering. We achieve that by modeling the volume density as a function of the geometry. This is in contrast to previous work modeling the geometry as a function of the volume density. In more detail, we define the volume density function as Laplace's cumulative distribution function (CDF) applied to a signed distance function (SDF) representation. This simple density representation has three benefits: (i) it provides a useful inductive bias to the geometry learned in the neural volume rendering process; (ii) it facilitates a bound on the opacity approximation error, leading to an accurate sampling of the viewing ray. Accurate sampling is important to provide a precise coupling of geometry and radiance; and (iii) it allows efficient unsupervised disentanglement of shape and appearance in volume rendering. Applying this new density representation to challenging scene multiview datasets produced high quality geometry reconstructions, outperforming relevant baselines. Furthermore, switching shape and appearance between scenes is possible due to the disentanglement of the two.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open issue. With a few exceptions, deep neural networks (DNNs) have seldom been applied to density estimation, mostly due to the unsupervised nature of the estimation task, and (especially) due to the need for constrained training algorithms that ended up realizing proper probabilistic models that satisfy Kolmogorov's axioms. Moreover, in spite of the well-known improvement in terms of modeling capabilities yielded by mixture models over plain single-density statistical estimators, no proper mixtures of multivariate DNN-based component densities have been investigated so far. The paper fills this gap by extending our previous work on Neural Mixture Densities (NMMs) to multivariate DNN mixtures. A maximum-likelihood (ML) algorithm for estimating Deep NMMs (DNMMs) is handed out, which satisfies numerically a combination of hard and soft constraints aimed at ensuring satisfaction of Kolmogorov's axioms. The class of probability density functions that can be modeled to any degree of precision via DNMMs is formally defined. A procedure for the automatic selection of the DNMM architecture, as well as of the hyperparameters for its ML training algorithm, is presented (exploiting the probabilistic nature of the DNMM). Experimental results on univariate and multivariate data are reported on, corroborating the effectiveness of the approach and its superiority to the most popular statistical estimation techniques.

In this research. we analyze the potential of Feature Density (HD) as a way to comparatively estimate machine learning (ML) classifier performance prior to training. The goal of the study is to aid in solving the problem of resource-intensive training of ML models which is becoming a serious issue due to continuously increasing dataset sizes and the ever rising popularity of Deep Neural Networks (DNN). The issue of constantly increasing demands for more powerful computational resources is also affecting the environment, as training large-scale ML models are causing alarmingly-growing amounts of CO2, emissions. Our approach 1s to optimize the resource-intensive training of ML models for Natural Language Processing to reduce the number of required experiments iterations. We expand on previous attempts on improving classifier training efficiency with FD while also providing an insight to the effectiveness of various linguistically-backed feature preprocessing methods for dialog classification, specifically cyberbullying detection.

Proposed as blanket structural materials for fusion power reactors, reduced activation ferritic/martensitic (RAFM) steel undergoes volume expanding and contracting in a cyclic mode under service environment. Particularly, being subjected to significant fluxes of fusion neutrons RAFM steel suffers considerable local volume variations in the radiation damage involved regions. It is necessary to study the structure properties of the alloying elements in contraction and expansion states. In this paper we studied local substitution structures of thirteen alloying elements Al, Co, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ta, Ti, V, and W in bcc Fe and calculated their substitutional energies in the volume variation range from -1.0% to 1.0%. From the structure relaxation results of the first five neighbor shells around the substitutional atom we find the relaxation in each neighbor shell keeps approximately uniform within the volume variation from -1.0% to 1.0% except those of Mn and the relaxation of the fifth neighbor shell is stronger than that of the third and forth, indicating that the lattice distortion due to the substitution atom is easier to spread in <111> direction than in other direction. The relaxation pattern and intensity are related to the size and electron structure of the substitutional atom. For some alloying elements, such as Mo, Nb, Ni, Ta, Ti and W, the substitutional energy decreases noticeably when the volume increases. Further analysis show that the substitutional energy comprises the energy variation originated from local structure relaxation and the chemical potential difference of the substitutional atom between its elemental crystalline state and the solid solution phase in bcc Fe. We think the approximately uniform relaxation of each neighbor shell around a substitutional atom give rise to a linear decrease in the substitutional energy with the increasing volume.

Deep generative models have been demonstrated as state-of-the-art density estimators. Yet, recent work has found that they often assign a higher likelihood to data from outside the training distribution. This seemingly paradoxical behavior has caused concerns over the quality of the attained density estimates. In the context of hierarchical variational autoencoders, we provide evidence to explain this behavior by out-of-distribution data having in-distribution low-level features. We argue that this is both expected and desirable behavior. With this insight in hand, we develop a fast, scalable and fully unsupervised likelihood-ratio score for OOD detection that requires data to be in-distribution across all feature-levels. We benchmark the method on a vast set of data and model combinations and achieve state-of-the-art results on out-of-distribution detection.

The training of large language models (LLMs) is expensive. In this paper, we study data-efficient approaches for pre-training LLMs, i.e., techniques that aim to optimize the Pareto frontier of model quality and training resource/data consumption. We seek to understand the tradeoffs associated with data selection routines based on (i) expensive-to-compute data-quality estimates, and (ii) maximization of coverage and diversity-based measures in the feature space. Our first technique, Ask-LLM, leverages the zero-shot reasoning capabilities of instruction-tuned LLMs to directly assess the quality of a training example. To target coverage, we propose Density sampling, which models the data distribution to select a diverse sample. In our comparison of 19 samplers, involving hundreds of evaluation tasks and pre-training runs, we find that Ask-LLM and Density are the best methods in their respective categories. Coverage sampling can recover the performance of the full data, while models trained on Ask-LLM data consistently outperform full-data training -- even when we reject 90% of the original dataset, while converging up to 70% faster.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required during training by using an alternative infinite series for the gradient. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid derivative saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.

Direct Preference Optimization (DPO) and its variants are increasingly used for aligning language models with human preferences. Although these methods are designed to teach a model to generate preferred responses more frequently relative to dispreferred responses, prior work has observed that the likelihood of preferred responses often decreases during training. The current work sheds light on the causes and implications of this counter-intuitive phenomenon, which we term likelihood displacement. We demonstrate that likelihood displacement can be catastrophic, shifting probability mass from preferred responses to responses with an opposite meaning. As a simple example, training a model to prefer No over Never can sharply increase the probability of Yes. Moreover, when aligning the model to refuse unsafe prompts, we show that such displacement can unintentionally lead to unalignment, by shifting probability mass from preferred refusal responses to harmful responses (e.g., reducing the refusal rate of Llama-3-8B-Instruct from 74.4% to 33.4%). We theoretically characterize that likelihood displacement is driven by preferences that induce similar embeddings, as measured by a centered hidden embedding similarity (CHES) score. Empirically, the CHES score enables identifying which training samples contribute most to likelihood displacement in a given dataset. Filtering out these samples effectively mitigated unintentional unalignment in our experiments. More broadly, our results highlight the importance of curating data with sufficiently distinct preferences, for which we believe the CHES score may prove valuable.

Recent advances in generative modeling have enabled significant progress in structure-based drug design (SBDD). Existing methods typically condition molecule generation on empty binding pockets from holo complexes, overlooking informative components such as the filler (ligands and solvent). Here, we leverage low-resolution electron density (ED) derived from the filler as a physically grounded condition for de novo drug design. We consider two types of ED, calculated and cryo-EM/X-ray, obtainable from computational or experimental sources, supporting unified pre-training and experimental integration. Compared with rigid pocket representations, experimental ED naturally captures conformational flexibility and provides a more faithful description of the binding environment. Based on this, we introduce EDMolGPT, a decoder-only autoregressive framework that generates molecules from low-resolution ED point clouds. By grounding generation in physically meaningful density signals, EDMolGPT mitigates structural bias and produces molecules with 3D conformations. Evaluations on 101 biological targets verify the effectiveness. Our project page: https://jiahaochen1.github.io/EDMolGPT_Page/.

With significant advancements in diffusion models, addressing the potential risks of dataset bias becomes increasingly important. Since generated outputs directly suffer from dataset bias, mitigating latent bias becomes a key factor in improving sample quality and proportion. This paper proposes time-dependent importance reweighting to mitigate the bias for the diffusion models. We demonstrate that the time-dependent density ratio becomes more precise than previous approaches, thereby minimizing error propagation in generative learning. While directly applying it to score-matching is intractable, we discover that using the time-dependent density ratio both for reweighting and score correction can lead to a tractable form of the objective function to regenerate the unbiased data density. Furthermore, we theoretically establish a connection with traditional score-matching, and we demonstrate its convergence to an unbiased distribution. The experimental evidence supports the usefulness of the proposed method, which outperforms baselines including time-independent importance reweighting on CIFAR-10, CIFAR-100, FFHQ, and CelebA with various bias settings. Our code is available at https://github.com/alsdudrla10/TIW-DSM.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to couple the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

The dynamic imbalance of the fore-background is a major challenge in video object counting, which is usually caused by the sparsity of target objects. This remains understudied in existing works and often leads to severe under-/over-prediction errors. To tackle this issue in video object counting, we propose a density-embedded Efficient Masked Autoencoder Counting (E-MAC) framework in this paper. To empower the model's representation ability on density regression, we develop a new Density-Embedded Masked mOdeling (DEMO) method, which first takes the density map as an auxiliary modality to perform multimodal self-representation learning for image and density map. Although DEMO contributes to effective cross-modal regression guidance, it also brings in redundant background information, making it difficult to focus on the foreground regions. To handle this dilemma, we propose an efficient spatial adaptive masking derived from density maps to boost efficiency. Meanwhile, we employ an optical flow-based temporal collaborative fusion strategy to effectively capture the dynamic variations across frames, aligning features to derive multi-frame density residuals. The counting accuracy of the current frame is boosted by harnessing the information from adjacent frames. In addition, considering that most existing datasets are limited to human-centric scenarios, we first propose a large video bird counting dataset, DroneBird, in natural scenarios for migratory bird protection. Extensive experiments on three crowd datasets and our DroneBird validate our superiority against the counterparts. The code and dataset are available.

Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of efficiently finding a global optimum of an expensive-to-evaluate black-box function. In general, a probabilistic regression model is widely used as a surrogate function to model an explicit distribution over function evaluations given an input to estimate and a training dataset. Beyond the probabilistic regression-based methods, density ratio estimation-based Bayesian optimization has been suggested in order to estimate a density ratio of the groups relatively close and relatively far to a global optimum. Developing this line of research further, supervised classifiers are employed to estimate a class probability for the two groups instead of a density ratio. However, the supervised classifiers used in this strategy are prone to be overconfident for known knowledge on global solution candidates. Supposing that we have access to unlabeled points, e.g., predefined fixed-size pools, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning to solve this challenge. Finally, we show the empirical results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool, and analyze the validity of our methods in diverse experiments.

Breast density estimation is one of the key tasks in recognizing individuals predisposed to breast cancer. It is often challenging because of low contrast and fluctuations in mammograms' fatty tissue background. Most of the time, the breast density is estimated manually where a radiologist assigns one of the four density categories decided by the Breast Imaging and Reporting Data Systems (BI-RADS). There have been efforts in the direction of automating a breast density classification pipeline. Breast density estimation is one of the key tasks performed during a screening exam. Dense breasts are more susceptible to breast cancer. The density estimation is challenging because of low contrast and fluctuations in mammograms' fatty tissue background. Traditional mammograms are being replaced by tomosynthesis and its other low radiation dose variants (for example Hologic' Intelligent 2D and C-View). Because of the low-dose requirement, increasingly more screening centers are favoring the Intelligent 2D view and C-View. Deep-learning studies for breast density estimation use only a single modality for training a neural network. However, doing so restricts the number of images in the dataset. In this paper, we show that a neural network trained on all the modalities at once performs better than a neural network trained on any single modality. We discuss these results using the area under the receiver operator characteristics curves.

Reinforcement learning from human feedback (RLHF) for 3D generation is now established across a number of works, but most existing pipelines optimise explicit surface representations, often by converting radiance fields into meshes and training heavily on surface-supervised data. We instead fine-tune a pretrained 3D-aware generative model directly from a learned reward over radiance-field density (σ) values, with no externally supplied mesh or shape prior. The reward model requires no pretraining, trains easily on a small set of preference samples, and yields robust improvement in 3D geometry. Working on an unconditional 3D-aware face GAN (EG3D), our reward reads the continuous 3D density field of the neural radiance field (NeRF) directly and supplies a geometry-only learning signal, requiring neither text conditioning, mesh extraction, nor multi-view rendering. A density-consistency constraint keeps the 2D appearance qualitatively similar while the geometry is reshaped, at a measurable but bounded distributional cost (FID-50k rises from 4.09 to 6.66): the fine-tuned generator, trained from the preferences of a single annotator as a proof of concept, produces face geometries preferred by users in 74.4% of pairwise comparisons.

Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the distribution of potential outcomes. In this work, we estimate the density of potential outcomes after interventions from observational data. For this, we propose a novel, fully-parametric deep learning method called Interventional Normalizing Flows. Specifically, we combine two normalizing flows, namely (i) a nuisance flow for estimating nuisance parameters and (ii) a target flow for parametric estimation of the density of potential outcomes. We further develop a tractable optimization objective based on a one-step bias correction for efficient and doubly robust estimation of the target flow parameters. As a result, our Interventional Normalizing Flows offer a properly normalized density estimator. Across various experiments, we demonstrate that our Interventional Normalizing Flows are expressive and highly effective, and scale well with both sample size and high-dimensional confounding. To the best of our knowledge, our Interventional Normalizing Flows are the first proper fully-parametric, deep learning method for density estimation of potential outcomes.

Estimating truncated density models is difficult, as these models have intractable normalising constants and hard to satisfy boundary conditions. Score matching can be adapted to solve the truncated density estimation problem, but requires a continuous weighting function which takes zero at the boundary and is positive elsewhere. Evaluation of such a weighting function (and its gradient) often requires a closed-form expression of the truncation boundary and finding a solution to a complicated optimisation problem. In this paper, we propose approximate Stein classes, which in turn leads to a relaxed Stein identity for truncated density estimation. We develop a novel discrepancy measure, truncated kernelised Stein discrepancy (TKSD), which does not require fixing a weighting function in advance, and can be evaluated using only samples on the boundary. We estimate a truncated density model by minimising the Lagrangian dual of TKSD. Finally, experiments show the accuracy of our method to be an improvement over previous works even without the explicit functional form of the boundary.

A prominent family of methods for learning data distributions relies on density ratio estimation (DRE), where a model is trained to classify between data samples and samples from some reference distribution. DRE-based models can directly output the likelihood for any given input, a highly desired property that is lacking in most generative techniques. Nevertheless, to date, DRE methods have failed in accurately capturing the distributions of complex high-dimensional data, like images, and have thus been drawing reduced research attention in recent years. In this work we present classification diffusion models (CDMs), a DRE-based generative method that adopts the formalism of denoising diffusion models (DDMs) while making use of a classifier that predicts the level of noise added to a clean signal. Our method is based on an analytical connection that we derive between the MSE-optimal denoiser for removing white Gaussian noise and the cross-entropy-optimal classifier for predicting the noise level. Our method is the first DRE-based technique that can successfully generate images beyond the MNIST dataset. Furthermore, it can output the likelihood of any input in a single forward pass, achieving state-of-the-art negative log likelihood (NLL) among methods with this property. Code is available on the project's webpage in https://shaharYadin.github.io/CDM/ .

Density ratio estimation is fundamental to tasks involving f-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports -- the density-chasm and the support-chasm problems. Additionally, prior approaches yield divergent time scores near boundaries, leading to instability. We design D^3RE, a unified framework for robust, stable and efficient density ratio estimation. We propose the dequantified diffusion bridge interpolant (DDBI), which expands support coverage and stabilizes time scores via diffusion bridges and Gaussian dequantization. Building on DDBI, the proposed dequantified Schr{\"o}dinger bridge interpolant (DSBI) incorporates optimal transport to solve the Schr{\"o}dinger bridge problem, enhancing accuracy and efficiency. Our method offers uniform approximation and bounded time scores in theory, and outperforms baselines empirically in mutual information and density estimation tasks.

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.

Recent advances in diffusion models bring state-of-the-art performance on image generation tasks. However, empirical results from previous research in diffusion models imply an inverse correlation between density estimation and sample generation performances. This paper investigates with sufficient empirical evidence that such inverse correlation happens because density estimation is significantly contributed by small diffusion time, whereas sample generation mainly depends on large diffusion time. However, training a score network well across the entire diffusion time is demanding because the loss scale is significantly imbalanced at each diffusion time. For successful training, therefore, we introduce Soft Truncation, a universally applicable training technique for diffusion models, that softens the fixed and static truncation hyperparameter into a random variable. In experiments, Soft Truncation achieves state-of-the-art performance on CIFAR-10, CelebA, CelebA-HQ 256x256, and STL-10 datasets.

Inference-time steering enables pretrained diffusion/flow models to be adapted to new tasks without retraining. A widely used approach is the ratio-of-densities method, which defines a time-indexed target path by reweighting probability-density trajectories from multiple models with positive, or in some cases, negative exponents. This construction, however, harbors a critical and previously unformalized failure mode: Marginal Path Collapse, where intermediate densities become non-normalizable even though endpoints remain valid. Collapse arises systematically when composing heterogeneous models trained on different noise schedules or datasets, including a common setting in molecular design where de-novo, conformer, and pocket-conditioned models must be combined for tasks such as flexible-pose scaffold decoration. We provide a novel and complete solution for the problem. First, we derive a simple path existence criterion that predicts exactly when collapse occurs from noise schedules and exponents alone. Second, we introduce Adaptive path Correction with Exponents (ACE), which extends Feynman-Kac steering to time-varying exponents and guarantees a valid probability path. On a synthetic 2D benchmark and on flexible-pose scaffold decoration, ACE eliminates collapse and enables high-guidance compositional generation, improving distributional and docking metrics over constant-exponent baselines and even specialized task-specific scaffold decoration models. Our work turns ratio-of-densities steering with heterogeneous experts from an unstable heuristic into a reliable tool for controllable generation.

Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction error is the squared error, and the data is continuous-valued. This has led to various proposals for sampling from this implicitly learned density function, using Langevin and Metropolis-Hastings MCMC. However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying data-generating distribution when the data are discrete, or using other forms of corruption process and reconstruction errors. Another issue is the mathematical justification which is only valid in the limit of small corruption noise. We propose here a different attack on the problem, which deals with all these issues: arbitrary (but noisy enough) corruption, arbitrary reconstruction loss (seen as a log-likelihood), handling both discrete and continuous-valued variables, and removing the bias due to non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).

Benchmark contamination is diagnosed with n-gram overlap, likelihood-based membership inference, or canary strings, and each needs something usually unavailable: the training corpus, a well-chosen test statistic, or foresight at release. A recent alternative reads it off a linear probe on internal activations. We show the natural way to do this does not work, specify one that survives measurement, then find that the correction making it work carries more variance than the null it is tested against. The protocol reports a zero-sum contrast on the depth profile of probe accuracy, recentred on a level-matched placebo baseline, tested against a label-permutation null, with the reference set twice the size of the suspect set. Each choice replaces a simpler alternative we rejected on measurement. Reporting the level of excess separability rather than its shape makes the false positive rate track the size of the analyst's own control set, 0.03 to 0.99 under a true null. Contrasting against a flat depth profile rejects a true null 0.72 of the time when surface decodability rises with depth, and loses all power when it falls. On real transformers the protocol fails a test the simulations did not pose. The recentring subtracts an estimate, and the permutation null holds it fixed. Re-estimated across split seeds on four audits of contaminated checkpoints, its standard deviation is 1.30 to 1.56 times the null's own in every arm: what is subtracted to remove a bias is more variable than what it corrects. The one nominally significant result, p = 0.0075, becomes 0.0745 once that variance is propagated, and no verdict is issued. The simulations missed this because their surface key is the covariate driving item variation; on real text it is a proxy, and degrading key quality in simulation reproduces it. We add a companion measurement and a widened null. No arm shows contamination.

A deep understanding of the physical world is a central goal for embodied AI and realistic simulation. While current models excel at capturing an object's surface geometry and appearance, they largely neglect its internal physical properties. This omission is critical, as properties like volumetric density are fundamental for predicting an object's center of mass, stability, and interaction dynamics in applications ranging from robotic manipulation to physical simulation. The primary bottleneck has been the absence of large-scale, real-world data. To bridge this gap, we introduce XDen-1K, the first large-scale, multi-modal dataset designed for real-world physical property estimation, with a particular focus on volumetric density. The core of this dataset consists of 1,000 real-world objects across 148 categories, for which we provide comprehensive multi-modal data, including a high-resolution 3D geometric model with part-level annotations and a corresponding set of real-world biplanar X-ray scans. Building upon this data, we introduce a novel optimization framework that recovers a high-fidelity volumetric density field of each object from its sparse X-ray views. To demonstrate its practical value, we add X-ray images as a conditioning signal to an existing segmentation network and perform volumetric segmentation. Furthermore, we conduct experiments on downstream robotics tasks. The results show that leveraging the dataset can effectively improve the accuracy of center-of-mass estimation and the success rate of robotic manipulation. We believe XDen-1K will serve as a foundational resource and a challenging new benchmark, catalyzing future research in physically grounded visual inference and embodied AI.

Multi-reward reinforcement learning trains large language models to satisfy multiple behavioral objectives simultaneously. Reward-wise normalization, as used in GDPO, preserves reward-specific relative information within rollout groups, but different objectives can still exhibit uneven learning progress. We study this behavior through advantage energy, the sum of a reward's squared advantages over a batch. Under idealized GDPO normalization, we show that this energy is proportional to active-group density: the fraction of rollout groups in which the reward provides nonzero relative advantages. This reveals a residual batch-level signal imbalance and provides a basis for calibrating reward contributions. Based on this relation, we propose Density-Aware Reward Aggregation (DARA). We derive an inverse-square-root density correction that gives greater weight to signals from less frequently active rewards. DARA computes its weights from each rollout batch, adapting to changes in reward activity throughout training without modifying the underlying policy optimization objective. Experiments on tool calling and mathematical reasoning show that DARA learns the targeted behaviors faster than GDPO, reaching high format compliance in up to 26% fewer training steps on tool calling and near-saturated length compliance in up to 65% fewer steps on mathematical reasoning, while remaining competitive in final performance. Our code is available at https://github.com/zhaihaotian/DARA.

End-to-end training with full-depth backpropagation remains the dominant paradigm for optimizing deep neural networks, but its efficiency deteriorates as models grow deeper. Since every block must be executed and differentiated under a single global objective, full-depth BP introduces substantial parameter redundancy, activation-memory cost, and training latency, especially when neighboring layers exhibit highly correlated learning patterns. Directly skipping or removing layers can reduce cost, but often weakens representation capacity or requires architecture-specific reuse designs. In this paper, we propose Replacement Learning (RepL), a training-time paradigm that reduces full-depth redundancy by replacing selected blocks rather than simply discarding them. For each removed block, RepL inserts a lightweight computing layer that synthesizes a surrogate operator from the parameters of its adjacent preceding and succeeding blocks through a learnable transformation, and applies the synthesized operator to the preceding activation. In this way, RepL preserves local contextual continuity while avoiding unnecessary full-layer computation. We instantiate RepL for CNNs and ViTs with tailored parameter-fusion blocks that handle convolutional channels, feature resolutions, and transformer submodules. Extensive experiments on CIFAR-10, SVHN, STL-10, ImageNet, COCO, and CityScapes show that RepL reduces trainable parameters, GPU memory usage, and training time while matching or surpassing standard end-to-end training across classification, detection, and segmentation. Additional results on WikiText-2, transfer learning, inference throughput, checkpointing, stochastic depth, and INT8 quantization further demonstrate its generality and compatibility.

The study conducted by Shumailov et al. (2024) demonstrates that repeatedly training a generative model on synthetic data leads to model collapse. This finding has generated considerable interest and debate, particularly given that current models have nearly exhausted the available data. In this work, we investigate the effects of fitting a distribution (through Kernel Density Estimation, or KDE) or a model to the data, followed by repeated sampling from it. Our objective is to develop a theoretical understanding of the phenomenon observed by Shumailov et al. (2024). Our results indicate that the outcomes reported are a statistical phenomenon and may be unavoidable.

A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be used if the transformation is specified by an ordinary differential equation. In this paper, we use Hutchinson's trace estimator to give a scalable unbiased estimate of the log-density. The result is a continuous-time invertible generative model with unbiased density estimation and one-pass sampling, while allowing unrestricted neural network architectures. We demonstrate our approach on high-dimensional density estimation, image generation, and variational inference, achieving the state-of-the-art among exact likelihood methods with efficient sampling.