Daily Papers

Understanding and controlling the behavior of large language models (LLMs) is an increasingly important topic in multilingual NLP. Beyond prompting or fine-tuning, , i.e.,~manipulating internal representations during inference, has emerged as a more efficient and interpretable technique for adapting models to a target language. Yet, no dedicated benchmarks or evaluation protocols exist to quantify the effectiveness of steering techniques. We introduce CLaS-Bench, a lightweight parallel-question benchmark for evaluating language-forcing behavior in LLMs across 32 languages, enabling systematic evaluation of multilingual steering methods. We evaluate a broad array of steering techniques, including residual-stream DiffMean interventions, probe-derived directions, language-specific neurons, PCA/LDA vectors, Sparse Autoencoders, and prompting baselines. Steering performance is measured along two axes: language control and semantic relevance, combined into a single harmonic-mean steering score. We find that across languages simple residual-based DiffMean method consistently outperforms all other methods. Moreover, a layer-wise analysis reveals that language-specific structure emerges predominantly in later layers and steering directions cluster based on language family. CLaS-Bench is the first standardized benchmark for multilingual steering, enabling both rigorous scientific analysis of language representations and practical evaluation of steering as a low-cost adaptation alternative.

Interpretability methods for large language models (LLMs) typically derive directions from textual supervision, which can lack external grounding. We propose using human brain activity not as a training signal but as a coordinate system for reading and steering LLM states. Using the SMN4Lang MEG dataset, we construct a word-level brain atlas of phase-locking value (PLV) patterns and extract latent axes via ICA. We validate axes with independent lexica and NER-based labels (POS/log-frequency used as sanity checks), then train lightweight adapters that map LLM hidden states to these brain axes without fine-tuning the LLM. Steering along the resulting brain-derived directions yields a robust lexical (frequency-linked) axis in a mid TinyLlama layer, surviving perplexity-matched controls, and a brain-vs-text probe comparison shows larger log-frequency shifts (relative to the text probe) with lower perplexity for the brain axis. A function/content axis (axis 13) shows consistent steering in TinyLlama, Qwen2-0.5B, and GPT-2, with PPL-matched text-level corroboration. Layer-4 effects in TinyLlama are large but inconsistent, so we treat them as secondary (Appendix). Axis structure is stable when the atlas is rebuilt without GPT embedding-change features or with word2vec embeddings (|r|=0.64-0.95 across matched axes), reducing circularity concerns. Exploratory fMRI anchoring suggests potential alignment for embedding change and log frequency, but effects are sensitive to hemodynamic modeling assumptions and are treated as population-level evidence only. These results support a new interface: neurophysiology-grounded axes provide interpretable and controllable handles for LLM behavior.

Probing studies what information is encoded in a frozen LLM's layer representations by training a lightweight predictor on top of them. Beyond analysis, probes are often used operationally in probe-then-steer pipelines: a learned concept vector is extracted from a probe and injected via additive activation steering by adding it to a layer representation during the forward pass. The effectiveness of this pipeline hinges on estimating concept vectors that are accurate, directionally stable under ablation, and inexpensive to obtain. Motivated by these desiderata, we propose RAPTOR (Ridge-Adaptive Logistic Probe), a simple L2-regularized logistic probe whose validation-tuned ridge strength yields concept vectors from normalized weights. Across extensive experiments on instruction-tuned LLMs and human-written concept datasets, RAPTOR matches or exceeds strong baselines in accuracy while achieving competitive directional stability and substantially lower training cost; these quantitative results are supported by qualitative downstream steering demonstrations. Finally, using the Convex Gaussian Min-max Theorem (CGMT), we provide a mechanistic characterization of ridge logistic regression in an idealized Gaussian teacher-student model in the high-dimensional few-shot regime, explaining how penalty strength mediates probe accuracy and concept-vector stability and yielding structural predictions that qualitatively align with trends observed on real LLM embeddings.

The polarization of an X-ray beam that produces electrons with velocity components perpendicular to the beam generates an azimuthal distribution of the ejected electrons. We present methods for simulating and for analyzing the angular dependence of electron detections which enable us to derive simple analytical expressions for useful statistical properties of observable data. The derivations are verified by simulations. While we confirm the results of previous work on this topic, we provide an extension needed for analytical treatment of the full range of possible polarization amplitudes.

We present a new approach to constructing and fitting dipoles and higher-order multipoles in synthetic galaxy samples over the sky. Within our Bayesian paradigm, we illustrate that this technique is robust to masked skies, allowing us to make credible inferences about the relative contributions of each multipole. We also show that dipoles can be recovered in surveys with small footprints, determining the requisite source counts required for concrete estimation of the dipole parameters. This work is motivated by recent probes of the cosmic dipole in galaxy catalogues. Namely, the kinematic dipole of the Cosmic Microwave Background, as arising from the motion of our heliocentric frame at approx 370 km,s^{-1}, implies that an analogous dipole should be observed in the number counts of galaxies in flux-density-limited samples. Recent studies have reported a dipole aligning with the kinematic dipole but with an anomalously large amplitude. Accordingly, our new technique will be important as forthcoming galaxy surveys are made available and for revisiting previous data.

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant when guidance scale is large. To address this issue, we propose characteristic guidance, a guidance method that provides first-principle non-linear correction for classifier-free guidance. Such correction forces the guided DDPMs to respect the Fokker-Planck (FP) equation of diffusion process, in a way that is training-free and compatible with existing sampling methods. Experiments show that characteristic guidance enhances semantic characteristics of prompts and mitigate irregularities in image generation, proving effective in diverse applications ranging from simulating magnet phase transitions to latent space sampling.

We present the wakefield conformal mapping technique that can be readily applied to the analysis of the radiation generated by an ultra-relativistic particle in the step transition and a collimator. We derive simple analytical expressions for the lower and upper bounds of both longitudinal and transverse wake potentials. We test the derived expressions against well-known formulas in several representative examples. The proposed method can greatly simplify the optimization of collimating sections, as well as become a useful tool in the shape optimization problems.

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

Training-free guided generation is a widely used and powerful technique that allows the end user to exert further control over the generative process of flow/diffusion models. Generally speaking, two families of techniques have emerged for solving this problem for gradient-based guidance: namely, posterior guidance (i.e., guidance via projecting the current sample to the target distribution via the target prediction model) and end-to-end guidance (i.e., guidance by performing backpropagation throughout the entire ODE solve). In this work, we show that these two seemingly separate families can actually be unified by looking at posterior guidance as a greedy strategy of end-to-end guidance. We explore the theoretical connections between these two families and provide an in-depth theoretical of these two techniques relative to the continuous ideal gradients. Motivated by this analysis we then show a method for interpolating between these two families enabling a trade-off between compute and accuracy of the guidance gradients. We then validate this work on several inverse image problems and property-guided molecular generation.

Geomagnetic map interpolation aims to infer unobserved geomagnetic data at spatial points, yielding critical applications in navigation and resource exploration. However, existing methods for scattered data interpolation are not specifically designed for geomagnetic maps, which inevitably leads to suboptimal performance due to detection noise and the laws of physics. Therefore, we propose a Physics-informed Diffusion Generation framework~(PDG) to interpolate incomplete geomagnetic maps. First, we design a physics-informed mask strategy to guide the diffusion generation process based on a local receptive field, effectively eliminating noise interference. Second, we impose a physics-informed constraint on the diffusion generation results following the kriging principle of geomagnetic maps, ensuring strict adherence to the laws of physics. Extensive experiments and in-depth analyses on four real-world datasets demonstrate the superiority and effectiveness of each component of PDG.

Given sparse observations of buoy velocities, oceanographers are interested in reconstructing ocean currents away from the buoys and identifying divergences in a current vector field. As a first and modular step, we focus on the time-stationary case - for instance, by restricting to short time periods. Since we expect current velocity to be a continuous but highly non-linear function of spatial location, Gaussian processes (GPs) offer an attractive model. But we show that applying a GP with a standard stationary kernel directly to buoy data can struggle at both current reconstruction and divergence identification, due to some physically unrealistic prior assumptions. To better reflect known physical properties of currents, we propose to instead put a standard stationary kernel on the divergence and curl-free components of a vector field obtained through a Helmholtz decomposition. We show that, because this decomposition relates to the original vector field just via mixed partial derivatives, we can still perform inference given the original data with only a small constant multiple of additional computational expense. We illustrate the benefits of our method with theory and experiments on synthetic and real ocean data.

We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify the locations and shapes of moving inhomogeneities when very limited data are available, even with only one pair of lateral Cauchy data, and enjoys remarkable numerical stability for noisy data and over an extended time horizon. The method is formulated in an abstract framework, and is applicable to linear and nonlinear parabolic problems, including linear, nonlinear, and mixed-type inhomogeneities. Numerical experiments across diverse scenarios show its effectiveness and robustness against the data noise.

We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of {\pi}/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincar\'e sphere, showing that the number of near-optimal solutions behaves according to a power law with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vector-like optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.

In this paper we introduce the concept of what we call "NUDAR" (NeUtrino Direction and Ranging), making the point that measurements of the observed energy and direction vectors can be employed to passively deduce the exact three-dimensional location and thermal power of geophysical and anthropogenic neutrino sources from even a single detector. We present the most precise background estimates to date, all handled in full three dimensions, as functions of depth and geographical location. For the present calculations, we consider a hypothetical 138 kiloton detector which can be transported to an ocean site and deployed to an operational depth. We present a Bayesian estimation framework to incorporate any a priori knowledge of the reactor that we are trying to detect, as well as the estimated uncertainty in the background and the oscillation parameters. Most importantly, we fully employ the knowledge of the reactor spectrum and the distance-dependent effects of neutrino oscillations on such spectra. The latter, in particular, makes possible determination of range from one location, given adequate signal statistics. Further, we explore the rich potential of improving detection with even modest improvements in individual neutrino direction determination. We conclude that a 300 MWth reactor can indeed be geolocated, and its operating power estimated with one or two detectors in the hundred kiloton class at ranges out to a few hundred kilometers. We note that such detectors would have natural and non-interfering utility for scientific studies of geo-neutrinos, neutrino oscillations, and astrophysical neutrinos. This motivates the development of cost effective methods of constructing and deploying such next generation detectors.

Diffusion models are among the most effective methods for image generation. This is in particular because, unlike GANs, they can be easily conditioned during training to produce elements with desired class or properties. However, guiding a pre-trained diffusion model to generate elements from previously unlabeled data is significantly more challenging. One of the possible solutions was given by the ADM-G guiding approach. Although ADM-G successfully generates elements from the given class, there is a significant quality gap compared to a model originally conditioned on this class. In particular, the FID score obtained by the ADM-G-guided diffusion model is nearly three times lower than the class-conditioned guidance. We demonstrate that this issue is partly due to ADM-G providing minimal guidance during the final stage of the denoising process. To address this problem, we propose GeoGuide, a guidance model based on tracing the distance of the diffusion model's trajectory from the data manifold. The main idea of GeoGuide is to produce normalized adjustments during the backward denoising process. As shown in the experiments, GeoGuide surpasses the probabilistic approach ADM-G with respect to both the FID scores and the quality of the generated images.

An experimental demonstration of directivities exceeding the fundamental Kildal limit, a phenomenon called superdirectivity, is provided for spherical high-index dielectric antennas with an electric dipole excitation. A directivity factor of about 10 with a total efficiency of more than 80\% for an antenna having a size of a third of the wavelength was measured. High directivities are shown to be associated with constructive interference of particular electric and magnetic modes of an open spherical resonator. Both analytic solution for a point dipole and a full-wave rigorous simulation for a realistic dipole antenna were employed for optimization and analysis, yielding an excellent agreement between experimentally measured and numerically predicted directivities. The use of high-index low-loss ceramics can significantly reduce the physical size of such antennas while maintaining their overall high radiation efficiency. Such antennas can be attractive for various high-frequency applications, such as antennas for the Internet of things, smart city systems, 5G network systems, and others. The demonstrated concept can be scaled in frequency.

When solving inverse problems, it is increasingly popular to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative capability of diffusion models. Despite their success in many imaging inverse problems, most existing methods rely on privileged information such as derivative, pseudo-inverse, or full knowledge about the forward model. This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications. To address this issue, we propose Ensemble Kalman Diffusion Guidance (EnKG) for diffusion models, a derivative-free approach that can solve inverse problems by only accessing forward model evaluations and a pre-trained diffusion model prior. We study the empirical effectiveness of our method across various inverse problems, including scientific settings such as inferring fluid flows and astronomical objects, which are highly non-linear inverse problems that often only permit black-box access to the forward model.

Large language models (LLMs) exhibit distinct and consistent personalities that greatly impact trust and engagement. While this means that personality frameworks would be highly valuable tools to characterize and control LLMs' behavior, current approaches remain either costly (post-training) or brittle (prompt engineering). Probing and steering via linear directions has recently emerged as a cheap and efficient alternative. In this paper, we investigate whether linear directions aligned with the Big Five personality traits can be used for probing and steering model behavior. Using Llama 3.3 70B, we generate descriptions of 406 fictional characters and their Big Five trait scores. We then prompt the model with these descriptions and questions from the Alpaca questionnaire, allowing us to sample hidden activations that vary along personality traits in known, quantifiable ways. Using linear regression, we learn a set of per-layer directions in activation space, and test their effectiveness for probing and steering model behavior. Our results suggest that linear directions aligned with trait-scores are effective probes for personality detection, while their steering capabilities strongly depend on context, producing reliable effects in forced-choice tasks but limited influence in open-ended generation or when additional context is present in the prompt.

Despite the success of physics-informed neural networks (PINNs) in approximating partial differential equations (PDEs), PINNs can sometimes fail to converge to the correct solution in problems involving complicated PDEs. This is reflected in several recent studies on characterizing the "failure modes" of PINNs, although a thorough understanding of the connection between PINN failure modes and sampling strategies is missing. In this paper, we provide a novel perspective of failure modes of PINNs by hypothesizing that training PINNs relies on successful "propagation" of solution from initial and/or boundary condition points to interior points. We show that PINNs with poor sampling strategies can get stuck at trivial solutions if there are propagation failures, characterized by highly imbalanced PDE residual fields. To mitigate propagation failures, we propose a novel Retain-Resample-Release sampling (R3) algorithm that can incrementally accumulate collocation points in regions of high PDE residuals with little to no computational overhead. We provide an extension of R3 sampling to respect the principle of causality while solving time-dependent PDEs. We theoretically analyze the behavior of R3 sampling and empirically demonstrate its efficacy and efficiency in comparison with baselines on a variety of PDE problems.

We consider the inverse problem of reconstructing the spatial layout of a place, a home floorplan for example, from a user`s movements inside that layout. Direct inversion is ill-posed since many floorplans can explain the same movement trajectories. We adopt a diffusion-based posterior sampler to generate layouts consistent with the measurements. While active research is in progress on generative inverse solvers, we find that the forward operator in our problem poses new challenges. The path-planning process inside a floorplan is a non-invertible, non-differentiable function, and causes instability while optimizing using the likelihood score. We break-away from existing approaches and reformulate the likelihood score in a smoother embedding space. The embedding space is trained with a contrastive loss which brings compatible floorplans and trajectories close to each other, while pushing mismatched pairs far apart. We show that a surrogate form of the likelihood score in this embedding space is a valid approximation of the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent floorplans from trajectories, and is more robust than differentiable-planner baselines and guided-diffusion methods.

Recent diffusion models achieve the state-of-the-art performance in image generation, but often suffer from semantic inconsistencies or hallucinations. While various inference-time guidance methods can enhance generation, they often operate indirectly by relying on external signals or architectural modifications, which introduces additional computational overhead. In this paper, we propose Tangential Amplifying Guidance (TAG), a more efficient and direct guidance method that operates solely on trajectory signals without modifying the underlying diffusion model. TAG leverages an intermediate sample as a projection basis and amplifies the tangential components of the estimated scores with respect to this basis to correct the sampling trajectory. We formalize this guidance process by leveraging a first-order Taylor expansion, which demonstrates that amplifying the tangential component steers the state toward higher-probability regions, thereby reducing inconsistencies and enhancing sample quality. TAG is a plug-and-play, architecture-agnostic module that improves diffusion sampling fidelity with minimal computational addition, offering a new perspective on diffusion guidance.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, physics-informed generative tasks, and imaging inverse problems demonstrate the effectiveness and flexibility of the proposed framework.

Foundation models are premised on the idea that sequence prediction can uncover deeper domain understanding, much like how Kepler's predictions of planetary motion later led to the discovery of Newtonian mechanics. However, evaluating whether these models truly capture deeper structure remains a challenge. We develop a technique for evaluating foundation models that examines how they adapt to synthetic datasets generated from some postulated world model. Our technique measures whether the foundation model's inductive bias aligns with the world model, and so we refer to it as an inductive bias probe. Across multiple domains, we find that foundation models can excel at their training tasks yet fail to develop inductive biases towards the underlying world model when adapted to new tasks. We particularly find that foundation models trained on orbital trajectories consistently fail to apply Newtonian mechanics when adapted to new physics tasks. Further analysis reveals that these models behave as if they develop task-specific heuristics that fail to generalize.

Large language models (LLMs) are trained on extensive datasets that encapsulate substantial world knowledge. However, their outputs often include confidently stated inaccuracies. Earlier works suggest that LLMs encode truthfulness as a distinct linear feature, termed the "truth direction", which can classify truthfulness reliably. We address several open questions about the truth direction: (i) whether LLMs universally exhibit consistent truth directions; (ii) whether sophisticated probing techniques are necessary to identify truth directions; and (iii) how the truth direction generalizes across diverse contexts. Our findings reveal that not all LLMs exhibit consistent truth directions, with stronger representations observed in more capable models, particularly in the context of logical negation. Additionally, we demonstrate that truthfulness probes trained on declarative atomic statements can generalize effectively to logical transformations, question-answering tasks, in-context learning, and external knowledge sources. Finally, we explore the practical application of truthfulness probes in selective question-answering, illustrating their potential to improve user trust in LLM outputs. These results advance our understanding of truth directions and provide new insights into the internal representations of LLM beliefs. Our code is public at https://github.com/colored-dye/truthfulness_probe_generalization

A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods for inverse problems, the 1D boundary data in different frequencies are preprocessed by a partial differential equation-based feature map to yield 2D harmonic extensions as different input channels. Then, by introducing learnable non-local kernels, the direct sampling is recast to a modified attention mechanism. The new method achieves superior accuracy over its predecessors and contemporary operator learners and shows robustness to noises in benchmarks. This research shall strengthen the insights that, despite being invented for natural language processing tasks, the attention mechanism offers great flexibility to be modified in conformity with the a priori mathematical knowledge, which ultimately leads to the design of more physics-compatible neural architectures.

Denoising diffusion models have emerged as the go-to framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution (OOD) tasks, which remains an under-explored challenge. Realistic reconstructions inconsistent with the measured data can be generated, hallucinating image features that are uniquely present in the training dataset. To simultaneously enforce data-consistency and leverage data-driven priors, we introduce a novel sampling framework called Steerable Conditional Diffusion. This framework adapts the denoising network specifically to the available measured data. Utilising our proposed method, we achieve substantial enhancements in OOD performance across diverse imaging modalities, advancing the robust deployment of denoising diffusion models in real-world applications.

Diffusion models (DMs) have achieved remarkable success in image and video generation. However, they still struggle with (1) physical alignment and (2) out-of-distribution (OOD) instruction following. We argue that these issues stem from the models' failure to learn causal directions and to disentangle causal factors for novel recombination. We introduce the Causal Scene Graph (CSG) and the Physical Alignment Probe (PAP) dataset to enable diagnostic interventions. This analysis yields three key insights. First, DMs struggle with multi-hop reasoning for elements not explicitly determined in the prompt. Second, the prompt embedding contains disentangled representations for texture and physics. Third, visual causal structure is disproportionately established during the initial, computationally limited denoising steps. Based on these findings, we introduce LINA (Learning INterventions Adaptively), a novel framework that learns to predict prompt-specific interventions, which employs (1) targeted guidance in the prompt and visual latent spaces, and (2) a reallocated, causality-aware denoising schedule. Our approach enforces both physical alignment and OOD instruction following in image and video DMs, achieving state-of-the-art performance on challenging causal generation tasks and the Winoground dataset. Our project page is at https://opencausalab.github.io/LINA.

Radio detection is now an established technique for the study of ultra-high-energy (UHE) cosmic rays with energies above sim10^{17} eV. The next-generation of radio experiments aims to extend this technique to the observation of UHE earth-skimming neutrinos, which requires the detection of very inclined extensive air showers (EAS). In this article we present a new reconstruction method for the arrival direction and the energy of EAS. It combines a point-source-like description of the radio wavefront with a phenomenological model: the Angular Distribution Function (ADF). The ADF describes the angular distribution of the radio signal amplitude in the 50-200 MHz frequency range, with a particular focus on the Cherenkov angle, a crucial feature of the radio amplitude pattern. The method is applicable to showers with zenith angles larger than 60^circ, and in principle up to neutrino-induced showers with up-going trajectories. It is tested here on a simulated data set of EAS induced by cosmic rays. A resolution better than 4 arc-minutes (0.07^circ) is achieved on arrival direction, as well as an intrinsic resolution of 5% on the electromagnetic energy, and around 15% on the primary energy.

Astrophysical uncertainties in dark matter direct detection experiments are typically addressed by parametrizing the velocity distribution in terms of a few uncertain parameters that vary around some central values. Here we propose a method to optimize over all velocity distributions lying within a given distance measure from a central distribution. We discretize the dark matter velocity distribution as a superposition of streams, and use a variety of information divergences to parametrize its uncertainties. With this, we bracket the limits on the dark matter-nucleon and dark matter-electron scattering cross sections, when the true dark matter velocity distribution deviates from the commonly assumed Maxwell-Boltzmann form. The methodology pursued is general and could be applied to other physics scenarios where a given physical observable depends on a function that is uncertain.

Denoising Diffusion Models (DDMs) have emerged as a strong competitor to Generative Adversarial Networks (GANs). However, despite their widespread use in image synthesis and editing applications, their latent space is still not as well understood. Recently, a semantic latent space for DDMs, coined `h-space', was shown to facilitate semantic image editing in a way reminiscent of GANs. The h-space is comprised of the bottleneck activations in the DDM's denoiser across all timesteps of the diffusion process. In this paper, we explore the properties of h-space and propose several novel methods for finding meaningful semantic directions within it. We start by studying unsupervised methods for revealing interpretable semantic directions in pretrained DDMs. Specifically, we show that global latent directions emerge as the principal components in the latent space. Additionally, we provide a novel method for discovering image-specific semantic directions by spectral analysis of the Jacobian of the denoiser w.r.t. the latent code. Next, we extend the analysis by finding directions in a supervised fashion in unconditional DDMs. We demonstrate how such directions can be found by relying on either a labeled data set of real images or by annotating generated samples with a domain-specific attribute classifier. We further show how to semantically disentangle the found direction by simple linear projection. Our approaches are applicable without requiring any architectural modifications, text-based guidance, CLIP-based optimization, or model fine-tuning.

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Magnetic navigation (MagNav) is a rising alternative to the Global Positioning System (GPS) and has proven useful for aircraft navigation. Traditional aircraft navigation systems, while effective, face limitations in precision and reliability in certain environments and against attacks. Airborne MagNav leverages the Earth's magnetic field to provide accurate positional information. However, external magnetic fields induced by aircraft electronics and Earth's large-scale magnetic fields disrupt the weaker signal of interest. We introduce a physics-informed approach using Tolles-Lawson coefficients for compensation and Liquid Time-Constant Networks (LTCs) to remove complex, noisy signals derived from the aircraft's magnetic sources. Using real flight data with magnetometer measurements and aircraft measurements, we observe up to a 64% reduction in aeromagnetic compensation error (RMSE nT), outperforming conventional models. This significant improvement underscores the potential of a physics-informed, machine learning approach for extracting clean, reliable, and accurate magnetic signals for MagNav positional estimation.

Despite increasing progress in development of methods for generating visual counterfactual explanations, especially with the recent rise of Denoising Diffusion Probabilistic Models, previous works consider them as an entirely local technique. In this work, we take the first step at globalizing them. Specifically, we discover that the latent space of Diffusion Autoencoders encodes the inference process of a given classifier in the form of global directions. We propose a novel proxy-based approach that discovers two types of these directions with the use of only single image in an entirely black-box manner. Precisely, g-directions allow for flipping the decision of a given classifier on an entire dataset of images, while h-directions further increase the diversity of explanations. We refer to them in general as Global Counterfactual Directions (GCDs). Moreover, we show that GCDs can be naturally combined with Latent Integrated Gradients resulting in a new black-box attribution method, while simultaneously enhancing the understanding of counterfactual explanations. We validate our approach on existing benchmarks and show that it generalizes to real-world use-cases.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

Partial differential equations (PDEs) are important tools to model physical systems, and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDE, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

Radio maps (RMs) serve as a critical foundation for enabling environment-aware wireless communication, as they provide the spatial distribution of wireless channel characteristics. Despite recent progress in RM construction using data-driven approaches, most existing methods focus solely on pathloss prediction in a fixed 2D plane, neglecting key parameters such as direction of arrival (DoA), time of arrival (ToA), and vertical spatial variations. Such a limitation is primarily due to the reliance on static learning paradigms, which hinder generalization beyond the training data distribution. To address these challenges, we propose UrbanRadio3D, a large-scale, high-resolution 3D RM dataset constructed via ray tracing in realistic urban environments. UrbanRadio3D is over 37times3 larger than previous datasets across a 3D space with 3 metrics as pathloss, DoA, and ToA, forming a novel 3Dtimes33D dataset with 7times3 more height layers than prior state-of-the-art (SOTA) dataset. To benchmark 3D RM construction, a UNet with 3D convolutional operators is proposed. Moreover, we further introduce RadioDiff-3D, a diffusion-model-based generative framework utilizing the 3D convolutional architecture. RadioDiff-3D supports both radiation-aware scenarios with known transmitter locations and radiation-unaware settings based on sparse spatial observations. Extensive evaluations on UrbanRadio3D validate that RadioDiff-3D achieves superior performance in constructing rich, high-dimensional radio maps under diverse environmental dynamics. This work provides a foundational dataset and benchmark for future research in 3D environment-aware communication. The dataset is available at https://github.com/UNIC-Lab/UrbanRadio3D.

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse rendering of geometry rely on silhouette gradients for topology changes, such signals are sparse. In contrast, our theory derives topological derivatives that relate the introduction of vanishing holes and phases to changes in image intensity. As a result, we enable differentiable shape perturbations in the form of hole or phase nucleation. We validate the proposed theory with optimization of closed curves in 2D and surfaces in 3D to lend insights into limitations of current methods and enable improved applications such as image vectorization, vector-graphics generation from text prompts, single-image reconstruction of shape ambigrams and multi-view 3D reconstruction.

In Marius von Senden's Space and Sight, a newly sighted blind patient describes the experience of a corner as lemon-like, because corners "prick" sight like lemons prick the tongue. Prickliness, here, is a dimension in the feature space of sensory experience, an effect of the perceived on the perceiver that arises where the two interact. In the account of the newly sighted, an effect familiar from one interaction translates to a novel context. Perception serves as the vehicle for generalization, in that an effect shared across different experiences produces a concrete abstraction grounded in those experiences. Cezanne and the post-impressionists, fluent in the language of experience translation, realized that the way to paint a concrete form that best reflected reality was to paint not what they saw, but what it was like to see. We envision a future of creation using AI where what it is like to see is replicable, transferrable, manipulable - part of the artist's palette that is both grounded in a particular context, and generalizable beyond it. An active line of research maps human-interpretable features onto directions in GAN latent space. Supervised and self-supervised approaches that search for anticipated directions or use off-the-shelf classifiers to drive image manipulation in embedding space are limited in the variety of features they can uncover. Unsupervised approaches that discover useful new directions show that the space of perceptually meaningful directions is nowhere close to being fully mapped. As this space is broad and full of creative potential, we want tools for direction discovery that capture the richness and generalizability of human perception. Our approach puts creators in the discovery loop during real-time tool use, in order to identify directions that are perceptually meaningful to them, and generate interpretable image translations along those directions.

Spatial embodied intelligence requires agents to act to acquire information under partial observability. While multimodal foundation models excel at passive perception, their capacity for active, self-directed exploration remains understudied. We propose Theory of Space, defined as an agent's ability to actively acquire information through self-directed, active exploration and to construct, revise, and exploit a spatial belief from sequential, partial observations. We evaluate this through a benchmark where the goal is curiosity-driven exploration to build an accurate cognitive map. A key innovation is spatial belief probing, which prompts models to reveal their internal spatial representations at each step. Our evaluation of state-of-the-art models reveals several critical bottlenecks. First, we identify an Active-Passive Gap, where performance drops significantly when agents must autonomously gather information. Second, we find high inefficiency, as models explore unsystematically compared to program-based proxies. Through belief probing, we diagnose that while perception is an initial bottleneck, global beliefs suffer from instability that causes spatial knowledge to degrade over time. Finally, using a false belief paradigm, we uncover Belief Inertia, where agents fail to update obsolete priors with new evidence. This issue is present in text-based agents but is particularly severe in vision-based models. Our findings suggest that current foundation models struggle to maintain coherent, revisable spatial beliefs during active exploration.

The Inversion-Denoising Paradigm, which is based on diffusion models, excels in diverse image editing and restoration tasks. We revisit its mechanism and reveal a critical, overlooked factor in reconstruction degradation: the approximate noise error. This error stems from approximating the noise at step t with the prediction at step t-1, resulting in severe error accumulation throughout the inversion process. We introduce Projection-Orthogonal Least Squares for Robust and Adaptive Inversion (POLARIS), which reformulates inversion from an error-compensation problem into an error-origin problem. Rather than optimizing embeddings or latent codes to offset accumulated drift, POLARIS treats the guidance scale ω as a step-wise variable and derives a mathematically grounded formula to minimize inversion error at each step. Remarkably, POLARIS improves inversion latent quality with just one line of code. With negligible performance overhead, it substantially mitigates noise approximation errors and consistently improves the accuracy of downstream tasks.

In most Vision-Language models (VL), the understanding of the image structure is enabled by injecting the position information (PI) about objects in the image. In our case study of LXMERT, a state-of-the-art VL model, we probe the use of the PI in the representation and study its effect on Visual Question Answering. We show that the model is not capable of leveraging the PI for the image-text matching task on a challenge set where only position differs. Yet, our experiments with probing confirm that the PI is indeed present in the representation. We introduce two strategies to tackle this: (i) Positional Information Pre-training and (ii) Contrastive Learning on PI using Cross-Modality Matching. Doing so, the model can correctly classify if images with detailed PI statements match. Additionally to the 2D information from bounding boxes, we introduce the object's depth as new feature for a better object localization in the space. Even though we were able to improve the model properties as defined by our probes, it only has a negligible effect on the downstream performance. Our results thus highlight an important issue of multimodal modeling: the mere presence of information detectable by a probing classifier is not a guarantee that the information is available in a cross-modal setup.

To measure the difference between two probability distributions, referred to as the source and target, respectively, we exploit both the chain rule and Bayes' theorem to construct conditional transport (CT), which is constituted by both a forward component and a backward one. The forward CT is the expected cost of moving a source data point to a target one, with their joint distribution defined by the product of the source probability density function (PDF) and a source-dependent conditional distribution, which is related to the target PDF via Bayes' theorem. The backward CT is defined by reversing the direction. The CT cost can be approximated by replacing the source and target PDFs with their discrete empirical distributions supported on mini-batches, making it amenable to implicit distributions and stochastic gradient descent-based optimization. When applied to train a generative model, CT is shown to strike a good balance between mode-covering and mode-seeking behaviors and strongly resist mode collapse. On a wide variety of benchmark datasets for generative modeling, substituting the default statistical distance of an existing generative adversarial network with CT is shown to consistently improve the performance. PyTorch code is provided.

Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

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.

As LLM-based judges become integral to industry applications, obtaining well-calibrated uncertainty estimates efficiently has become critical for production deployment. However, existing techniques, such as verbalized confidence and multi-generation methods, are often either poorly calibrated or computationally expensive. We introduce linear probes trained with a Brier score-based loss to provide calibrated uncertainty estimates from reasoning judges' hidden states, requiring no additional model training. We evaluate our approach on both objective tasks (reasoning, mathematics, factuality, coding) and subjective human preference judgments. Our results demonstrate that probes achieve superior calibration compared to existing methods with approx10x computational savings, generalize robustly to unseen evaluation domains, and deliver higher accuracy on high-confidence predictions. However, probes produce conservative estimates that underperform on easier datasets but may benefit safety-critical deployments prioritizing low false-positive rates. Overall, our work demonstrates that interpretability-based uncertainty estimation provides a practical and scalable plug-and-play solution for LLM judges in production.

It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}Ψprobability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this probability axiom to the complex plane, we first attempt to find a probability density by solving an appropriate conservation equation. The characteristic curves of this conservation equation are found to be the same as the complex paths of particles in the new representation. The boundary condition in this case is that the extended probability density should agree with the quantum probability rule along the real line. For the simple, time-independent, one-dimensional problems worked out here, we find that a conserved probability density can be derived from the velocity field of particles, except in regions where the trajectories were previously suspected to be nonviable. An alternative method to find this probability density in terms of a trajectory integral, which is easier to implement on a computer and useful for single particle solutions, is also presented. Most importantly, we show, by using the complex extension of Schrodinger equation, that the desired conservation equation can be derived from this definition of probability density.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Ultrasound Localization Microscopy (ULM) enables imaging of vascular structures in the micrometer range by accumulating contrast agent particle locations over time. Precise and efficient target localization accuracy remains an active research topic in the ULM field to further push the boundaries of this promising medical imaging technology. Existing work incorporates Delay-And-Sum (DAS) beamforming into particle localization pipelines, which ultimately determines the ULM image resolution capability. In this paper we propose to feed unprocessed Radio-Frequency (RF) data into a super-resolution network while bypassing DAS beamforming and its limitations. To facilitate this, we demonstrate label projection and inverse point transformation between B-mode and RF coordinate space as required by our approach. We assess our method against state-of-the-art techniques based on a public dataset featuring in silico and in vivo data. Results from our RF-trained network suggest that excluding DAS beamforming offers a great potential to optimize on the ULM resolution performance.

Training-free guided sampling in diffusion models leverages off-the-shelf pre-trained networks, such as an aesthetic evaluation model, to guide the generation process. Current training-free guided sampling algorithms obtain the guidance energy function based on a one-step estimate of the clean image. However, since the off-the-shelf pre-trained networks are trained on clean images, the one-step estimation procedure of the clean image may be inaccurate, especially in the early stages of the generation process in diffusion models. This causes the guidance in the early time steps to be inaccurate. To overcome this problem, we propose Symplectic Adjoint Guidance (SAG), which calculates the gradient guidance in two inner stages. Firstly, SAG estimates the clean image via n function calls, where n serves as a flexible hyperparameter that can be tailored to meet specific image quality requirements. Secondly, SAG uses the symplectic adjoint method to obtain the gradients accurately and efficiently in terms of the memory requirements. Extensive experiments demonstrate that SAG generates images with higher qualities compared to the baselines in both guided image and video generation tasks.

Textual Inversion (TI) is an efficient approach to text-to-image personalization but often fails on complex prompts. We trace these failures to embedding norm inflation: learned tokens drift to out-of-distribution magnitudes, degrading prompt conditioning in pre-norm Transformers. Empirically, we show semantics are primarily encoded by direction in CLIP token space, while inflated norms harm contextualization; theoretically, we analyze how large magnitudes attenuate positional information and hinder residual updates in pre-norm blocks. We propose Directional Textual Inversion (DTI), which fixes the embedding magnitude to an in-distribution scale and optimizes only direction on the unit hypersphere via Riemannian SGD. We cast direction learning as MAP with a von Mises-Fisher prior, yielding a constant-direction prior gradient that is simple and efficient to incorporate. Across personalization tasks, DTI improves text fidelity over TI and TI-variants while maintaining subject similarity. Crucially, DTI's hyperspherical parameterization enables smooth, semantically coherent interpolation between learned concepts (slerp), a capability that is absent in standard TI. Our findings suggest that direction-only optimization is a robust and scalable path for prompt-faithful personalization.

Sophisticated instrumentation for AI systems might have indicators that signal misalignment from human values, not unlike a "check engine" light in cars. One such indicator of misalignment is deceptiveness in generated responses. Future AI instrumentation may have the ability to detect when an LLM generates deceptive responses while reasoning about seemingly plausible but incorrect answers to factual questions. In this work, we demonstrate that linear probes on LLMs internal activations can detect deception in their responses with extremely high accuracy. Our probes reach a maximum of greater than 90% accuracy in distinguishing between deceptive and non-deceptive arguments generated by llama and qwen models ranging from 1.5B to 14B parameters, including their DeepSeek-r1 finetuned variants. We observe that probes on smaller models (1.5B) achieve chance accuracy at detecting deception, while larger models (greater than 7B) reach 70-80%, with their reasoning counterparts exceeding 90%. The layer-wise probe accuracy follows a three-stage pattern across layers: near-random (50%) in early layers, peaking in middle layers, and slightly declining in later layers. Furthermore, using an iterative null space projection approach, we find multitudes of linear directions that encode deception, ranging from 20 in Qwen 3B to nearly 100 in DeepSeek 7B and Qwen 14B models.

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and plug-and-play guidance for conditioning. Our method first trains an unconditional discretization-agnostic denoising model using neural operator architectures. At inference, we refine the samples to satisfy sparse observation data via a gradient-based guidance mechanism. Through rigorous mathematical analysis, we extend Tweedie's formula to infinite-dimensional Hilbert spaces, providing the theoretical foundation for our posterior sampling approach. Our method (FunDPS) accurately captures posterior distributions in function spaces under minimal supervision and severe data scarcity. Across five PDE tasks with only 3% observation, our method achieves an average 32% accuracy improvement over state-of-the-art fixed-resolution diffusion baselines while reducing sampling steps by 4x. Furthermore, multi-resolution fine-tuning ensures strong cross-resolution generalizability. To the best of our knowledge, this is the first diffusion-based framework to operate independently of discretization, offering a practical and flexible solution for forward and inverse problems in the context of PDEs. Code is available at https://github.com/neuraloperator/FunDPS

Text-to-image diffusion models excel at generating photorealistic images, but commonly struggle to render accurate spatial relationships described in text prompts. We identify two core issues underlying this common failure: 1) the ambiguous nature of spatial-related data in existing datasets, and 2) the inability of current text encoders to accurately interpret the spatial semantics of input descriptions. We address these issues with CoMPaSS, a versatile training framework that enhances spatial understanding of any T2I diffusion model. CoMPaSS solves the ambiguity of spatial-related data with the Spatial Constraints-Oriented Pairing (SCOP) data engine, which curates spatially-accurate training data through a set of principled spatial constraints. To better exploit the curated high-quality spatial priors, CoMPaSS further introduces a Token ENcoding ORdering (TENOR) module to allow better exploitation of high-quality spatial priors, effectively compensating for the shortcoming of text encoders. Extensive experiments on four popular open-weight T2I diffusion models covering both UNet- and MMDiT-based architectures demonstrate the effectiveness of CoMPaSS by setting new state-of-the-arts with substantial relative gains across well-known benchmarks on spatial relationships generation, including VISOR (+98%), T2I-CompBench Spatial (+67%), and GenEval Position (+131%). Code will be available at https://github.com/blurgyy/CoMPaSS.

We present Readout Guidance, a method for controlling text-to-image diffusion models with learned signals. Readout Guidance uses readout heads, lightweight networks trained to extract signals from the features of a pre-trained, frozen diffusion model at every timestep. These readouts can encode single-image properties, such as pose, depth, and edges; or higher-order properties that relate multiple images, such as correspondence and appearance similarity. Furthermore, by comparing the readout estimates to a user-defined target, and back-propagating the gradient through the readout head, these estimates can be used to guide the sampling process. Compared to prior methods for conditional generation, Readout Guidance requires significantly fewer added parameters and training samples, and offers a convenient and simple recipe for reproducing different forms of conditional control under a single framework, with a single architecture and sampling procedure. We showcase these benefits in the applications of drag-based manipulation, identity-consistent generation, and spatially aligned control. Project page: https://readout-guidance.github.io.

We analyse the observational signatures of galactic magnetic fields that are self-consistently generated in magnetohydrodynamic simulations of the interstellar medium through turbulence driven by supernova (SN) explosions and differential rotation. In particular, we study the time evolution of the Faraday rotation measure (RM), synchrotron radiation, and Stokes parameters by characterising the typical structures formed in the plane of observation. We do this by defining two distinct models for both thermal and cosmic ray (CR) electron distributions. Our results indicate that the maps of RM have structures which are sheared and rendered anisotropically by differential rotation and that they depend on the choice of thermal electrons model as well as the SN rate. Synchrotron maps are qualitatively similar to the maps of the mean magnetic field along the line of sight and structures are only marginally affected by the CR model. Stokes parameters and related quantities, such as the degree of linear polarisation, are highly dependent on both frequency and resolution of the observation.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

This work examines whether activating latent subspaces in language models (LLMs) can steer scientific code generation toward a specific programming language. Five causal LLMs were first evaluated on scientific coding prompts to quantify their baseline bias among four programming languages. A static neuron-attribution method, perturbing the highest activated MLP weight for a C++ or CPP token, proved brittle and exhibited limited generalization across prompt styles and model scales. To address these limitations, a gradient-refined adaptive activation steering framework (G-ACT) was developed: per-prompt activation differences are clustered into a small set of steering directions, and lightweight per-layer probes are trained and refined online to select the appropriate steering vector. In LLaMA-3.2 3B, this approach reliably biases generation towards the CPP language by increasing the average probe classification accuracy by 15% and the early layers (0-6) improving the probe classification accuracy by 61.5% compared to the standard ACT framework. For LLaMA-3.3 70B, where attention-head signals become more diffuse, targeted injections at key layers still improve language selection. Although per-layer probing introduces a modest inference overhead, it remains practical by steering only a subset of layers and enables reproducible model behavior. These results demonstrate a scalable, interpretable and efficient mechanism for concept-level control for practical agentic systems.

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Radio frequency (RF) signal mapping, which is the process of analyzing and predicting the RF signal strength and distribution across specific areas, is crucial for cellular network planning and deployment. Traditional approaches to RF signal mapping rely on statistical models constructed based on measurement data, which offer low complexity but often lack accuracy, or ray tracing tools, which provide enhanced precision for the target area but suffer from increased computational complexity. Recently, machine learning (ML) has emerged as a data-driven method for modeling RF signal propagation, which leverages models trained on synthetic datasets to perform RF signal mapping in "unseen" areas. In this paper, we present Geo2SigMap, an ML-based framework for efficient and high-fidelity RF signal mapping using geographic databases. First, we develop an automated framework that seamlessly integrates three open-source tools: OpenStreetMap (geographic databases), Blender (computer graphics), and Sionna (ray tracing), enabling the efficient generation of large-scale 3D building maps and ray tracing models. Second, we propose a cascaded U-Net model, which is pre-trained on synthetic datasets and employed to generate detailed RF signal maps, leveraging environmental information and sparse measurement data. Finally, we evaluate the performance of Geo2SigMap via a real-world measurement campaign, where three types of user equipment (UE) collect over 45,000 data points related to cellular information from six LTE cells operating in the citizens broadband radio service (CBRS) band. Our results show that Geo2SigMap achieves an average root-mean-square-error (RMSE) of 6.04 dB for predicting the reference signal received power (RSRP) at the UE, representing an average RMSE improvement of 3.59 dB compared to existing methods.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

The observation of the shadow of the supermassive black hole M87^{*} by the Event Horizon Telescope (EHT) is sensitive to the spacetime geometry near the circular photon orbit and beyond, and it thus has the potential to test general relativity in the strong field regime. Obstacles to this program, however, include degeneracies between putative deviations from general relativity and both the description of the accretion flow and the uncertainties on "calibration parameters", such as e.g. the mass and spin of the black hole. In this work, we introduce a formalism, based on a principal component analysis, capable of reconstructing the black hole metric (i.e. the "signal") in an agnostic way, while subtracting the "foreground" due to the uncertainties in the calibration parameters and the modelling of the accretion flow. We apply our technique to simulated mock data for spherically symmetric black holes surrounded by a thick accretion disk. We show that separation of signal and foreground may be possible with next generation EHT-like experiments.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

This paper deals with the problem of informative path planning for a UAV deployed for precision agriculture applications. First, we observe that the ``fear of missing out'' data lead to uniform, conservative scanning policies over the whole agricultural field. Consequently, employing a non-uniform scanning approach can mitigate the expenditure of time in areas with minimal or negligible real value, while ensuring heightened precision in information-dense regions. Turning to the available informative path planning methodologies, we discern that certain methods entail intensive computational requirements, while others necessitate training on an ideal world simulator. To address the aforementioned issues, we propose an active sensing coverage path planning approach, named OverFOMO, that regulates the speed of the UAV in accordance with both the relative quantity of the identified classes, i.e. crops and weeds, and the confidence level of such detections. To identify these instances, a robust Deep Learning segmentation model is deployed. The computational needs of the proposed algorithm are independent of the size of the agricultural field, rendering its applicability on modern UAVs quite straightforward. The proposed algorithm was evaluated with a simu-realistic pipeline, combining data from real UAV missions and the high-fidelity dynamics of AirSim simulator, showcasing its performance improvements over the established state of affairs for this type of missions. An open-source implementation of the algorithm and the evaluation pipeline is also available: https://github.com/emmarapt/OverFOMO.

We study the degree of reliability of extrapolation of complex electromagnetic permittivity functions based on their analyticity properties. Given two analytic functions, representing extrapolants of the same experimental data, we examine how much they can differ at an extrapolation point outside of the experimentally accessible frequency band. We give a sharp upper bound on the worst case extrapolation error, in terms of a solution of an integral equation of Fredholm type. We conjecture and give numerical evidence that this bound exhibits a power law precision deterioration as one moves further away from the frequency band containing measurement data.

Generative Adversarial Networks (GANs) have been widely applied in modeling diverse image distributions. However, despite its impressive applications, the structure of the latent space in GANs largely remains as a black-box, leaving its controllable generation an open problem, especially when spurious correlations between different semantic attributes exist in the image distributions. To address this problem, previous methods typically learn linear directions or individual channels that control semantic attributes in the image space. However, they often suffer from imperfect disentanglement, or are unable to obtain multi-directional controls. In this work, in light of the above challenges, we propose a novel approach that discovers nonlinear controls, which enables multi-directional manipulation as well as effective disentanglement, based on gradient information in the learned GAN latent space. More specifically, we first learn interpolation directions by following the gradients from classification networks trained separately on the attributes, and then navigate the latent space by exclusively controlling channels activated for the target attribute in the learned directions. Empirically, with small training data, our approach is able to gain fine-grained controls over a diverse set of bi-directional and multi-directional attributes, and we showcase its ability to achieve disentanglement significantly better than state-of-the-art methods both qualitatively and quantitatively.

Large-scale scene data is essential for training and testing in robot learning. Neural reconstruction methods have promised the capability of reconstructing large physically-grounded outdoor scenes from captured sensor data. However, these methods have baked-in static environments and only allow for limited scene control -- they are functionally constrained in scene and trajectory diversity by the captures from which they are reconstructed. In contrast, generating driving data with recent image or video diffusion models offers control, however, at the cost of geometry grounding and causality. In this work, we aim to bridge this gap and present a method that directly generates large-scale 3D driving scenes with accurate geometry, allowing for causal novel view synthesis with object permanence and explicit 3D geometry estimation. The proposed method combines the generation of a proxy geometry and environment representation with score distillation from learned 2D image priors. We find that this approach allows for high controllability, enabling the prompt-guided geometry and high-fidelity texture and structure that can be conditioned on map layouts -- producing realistic and geometrically consistent 3D generations of complex driving scenes.

Recent advancements in Text-to-Image (T2I) diffusion models have demonstrated impressive success in generating high-quality images with zero-shot generalization capabilities. Yet, current models struggle to closely adhere to prompt semantics, often misrepresenting or overlooking specific attributes. To address this, we propose a simple, training-free approach that modulates the guidance direction of diffusion models during inference. We first decompose the prompt semantics into a set of concepts, and monitor the guidance trajectory in relation to each concept. Our key observation is that deviations in model's adherence to prompt semantics are highly correlated with divergence of the guidance from one or more of these concepts. Based on this observation, we devise a technique to steer the guidance direction towards any concept from which the model diverges. Extensive experimentation validates that our method improves the semantic alignment of images generated by diffusion models in response to prompts. Project page is available at: https://korguy.github.io/

Echocardiography is crucial for cardiovascular disease detection but relies heavily on experienced sonographers. Echocardiography probe guidance systems, which provide real-time movement instructions for acquiring standard plane images, offer a promising solution for AI-assisted or fully autonomous scanning. However, developing effective machine learning models for this task remains challenging, as they must grasp heart anatomy and the intricate interplay between probe motion and visual signals. To address this, we present EchoWorld, a motion-aware world modeling framework for probe guidance that encodes anatomical knowledge and motion-induced visual dynamics, while effectively leveraging past visual-motion sequences to enhance guidance precision. EchoWorld employs a pre-training strategy inspired by world modeling principles, where the model predicts masked anatomical regions and simulates the visual outcomes of probe adjustments. Built upon this pre-trained model, we introduce a motion-aware attention mechanism in the fine-tuning stage that effectively integrates historical visual-motion data, enabling precise and adaptive probe guidance. Trained on more than one million ultrasound images from over 200 routine scans, EchoWorld effectively captures key echocardiographic knowledge, as validated by qualitative analysis. Moreover, our method significantly reduces guidance errors compared to existing visual backbones and guidance frameworks, excelling in both single-frame and sequential evaluation protocols. Code is available at https://github.com/LeapLabTHU/EchoWorld.

Accurate subsurface scattering solutions require the integration of optical material properties along many complicated light paths. We present a method that learns a simple geometric approximation of random paths in a homogeneous volume of translucent material. The generated representation allows determining the absorption along the path as well as a direct lighting contribution, which is representative of all scattering events along the path. A sequence of conditional variational auto-encoders (CVAEs) is trained to model the statistical distribution of the photon paths inside a spherical region in presence of multiple scattering events. A first CVAE learns to sample the number of scattering events, occurring on a ray path inside the sphere, which effectively determines the probability of the ray being absorbed. Conditioned on this, a second model predicts the exit position and direction of the light particle. Finally, a third model generates a representative sample of photon position and direction along the path, which is used to approximate the contribution of direct illumination due to in-scattering. To accelerate the tracing of the light path through the volumetric medium toward the solid boundary, we employ a sphere-tracing strategy that considers the light absorption and is able to perform statistically accurate next-event estimation. We demonstrate efficient learning using shallow networks of only three layers and no more than 16 nodes. In combination with a GPU shader that evaluates the CVAEs' predictions, performance gains can be demonstrated for a variety of different scenarios. A quality evaluation analyzes the approximation error that is introduced by the data-driven scattering simulation and sheds light on the major sources of error in the accelerated path tracing process.

In Ultrasound Localization Microscopy (ULM),achieving high-resolution images relies on the precise localization of contrast agent particles across consecutive beam-formed frames. However, our study uncovers an enormous potential: The process of delay-and-sum beamforming leads to an irreversible reduction of Radio-Frequency (RF) data, while its implications for localization remain largely unexplored. The rich contextual information embedded within RF wavefronts, including their hyperbolic shape and phase, offers great promise for guiding Deep Neural Networks (DNNs) in challenging localization scenarios. To fully exploit this data, we propose to directly localize scatterers in RF signals. Our approach involves a custom super-resolution DNN using learned feature channel shuffling and a novel semi-global convolutional sampling block tailored for reliable and accurate wavefront localization. Additionally, we introduce a geometric point transformation that facilitates seamless mapping between RF and B-mode coordinate space. To understand the impact of beamforming on ULM, we validate the effectiveness of our method by conducting an extensive comparison with State-Of-The-Art (SOTA) techniques. We present the inaugural in vivo results from an RF-trained DNN, highlighting its real-world practicality. Our findings show that RF-ULM bridges the domain gap between synthetic and real datasets, offering a considerable advantage in terms of precision and complexity. To enable the broader research community to benefit from our findings, our code and the associated SOTA methods are made available at https://github.com/hahnec/rf-ulm.

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft constraints are often considered to be the sources of the complexity in the training phase of PINNs. Here, we demonstrate that the challenge of training (i) persists even when the boundary conditions are strictly enforced, and (ii) is closely related to the Kolmogorov n-width associated with problems demonstrating transport, convection, traveling waves, or moving fronts. Given this realization, we describe the mechanism underlying the training schemes such as those used in eXtended PINNs (XPINN), curriculum regularization, and sequence-to-sequence learning. For an important category of PDEs, i.e., governed by non-linear convection-diffusion equation, we propose reformulating PINNs on a Lagrangian frame of reference, i.e., LPINNs, as a PDE-informed solution. A parallel architecture with two branches is proposed. One branch solves for the state variables on the characteristics, and the second branch solves for the low-dimensional characteristics curves. The proposed architecture conforms to the causality innate to the convection, and leverages the direction of travel of the information in the domain. Finally, we demonstrate that the loss landscapes of LPINNs are less sensitive to the so-called "complexity" of the problems, compared to those in the traditional PINNs in the Eulerian framework.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

Forthcoming space-based gravitational-wave (GW) detectors will employ second-generation time-delay interferometry (TDI) to suppress laser frequency noise and achieve the sensitivity required for GW detection. We introduce an inverse light-path operator P_{i_{1}i_{2}i_{3}ldots i_{n-1}i_{n}}, which enables simple representation of second-generation TDI combinations and a concise description of light propagation. Analytical expressions and high-accuracy approximate formulas are derived for the sky- and polarization-averaged response functions, noise power spectral densities (PSDs), and sensitivity curves of TDI Michelson, (alpha,beta,gamma), Monitor, Beacon, Relay, and Sagnac combinations, as well as their orthogonal A, E, T channels. Our results show that: (i) second-generation TDIs have the same sensitivities as their first-generation counterparts; (ii) the A, E, T sensitivities and the optimal sensitivity are independent of the TDI generation and specific combination; (iii) the A and E channels have equal averaged responses, noise PSDs, and sensitivities, while the T channel has much weaker response and sensitivity at low frequencies (2pi fL/clesssim3); (iv) except for the (alpha,beta,gamma) and zeta combinations and the T channel, all sensitivity curves exhibit a flat section in the range f_{n}<flesssim 1.5/(2pi L/c), where the noise-balance frequency f_{n} separates the proof-mass- and optical-path-dominated regimes, while the response-transition frequency sim 1.5/(2pi L/c) separates the response function's low- and high-frequency behaviors; (v) the averaged response, noise PSD, and sensitivity of zeta scales with those of the T channel. These analytical and approximate formulations provide useful benchmarks for instrument optimization and data-analysis studies for future space-based GW detectors.

Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.

We present the results from four stellar occultations by (486958) Arrokoth, the flyby target of the New Horizons extended mission. Three of the four efforts led to positive detections of the body, and all constrained the presence of rings and other debris, finding none. Twenty-five mobile stations were deployed for 2017 June 3 and augmented by fixed telescopes. There were no positive detections from this effort. The event on 2017 July 10 was observed by SOFIA with one very short chord. Twenty-four deployed stations on 2017 July 17 resulted in five chords that clearly showed a complicated shape consistent with a contact binary with rough dimensions of 20 by 30 km for the overall outline. A visible albedo of 10% was derived from these data. Twenty-two systems were deployed for the fourth event on 2018 Aug 4 and resulted in two chords. The combination of the occultation data and the flyby results provides a significant refinement of the rotation period, now estimated to be 15.9380 pm 0.0005 hours. The occultation data also provided high-precision astrometric constraints on the position of the object that were crucial for supporting the navigation for the New Horizons flyby. This work demonstrates an effective method for obtaining detailed size and shape information and probing for rings and dust on distant Kuiper Belt objects as well as being an important source of positional data that can aid in spacecraft navigation that is particularly useful for small and distant bodies.

Designing nanophotonic structures traditionally grapples with the complexities of discrete parameters, such as real materials, often resorting to costly global optimization methods. This paper introduces an approach that leverages generative deep learning to map discrete parameter sets into a continuous latent space, enabling direct gradient-based optimization. For scenarios with non-differentiable physics evaluation functions, a neural network is employed as a differentiable surrogate model. The efficacy of this methodology is demonstrated by optimizing the directional scattering properties of core-shell nanoparticles composed of a selection of realistic materials. We derive suggestions for core-shell geometries with strong forward scattering and minimized backscattering. Our findings reveal significant improvements in computational efficiency and performance when compared to global optimization techniques. Beyond nanophotonics design problems, this framework holds promise for broad applications across all types of inverse problems constrained by discrete variables.

In the Lagrange-Newton method, where Newton's method is applied to a Lagrangian function that includes equality constraints, all stationary points are saddle points. It is therefore not possible to use a line-search method based on the value of the objective function; instead, the line search can operate on merit functions. In this report, we explore an alternative line-search method which is applicable to this case; it particulary addresses the damping of the step length in tight valleys. We propose a line-search criterion based on the divergence of the field of Newton step vectors. The visualization of the criterion for two-dimensional test functions reveals a network of ravines with flat bottom at the zero points of the criterion. The ravines are typically connected to stationary points. To traverse this ravine network in order to approach a stationary point, a zigzag strategy is devised. Numerical experiments demonstrate that the novel line-search strategy succeeds from most starting points in all test functions, but only exhibits the desired damping of the step length in some situations. At the present stage it is therefore difficult to appraise the utility of this contribution.

Agents navigating in 3D environments require some form of memory, which should hold a compact and actionable representation of the history of observations useful for decision taking and planning. In most end-to-end learning approaches the representation is latent and usually does not have a clearly defined interpretation, whereas classical robotics addresses this with scene reconstruction resulting in some form of map, usually estimated with geometry and sensor models and/or learning. In this work we propose to learn an actionable representation of the scene independently of the targeted downstream task and without explicitly optimizing reconstruction. The learned representation is optimized by a blind auxiliary agent trained to navigate with it on multiple short sub episodes branching out from a waypoint and, most importantly, without any direct visual observation. We argue and show that the blindness property is important and forces the (trained) latent representation to be the only means for planning. With probing experiments we show that the learned representation optimizes navigability and not reconstruction. On downstream tasks we show that it is robust to changes in distribution, in particular the sim2real gap, which we evaluate with a real physical robot in a real office building, significantly improving performance.

Correlative computational microscopy is accelerating the mapping of dynamic biological systems by integrating morphological and molecular measurements across spatial scales, from organelles to entire organisms. Visualization, measurement, and prediction of interactions among the components of biological systems can be accelerated by generalist computational imaging frameworks that relax the trade-offs imposed by multiplex dynamic imaging. This work reports a generalist framework for wave optical imaging of the architectural order (waveOrder) among biomolecules for encoding and decoding multiple specimen properties from a minimal set of acquired channels, with or without fluorescent labels. waveOrder expresses material properties in terms of elegant physically motivated basis vectors directly interpretable as phase, absorption, birefringence, diattenuation, and fluorophore density; and it expresses image data in terms of directly measurable Stokes parameters. We report a corresponding multi-channel reconstruction algorithm to recover specimen properties in multiple contrast modes. With this framework, we implement multiple 3D computational microscopy methods, including quantitative phase imaging, quantitative label-free imaging with phase and polarization, and fluorescence deconvolution imaging, across scales ranging from organelles to whole zebrafish. These advances are available via an extensible open-source computational imaging library, waveOrder, and a napari plugin, recOrder.

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative diffusion models as a constrained optimization problem, steering the generated data distribution to remain within a specified region to ensure adherence to the given constraints. These capabilities are validated on applications featuring both convex and challenging, non-convex, constraints as well as ordinary differential equations, in domains spanning from synthesizing new materials with precise morphometric properties, generating physics-informed motion, optimizing paths in planning scenarios, and human motion synthesis.

Our world is full of asymmetries. Gravity and wind can make reaching a place easier than coming back. Social artifacts such as genealogy charts and citation graphs are inherently directed. In reinforcement learning and control, optimal goal-reaching strategies are rarely reversible (symmetrical). Distance functions supported on these asymmetrical structures are called quasimetrics. Despite their common appearance, little research has been done on the learning of quasimetrics. Our theoretical analysis reveals that a common class of learning algorithms, including unconstrained multilayer perceptrons (MLPs), provably fails to learn a quasimetric consistent with training data. In contrast, our proposed Poisson Quasimetric Embedding (PQE) is the first quasimetric learning formulation that both is learnable with gradient-based optimization and enjoys strong performance guarantees. Experiments on random graphs, social graphs, and offline Q-learning demonstrate its effectiveness over many common baselines.

Transformer-based models generate hidden states that are difficult to interpret. In this work, we analyze hidden states and modify them at inference, with a focus on motion forecasting. We use linear probing to analyze whether interpretable features are embedded in hidden states. Our experiments reveal high probing accuracy, indicating latent space regularities with functionally important directions. Building on this, we use the directions between hidden states with opposing features to fit control vectors. At inference, we add our control vectors to hidden states and evaluate their impact on predictions. Remarkably, such modifications preserve the feasibility of predictions. We further refine our control vectors using sparse autoencoders (SAEs). This leads to more linear changes in predictions when scaling control vectors. Our approach enables mechanistic interpretation as well as zero-shot generalization to unseen dataset characteristics with negligible computational overhead.

The success of pre-trained contextualized representations has prompted researchers to analyze them for the presence of linguistic information. Indeed, it is natural to assume that these pre-trained representations do encode some level of linguistic knowledge as they have brought about large empirical improvements on a wide variety of NLP tasks, which suggests they are learning true linguistic generalization. In this work, we focus on intrinsic probing, an analysis technique where the goal is not only to identify whether a representation encodes a linguistic attribute but also to pinpoint where this attribute is encoded. We propose a novel latent-variable formulation for constructing intrinsic probes and derive a tractable variational approximation to the log-likelihood. Our results show that our model is versatile and yields tighter mutual information estimates than two intrinsic probes previously proposed in the literature. Finally, we find empirical evidence that pre-trained representations develop a cross-lingually entangled notion of morphosyntax.

Diffusion models have emerged as a formidable tool for training-free conditional generation.However, a key hurdle in inference-time guidance techniques is the need for compute-heavy backpropagation through the diffusion network for estimating the guidance direction. Moreover, these techniques often require handcrafted parameter tuning on a case-by-case basis. Although some recent works have introduced minimal compute methods for linear inverse problems, a generic lightweight guidance solution to both linear and non-linear guidance problems is still missing. To this end, we propose Dreamguider, a method that enables inference-time guidance without compute-heavy backpropagation through the diffusion network. The key idea is to regulate the gradient flow through a time-varying factor. Moreover, we propose an empirical guidance scale that works for a wide variety of tasks, hence removing the need for handcrafted parameter tuning. We further introduce an effective lightweight augmentation strategy that significantly boosts the performance during inference-time guidance. We present experiments using Dreamguider on multiple tasks across multiple datasets and models to show the effectiveness of the proposed modules. To facilitate further research, we will make the code public after the review process.

Switchbacks are discrete angular deflections in the solar wind magnetic field that have been observed throughout the heliosphere. Recent observations by Parker Solar Probe (PSP) have revealed the presence of patches of switchbacks on the scale of hours to days, separated by 'quieter' radial fields. We aim to further diagnose the origin of these patches using measurements of proton temperature anisotropy that can illuminate possible links to formation processes in the solar corona. We fitted 3D bi-Maxwellian functions to the core of proton velocity distributions measured by the SPAN-Ai instrument onboard PSP to obtain the proton parallel, T_{p,|}, and perpendicular, T_{p,perp}, temperature. We show that the presence of patches is highlighted by a transverse deflection in the flow and magnetic field away from the radial direction. These deflections are correlated with enhancements in T_{p,|}, while T_{p,perp} remains relatively constant. Patches sometimes exhibit small proton and electron density enhancements. We interpret that patches are not simply a group of switchbacks, but rather switchbacks are embedded within a larger-scale structure identified by enhanced T_{p,|} that is distinct from the surrounding solar wind. We suggest that these observations are consistent with formation by reconnection-associated mechanisms in the corona.

Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child structures of arbitrary resolution (i.e., pixel or voxel numbers) and number of phases (i.e., material phases/species) can be generated by means of trivial embedding based phase extension, application of kernels and/or phase coalescence, such that the generated structures inherit the two-point-correlation equivalence. Proofs of the inheritance property are provided by means of the Discrete Fourier Transform theory. A Python 3 implementation of the results is offered by the authors through the Github repository https://github.com/DataAnalyticsEngineering/EQ2PC in order to make the provided results reproducible and useful for all interested readers. Examples for the generation of structures are demonstrated, together with applications in the homogenization theory of periodic media.

The planned space-based gravitational wave detector, LISA, will provide a fundamentally new means of studying the orbital alignment of close white dwarf binaries. However, due to the inherent symmetry of their gravitational wave signals, a fourfold degeneracy arises in the transverse projections of their angular momentum vectors. In this paper, we demonstrate that by incorporating timing information from electromagnetic observations, such as radial velocity modulations and light curves, this degeneracy can be reduced to twofold.

General full-wave electromagnetic solvers, such as those utilizing the finite-difference time-domain (FDTD) method, are computationally demanding for simulating practical GPR problems. We explore the performance of a near-real-time, forward modeling approach for GPR that is based on a machine learning (ML) architecture. To ease the process, we have developed a framework that is capable of generating these ML-based forward solvers automatically. The framework uses an innovative training method that combines a predictive dimensionality reduction technique and a large data set of modeled GPR responses from our FDTD simulation software, gprMax. The forward solver is parameterized for a specific GPR application, but the framework can be extended in a straightforward manner to different electromagnetic problems.

Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the Controlled Monte Carlo Diffusion sampler (CMCD) for Bayesian computation, a score-based annealing technique that crucially adapts both forward and backward dynamics in a diffusion model. On the way, we clarify the relationship between the EM-algorithm and iterative proportional fitting (IPF) for Schr{\"o}dinger bridges, deriving as well a regularised objective that bypasses the iterative bottleneck of standard IPF-updates. Finally, we show that CMCD has a strong foundation in the Jarzinsky and Crooks identities from statistical physics, and that it convincingly outperforms competing approaches across a wide array of experiments.

The Stokes V parameter characterizes asymmetry of amplitudes between right- and left-handed waves, and non-vanishing value of the V parameter yields a circularly polarized signal. Cosmologically, V parameter may be a direct probe for parity violation in the universe. In this paper, we theoretically investigate a measurement of this parameter, particularly focusing on the gravitational-wave backgrounds observed via ground-based interferometers. In contrast to the traditional analysis that only considers the total amplitude (or equivalently Omega_{GW}), the signal analysis including a circular-polarized mode has a rich structure due to the multi-dimensionality of target parameters. We show that, by using the network of next-generation detectors, separation between polarized and unpolarized modes can be performed with small statistical loss induced by their correlation.

As unmanned aerial systems (UASs) increasingly integrate into the US national airspace system, there is an increasing need to characterize how commercial and recreational UASs may encounter each other. To inform the development and evaluation of safety critical technologies, we demonstrate a methodology to analytically calculate all potential relative geometries between different UAS operations performing inspection missions. This method is based on a previously demonstrated technique that leverages open source geospatial information to generate representative unmanned aircraft trajectories. Using open source data and parallel processing techniques, we performed trillions of calculations to estimate the relative horizontal distance between geospatial points across sixteen locations.

Generative models have had a profound impact on vision and language, paving the way for a new era of multimodal generative applications. While these successes have inspired researchers to explore using generative models in science and engineering to accelerate the design process and reduce the reliance on iterative optimization, challenges remain. Specifically, engineering optimization methods based on physics still outperform generative models when dealing with constrained environments where data is scarce and precision is paramount. To address these challenges, we introduce Diffusion Optimization Models (DOM) and Trajectory Alignment (TA), a learning framework that demonstrates the efficacy of aligning the sampling trajectory of diffusion models with the optimization trajectory derived from traditional physics-based methods. This alignment ensures that the sampling process remains grounded in the underlying physical principles. Our method allows for generating feasible and high-performance designs in as few as two steps without the need for expensive preprocessing, external surrogate models, or additional labeled data. We apply our framework to structural topology optimization, a fundamental problem in mechanical design, evaluating its performance on in- and out-of-distribution configurations. Our results demonstrate that TA outperforms state-of-the-art deep generative models on in-distribution configurations and halves the inference computational cost. When coupled with a few steps of optimization, it also improves manufacturability for out-of-distribution conditions. By significantly improving performance and inference efficiency, DOM enables us to generate high-quality designs in just a few steps and guide them toward regions of high performance and manufacturability, paving the way for the widespread application of generative models in large-scale data-driven design.

This work explores whether language models encode meaningfully grounded representations of sounds of objects. We learn a linear probe that retrieves the correct text representation of an object given a snippet of audio related to that object, where the sound representation is given by a pretrained audio model. This probe is trained via a contrastive loss that pushes the language representations and sound representations of an object to be close to one another. After training, the probe is tested on its ability to generalize to objects that were not seen during training. Across different language models and audio models, we find that the probe generalization is above chance in many cases, indicating that despite being trained only on raw text, language models encode grounded knowledge of sounds for some objects.

Frontier language model capabilities are improving rapidly. We thus need stronger mitigations against bad actors misusing increasingly powerful systems. Prior work has shown that activation probes may be a promising misuse mitigation technique, but we identify a key remaining challenge: probes fail to generalize under important production distribution shifts. In particular, we find that the shift from short-context to long-context inputs is difficult for existing probe architectures. We propose several new probe architecture that handle this long-context distribution shift. We evaluate these probes in the cyber-offensive domain, testing their robustness against various production-relevant shifts, including multi-turn conversations, static jailbreaks, and adaptive red teaming. Our results demonstrate that while multimax addresses context length, a combination of architecture choice and training on diverse distributions is required for broad generalization. Additionally, we show that pairing probes with prompted classifiers achieves optimal accuracy at a low cost due to the computational efficiency of probes. These findings have informed the successful deployment of misuse mitigation probes in user-facing instances of Gemini, Google's frontier language model. Finally, we find early positive results using AlphaEvolve to automate improvements in both probe architecture search and adaptive red teaming, showing that automating some AI safety research is already possible.

Optimal transport (OT) theory has been been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another. Recent works have drawn inspiration from Brenier's theorem, which states that when the ground cost is the squared-Euclidean distance, the ``best'' map to morph a continuous measure in P(Rd) into another must be the gradient of a convex function. To exploit that result, [Makkuva+ 2020, Korotin+2020] consider maps T=nabla f_theta, where f_theta is an input convex neural network (ICNN), as defined by Amos+2017, and fit theta with SGD using samples. Despite their mathematical elegance, fitting OT maps with ICNNs raises many challenges, due notably to the many constraints imposed on theta; the need to approximate the conjugate of f_theta; or the limitation that they only work for the squared-Euclidean cost. More generally, we question the relevance of using Brenier's result, which only applies to densities, to constrain the architecture of candidate maps fitted on samples. Motivated by these limitations, we propose a radically different approach to estimating OT maps: Given a cost c and a reference measure rho, we introduce a regularizer, the Monge gap M^c_{rho}(T) of a map T. That gap quantifies how far a map T deviates from the ideal properties we expect from a c-OT map. In practice, we drop all architecture requirements for T and simply minimize a distance (e.g., the Sinkhorn divergence) between Tsharpmu and nu, regularized by M^c_rho(T). We study M^c_{rho}, and show how our simple pipeline outperforms significantly other baselines in practice.

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this work, we give an equivalent definition of the EIM approximation, in which the two variables play symmetric roles. Then, we give a proof for the existence of this approximation, and extend it up to the convergence of the EIM, and for any norm chosen to compute the error in the greedy step. Finally, we introduce a way to compute a separated representation in the case where the number of selected values is different for each variable. In the case of a physical field measured by sensors, this is useful to discard a broken sensor while keeping the information provided by the associated selected field.

Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed. In this work, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a block-coordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the direction-dependent effects (DDEs). As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, i.e. spatially band-limited. Finally, we show through simulations the efficiency of our method, for the reconstruction of both images of point sources and complex extended sources. MATLAB code is available on GitHub.

Recently, various methods have been proposed to address the inconsistency issue of DDIM inversion to enable image editing, such as EDICT [36] and Null-text inversion [22]. However, the above methods introduce considerable computational overhead. In this paper, we propose a new technique, named bi-directional integration approximation (BDIA), to perform exact diffusion inversion with neglible computational overhead. Suppose we would like to estimate the next diffusion state z_{i-1} at timestep t_i with the historical information (i,z_i) and (i+1,z_{i+1}). We first obtain the estimated Gaussian noise boldsymbol{epsilon}(z_i,i), and then apply the DDIM update procedure twice for approximating the ODE integration over the next time-slot [t_i, t_{i-1}] in the forward manner and the previous time-slot [t_i, t_{t+1}] in the backward manner. The DDIM step for the previous time-slot is used to refine the integration approximation made earlier when computing z_i. A nice property of BDIA-DDIM is that the update expression for z_{i-1} is a linear combination of (z_{i+1}, z_i, boldsymbol{epsilon}(z_i,i)). This allows for exact backward computation of z_{i+1} given (z_i, z_{i-1}), thus leading to exact diffusion inversion. It is demonstrated with experiments that (round-trip) BDIA-DDIM is particularly effective for image editing. Our experiments further show that BDIA-DDIM produces markedly better image sampling qualities than DDIM for text-to-image generation. BDIA can also be applied to improve the performance of other ODE solvers in addition to DDIM. In our work, it is found that applying BDIA to the EDM sampling procedure produces consistently better performance over four pre-trained models.

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior sampling methods proposed for solving common BIPs rely on heuristic approximations to the generative process. To exploit the generative capability of DMs and avoid the usage of such approximations, we propose an ensemble-based algorithm that performs posterior sampling without the use of heuristic approximations. Our algorithm is motivated by existing works that combine DM-based methods with the sequential Monte Carlo (SMC) method. By examining how the prior evolves through the diffusion process encoded by the pre-trained score function, we derive a modified partial differential equation (PDE) governing the evolution of the corresponding posterior distribution. This PDE includes a modified diffusion term and a reweighting term, which can be simulated via stochastic weighted particle methods. Theoretically, we prove that the error between the true posterior distribution can be bounded in terms of the training error of the pre-trained score function and the number of particles in the ensemble. Empirically, we validate our algorithm on several inverse problems in imaging to show that our method gives more accurate reconstructions compared to existing DM-based methods.

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.

Diffusion models (DMs) excel in photorealism, image editing, and solving inverse problems, aided by classifier-free guidance and image inversion techniques. However, rectified flow models (RFMs) remain underexplored for these tasks. Existing DM-based methods often require additional training, lack generalization to pretrained latent models, underperform, and demand significant computational resources due to extensive backpropagation through ODE solvers and inversion processes. In this work, we first develop a theoretical and empirical understanding of the vector field dynamics of RFMs in efficiently guiding the denoising trajectory. Our findings reveal that we can navigate the vector field in a deterministic and gradient-free manner. Utilizing this property, we propose FlowChef, which leverages the vector field to steer the denoising trajectory for controlled image generation tasks, facilitated by gradient skipping. FlowChef is a unified framework for controlled image generation that, for the first time, simultaneously addresses classifier guidance, linear inverse problems, and image editing without the need for extra training, inversion, or intensive backpropagation. Finally, we perform extensive evaluations and show that FlowChef significantly outperforms baselines in terms of performance, memory, and time requirements, achieving new state-of-the-art results. Project Page: https://flowchef.github.io.

3D LiDAR sensors are essential for autonomous navigation, environmental monitoring, and precision mapping in remote sensing applications. To efficiently process the massive point clouds generated by these sensors, LiDAR data is often projected into 2D range images that organize points by their angular positions and distances. While these range image representations enable efficient processing, conventional projection methods suffer from fundamental geometric inconsistencies that cause irreversible information loss, compromising high-fidelity applications. We present ALICE-LRI (Automatic LiDAR Intrinsic Calibration Estimation for Lossless Range Images), the first general, sensor-agnostic method that achieves lossless range image generation from spinning LiDAR point clouds without requiring manufacturer metadata or calibration files. Our algorithm automatically reverse-engineers the intrinsic geometry of any spinning LiDAR sensor by inferring critical parameters including laser beam configuration, angular distributions, and per-beam calibration corrections, enabling lossless projection and complete point cloud reconstruction with zero point loss. Comprehensive evaluation across the complete KITTI and DurLAR datasets demonstrates that ALICE-LRI achieves perfect point preservation, with zero points lost across all point clouds. Geometric accuracy is maintained well within sensor precision limits, establishing geometric losslessness with real-time performance. We also present a compression case study that validates substantial downstream benefits, demonstrating significant quality improvements in practical applications. This paradigm shift from approximate to lossless LiDAR projections opens new possibilities for high-precision remote sensing applications requiring complete geometric preservation.

Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover the missing information on the sensing model, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not employ any training signal, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue. We here address blind calibration as a non-convex problem for linear random sensing models, in which we aim to recover an unknown signal from its projections on sub-Gaussian random vectors, each subject to an unknown positive multiplicative factor (or gain). To solve this optimisation problem we resort to projected gradient descent starting from a suitable, carefully chosen initialisation point. An analysis of this algorithm allows us to show that it converges to the exact solution provided a sample complexity requirement is met, i.e., relating convergence to the amount of information collected during the sensing process. Interestingly, we show that this requirement grows linearly (up to log factors) in the number of unknowns of the problem. This sample complexity is found both in absence of prior information, as well as when subspace priors are available for both the signal and gains, allowing a further reduction of the number of observations required for our recovery guarantees to hold. Moreover, in the presence of noise we show how our descent algorithm yields a solution whose accuracy degrades gracefully with the amount of noise affecting the measurements. Finally, we present some numerical experiments in an imaging context, where our algorithm allows for a simple solution to blind calibration of the gains in a sensor array.

This monograph presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions. The goal is to learn a reverse process that transforms noise back into data while recovering the same intermediates. We describe three complementary views. The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution, indicating how to nudge samples toward more likely regions. The flow-based view, related to normalizing flows, treats generation as following a smooth path that moves samples from noise to data under a learned velocity field. These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data. Sampling then amounts to solving a differential equation that evolves noise into data along a continuous trajectory. On this foundation, the monograph discusses guidance for controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models that learn direct mappings between arbitrary times. It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.

The emergence of large-scale multi-modal generative models has drastically advanced artificial intelligence, introducing unprecedented levels of performance and functionality. However, optimizing these models remains challenging due to historically isolated paths of model-centric and data-centric developments, leading to suboptimal outcomes and inefficient resource utilization. In response, we present a novel sandbox suite tailored for integrated data-model co-development. This sandbox provides a comprehensive experimental platform, enabling rapid iteration and insight-driven refinement of both data and models. Our proposed "Probe-Analyze-Refine" workflow, validated through applications on state-of-the-art LLaVA-like and DiT based models, yields significant performance boosts, such as topping the VBench leaderboard. We also uncover fruitful insights gleaned from exhaustive benchmarks, shedding light on the critical interplay between data quality, diversity, and model behavior. With the hope of fostering deeper understanding and future progress in multi-modal data and generative modeling, our codes, datasets, and models are maintained and accessible at https://github.com/modelscope/data-juicer/blob/main/docs/Sandbox.md.

When studying unconstrained behaviour and allowing mice to leave their cage to navigate a complex labyrinth, the mice exhibit foraging behaviour in the labyrinth searching for rewards, returning to their home cage now and then, e.g. to drink. Surprisingly, when executing such a ``home run'', the mice do not follow the exact reverse path, in fact, the entry path and home path have very little overlap. Recent work proposed a hierarchical active inference model for navigation, where the low level model makes inferences about hidden states and poses that explain sensory inputs, whereas the high level model makes inferences about moving between locations, effectively building a map of the environment. However, using this ``map'' for planning, only allows the agent to find trajectories that it previously explored, far from the observed mice's behaviour. In this paper, we explore ways of incorporating before-unvisited paths in the planning algorithm, by using the low level generative model to imagine potential, yet undiscovered paths. We demonstrate a proof of concept in a grid-world environment, showing how an agent can accurately predict a new, shorter path in the map leading to its starting point, using a generative model learnt from pixel-based observations.

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed, as user-specified rewards are usually only well defined on the data distribution at the end of generation. While common workarounds to this problem are to use a denoiser to estimate what a sample would have been at the end of generation, we propose a simple solution to this problem by working directly with a flow map. By exploiting a relationship between the flow map and velocity field governing the instantaneous transport, we construct an algorithm, Flow Map Trajectory Tilting (FMTT), which provably performs better ascent on the reward than standard test-time methods involving the gradient of the reward. The approach can be used to either perform exact sampling via importance weighting or principled search that identifies local maximizers of the reward-tilted distribution. We demonstrate the efficacy of our approach against other look-ahead techniques, and show how the flow map enables engagement with complicated reward functions that make possible new forms of image editing, e.g. by interfacing with vision language models.

Do large language models (LLMs) anticipate when they will answer correctly? To study this, we extract activations after a question is read but before any tokens are generated, and train linear probes to predict whether the model's forthcoming answer will be correct. Across three open-source model families ranging from 7 to 70 billion parameters, projections on this "in-advance correctness direction" trained on generic trivia questions predict success in distribution and on diverse out-of-distribution knowledge datasets, outperforming black-box baselines and verbalised predicted confidence. Predictive power saturates in intermediate layers, suggesting that self-assessment emerges mid-computation. Notably, generalisation falters on questions requiring mathematical reasoning. Moreover, for models responding "I don't know", doing so strongly correlates with the probe score, indicating that the same direction also captures confidence. By complementing previous results on truthfulness and other behaviours obtained with probes and sparse auto-encoders, our work contributes essential findings to elucidate LLM internals.

Fluorescence LiDAR (FLiDAR), a Light Detection and Ranging (LiDAR) technology employed for distance and depth estimation across medical, automotive, and other fields, encounters significant computational challenges in scattering media. The complex nature of the acquired FLiDAR signal, particularly in such environments, makes isolating photon time-of-flight (related to target depth) and intrinsic fluorescence lifetime exceptionally difficult, thus limiting the effectiveness of current analytical and computational methodologies. To overcome this limitation, we present a Physics-Guided Mixture-of-Experts (MoE) framework tailored for specialized modeling of diverse temporal components. In contrast to the conventional MoE approaches our expert models are informed by underlying physics, such as the radiative transport equation governing photon propagation in scattering media. Central to our approach is EvidenceMoE, which integrates Evidence-Based Dirichlet Critics (EDCs). These critic models assess the reliability of each expert's output by providing per-expert quality scores and corrective feedback. A Decider Network then leverages this information to fuse expert predictions into a robust final estimate adaptively. We validate our method using realistically simulated Fluorescence LiDAR (FLiDAR) data for non-invasive cancer cell depth detection generated from photon transport models in tissue. Our framework demonstrates strong performance, achieving a normalized root mean squared error (NRMSE) of 0.030 for depth estimation and 0.074 for fluorescence lifetime.

We introduce a novel score-based diffusion framework named Twigs that incorporates multiple co-evolving flows for enriching conditional generation tasks. Specifically, a central or trunk diffusion process is associated with a primary variable (e.g., graph structure), and additional offshoot or stem processes are dedicated to dependent variables (e.g., graph properties or labels). A new strategy, which we call loop guidance, effectively orchestrates the flow of information between the trunk and the stem processes during sampling. This approach allows us to uncover intricate interactions and dependencies, and unlock new generative capabilities. We provide extensive experiments to demonstrate strong performance gains of the proposed method over contemporary baselines in the context of conditional graph generation, underscoring the potential of Twigs in challenging generative tasks such as inverse molecular design and molecular optimization.

This article presents a comprehensive review of and analysis of state-of-the-art mapping algorithms for UAV (Unmanned Aerial Vehicle) applications, focusing on canopy-level and high-speed scenarios. This article presents a comprehensive exploration of sensor technologies suitable for UAV mapping, assessing their capabilities to provide measurements that meet the requirements of fast UAV mapping. Furthermore, the study conducts extensive experiments in a simulated environment to evaluate the performance of three distinct mapping algorithms: Direct Sparse Odometry (DSO), Stereo DSO (SDSO), and DSO Lite (DSOL). The experiments delve into mapping accuracy and mapping speed, providing valuable insights into the strengths and limitations of each algorithm. The results highlight the versatility and shortcomings of these algorithms in meeting the demands of modern UAV applications. The findings contribute to a nuanced understanding of UAV mapping dynamics, emphasizing their applicability in complex environments and high-speed scenarios. This research not only serves as a benchmark for mapping algorithm comparisons but also offers practical guidance for selecting sensors tailored to specific UAV mapping applications.

Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains. In many real-world and scientific problems, systems that generate data are governed by physical laws. Recent work shows that it provides potential benefits for machine learning models by incorporating the physical prior and collected data, which makes the intersection of machine learning and physics become a prevailing paradigm. By integrating the data and mathematical physics models seamlessly, it can guide the machine learning model towards solutions that are physically plausible, improving accuracy and efficiency even in uncertain and high-dimensional contexts. In this survey, we present this learning paradigm called Physics-Informed Machine Learning (PIML) which is to build a model that leverages empirical data and available physical prior knowledge to improve performance on a set of tasks that involve a physical mechanism. We systematically review the recent development of physics-informed machine learning from three perspectives of machine learning tasks, representation of physical prior, and methods for incorporating physical prior. We also propose several important open research problems based on the current trends in the field. We argue that encoding different forms of physical prior into model architectures, optimizers, inference algorithms, and significant domain-specific applications like inverse engineering design and robotic control is far from being fully explored in the field of physics-informed machine learning. We believe that the interdisciplinary research of physics-informed machine learning will significantly propel research progress, foster the creation of more effective machine learning models, and also offer invaluable assistance in addressing long-standing problems in related disciplines.

Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions -- which are SE(n) equivariant and depend on relative states -- from external global field effects -- which depend on absolute states. We model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.