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We introduce generator matching, a modality-agnostic framework for generative modeling using arbitrary Markov processes. Generators characterize the infinitesimal evolution of a Markov process, which we leverage for generative modeling in a similar vein to flow matching: we construct conditional generators which generate single data points, then learn to approximate the marginal generator which generates the full data distribution. We show that generator matching unifies various generative modeling methods, including diffusion models, flow matching and discrete diffusion models. Furthermore, it provides the foundation to expand the design space to new and unexplored Markov processes such as jump processes. Finally, generator matching enables the construction of superpositions of Markov generative processes and enables the construction of multimodal models in a rigorous manner. We empirically validate our method on protein and image structure generation, showing that superposition with a jump process improves image generation.

This review explores the most recent advancements in transformer-based data fusion techniques in agricultural remote sensing (RS), with a particular focus on soil analysis. Utilizing a systematic, data-driven approach, we demonstrate that transformers have significantly outperformed conventional deep learning and machine learning methods since 2022, achieving prediction performance between 92% and 97%. The review is specifically focused on soil analysis, due to the importance of soil condition in optimizing crop productivity and ensuring sustainable farming practices. Transformer-based models have shown remarkable capabilities in handling complex multivariate soil data, improving the accuracy of soil moisture prediction, soil element analysis, and other soil-related applications. This systematic review primarily focuses on 1) analysing research trends and patterns in the literature, both chronologically and technically, and 2) conducting a comparative analysis of data fusion approaches, considering factors such as data types, techniques, and RS applications. Finally, we propose a roadmap for implementing data fusion methods in agricultural RS., Comment: 14 pages, 9 figures, 4 tables, Journal

The Central Molecular Zone (CMZ) is the largest reservoir of dense molecular gas in the Galaxy and is heavily obscured in the optical and near-IR. We present an overview of the far-IR dust continuum, where the molecular clouds are revealed, provided by Herschel in the inner 40\deg($|l| <$ 20\deg) of the Milky Way with a particular focus on the CMZ. We report a total dense gas ($N$(H$_2$) $> 10^{23}$ cm$^{-2}$) CMZ mass of M=$2\substack{+2 \\ -1} \times 10^7$ M$_{\odot}$ and confirm that there is a highly asymmetric distribution of dense gas, with about 70-75% at positive longitudes. We create and publicly release complete fore/background-subtracted column density and dust temperature maps in the inner 40\deg ($|l| <$ 20\deg) of the Galaxy. We find that the CMZ clearly stands out as a distinct structure, with an average mass per longitude that is at least $3\times$ higher than the rest of the inner Galaxy contiguously from 1.8\deg $> \ell >$ -1.3\deg. This CMZ extent is larger than previously assumed, but is consistent with constraints from velocity information. The inner Galaxy's column density peaks towards the SgrB2 complex with a value of about 2 $\times$ 10$^{24}$ cm$^{-2}$, and typical CMZ molecular clouds are about N(H$_2$)=10$^{23}$ cm$^{-2}$. Typical CMZ dust temperatures range from about $12-35$ K with relatively little variation. We identify a ridge of warm dust in the inner CMZ that potentially traces the base of the northern Galactic outflow seen with MEERKAT., Comment: Submitted to ApJ, 16 pages, project website: https://centralmolecularzone.github.io/3D_CMZ/

The Central Molecular Zone (CMZ) is the way station at the heart of our Milky Way Galaxy, connecting gas flowing in from Galactic scales with the central nucleus. Key open questions remain about its 3-D structure, star formation properties, and role in regulating this gas inflow. In this work, we identify a hierarchy of discrete structures in the CMZ using column density and dust temperature maps from Paper I (Battersby et al., submitted). We calculate the physical ($N$(H$_2$), $T_{\rm{dust}}$, mass, radius) and kinematic (HNCO, HCN, and HC$_3$N moments) properties of each structure as well as their bolometric luminosities and star formation rates (SFRs). We compare these properties with regions in the Milky Way disk and external galaxies. We perform power-law fits to the column density probability distribution functions (N-PDFs) of the inner 100 pc, SgrB2, and the outer 100 pc of the CMZ as well as several individual molecular cloud structures and find generally steeper power-law slopes ($-9<\alpha<-2$) compared with the literature ($-6 < \alpha < -1$). We find that individual CMZ structures require a large external pressure ($P_e$/k$_B$ $> 10^{7-9}$ K cm$^{-3}$) to be considered bound. Despite the fact that the CMZ overall is well below the Gao-Solomon dense gas star-formation relation (and in modest agreement with the Schmidt-Kennicutt relation), individual structures on the scale of molecular clouds generally follow these star-formation relations and agree well with other Milky Way and extragalactic regions., Comment: Submitted to ApJ, 22 pages, project website: https://centralmolecularzone.github.io/3D_CMZ/

A comprehensive 3-D model of the central 300 pc of the Milky Way, the Central Molecular Zone (CMZ) is of fundamental importance in understanding energy cycles in galactic nuclei, since the 3-D structure influences the location and intensity of star formation, feedback, and black hole accretion. Current observational constraints are insufficient to distinguish between existing 3-D models. Dust extinction is one diagnostic tool that can help determine the location of dark molecular clouds relative to the bright Galactic Center emission. By combining Herschel and Spitzer observations, we developed three new dust extinction techniques to estimate the likely near/far locations for each cloud in the CMZ. We compare our results to four geometric CMZ orbital models. Our extinction methods show good agreement with each other, and with results from spectral line absorption analysis from Walker et al. (submitted). Our near/far results for CMZ clouds are inconsistent with a projected version of the Sofue (1995) two spiral arms model, and show disagreement in position-velocity space with the Molinari et al. (2011) closed elliptical orbit. Our results are in reasonable agreement with the Kruijssen et al. (2015) open streams. We find that a simplified toy-model elliptical orbit which conserves angular momentum shows promising fits in both position-position and position-velocity space. We conclude that all current CMZ orbital models lack the complexity needed to describe the motion of gas in the CMZ, and further work is needed to construct a complex orbital model to accurately describe gas flows in the CMZ., Comment: Submitted to ApJ; 36 pages; Project series website with relevant code, data, and results: https://centralmolecularzone.github.io/3D_CMZ/

The Milky Way's Central Molecular Zone (CMZ) is the largest concentration of dense molecular gas in the Galaxy, the structure of which is shaped by the complex interplay between Galactic-scale dynamics and extreme physical conditions. Understanding the 3-D geometry of this gas is crucial as it determines the locations of star formation and subsequent feedback. We present a catalogue of clouds in the CMZ using Herschel data. Using archival data from the APEX and MOPRA CMZ surveys, we measure averaged kinematic properties of the clouds at 1mm and 3mm. We use archival ATCA data of the H$_{2}$CO (1$_{1,0}$ - 1$_{1,1}$) 4.8 GHz line to search for absorption towards the clouds, and 4.85 GHz GBT C-band data to measure the radio continuum emission. We measure the absorption against the continuum to provide new constraints for the line-of-sight positions of the clouds relative to the Galactic centre, and find a highly asymmetric distribution, with most clouds residing in front of the Galactic centre. The results are compared with different orbital models, and we introduce a revised toy model of a vertically-oscillating closed elliptical orbit. We find that most models describe the PPV structure of the gas reasonably well, but find significant inconsistencies in all cases regarding the near vs. far placement of individual clouds. Our results highlight that the CMZ is likely more complex than can be captured by these simple geometric models, along with the need for new data to provide further constraints on the true 3-D structure of the CMZ., Comment: Submitted to ApJ, 30 pages, project website: https://centralmolecularzone.github.io/3D_CMZ/

This paper presents an efficient dual-band rectifier for radiofrequency energy harvesting (RFEH) applications at FM and GSM bands. The single-port rectifier circuit, which comprises a 3-port network, optimized T-matching circuits and voltage doubler, is designed, simulated and fabricated to obtain a high RF-to-DC power conversion efficiency (PCE). Measurement results show PCE of 26% and 22% at -20 dBm, and also 58% and 51% at -10 dBm with a maximum amount of 69% and 65% at -2.5 dBm and -5 dBm, with single tone at 95 and 925 MHz, respectively. Besides, the fractional bandwidth of 21% at FM and 11% at GSM band is achieved. The measurement and simulation results are in good agreement. Consequently, the proposed rectifier can be a potential candidate for ambient RF energy harvesting and wireless power transfer (WPT). It should be noted that a 3-port network as a duplexer is designed to be integrated with single-port antennas which cover both FM and GSM bands as a low-cost solution. Moreover, based on simulation results, PCE has small variations when the load resistor varies from 10 to 18 k$\Omega$. Therefore, this rectifier can be utilized for any desired resistance within the range, such as sensors and IoT devices.

This paper presents a highly sensitive microwave sensor for dielectric sensing. One of the main disadvantages of microwave resonant-based sensors is cross-sensitivity originated by time-dependent uncontrolled environmental factors such as temperature that affect the material under test (MUT) behavior, leading to undesirable frequency shifts and, hence, lower accuracy. However, this work eliminates the unwanted errors using the differential measurement technique by comparing two transmission resonance frequencies during a unit test setup to measure the permittivity of MUT over time. The proposed structure comprises a spiral resonator with an extended horizontal microstrip line (EH-ML) coupled to a microstrip transmission line (MTL). Creating EH-ML within the structure comprises two primary contributions: enhanced sensitivity resulting from stronger fringing fields generated by increasing the effective area and improved resolution due to higher resonance frequencies caused by a lower total capacitive coupling effect. The proposed sensor is fabricated and tested using MUTs with a permittivity of less than 80 to verify the performance. In this regard, a frequency detection resolution (FDR) of 44MHz and a sensitivity of 0.85% are achieved at a maximum permittivity of 78.3. The results of theoretical analysis, simulation, and measurement are in relatively good agreement. Consequently, the proposed highly sensitive microwave sensor offers significant advantages, such as low complexity in design and fabrication. It also offers high resolution and precision in a wide range of permittivity, which can be an attractive candidate for dielectric sensing in health, chemical and agriculture applications.

This paper presents a highly sensitive differential soil moisture sensor (DSMS) using a microstrip line loaded with triangular two turn resonator(T2 SR) and complementary of the rectangular two turn spiral resonator(CR2 SR),simultaneously.Volumetric Water Content (VWC) or permittivity sensing is conducted by loading the T2 SR side with dielectric samples.Two transmission notches are observed for identical loads relating to T2 SR and CR2 SR.The CR2 SR notch at 4.39 GHz is used as a reference for differential permittivity measurement method.Further, the resonance frequency of T2 SR is measured relative to the reference value. Based on this frequency difference,the permittivity of soil is calculated which is related to the soil VWC.Triangular two turn resonator (T2 SR) resonance frequency changes from 4 to 2.38 GHz when VWC varies 0 percent to 30 percent.The sensor's operation principle is described through circuit model analysis and simulations.To validate the differential sensing concept, prototype of the designed 3 cell DSMS is fabricated and measured.The proposed sensor exhibits frequency shift of 110 MHz for 1 percent change at the highest soil moisture content (30 percent) for sandy type soil.This work proves the differential microwave sensing concept for precision agriculture.

Slant-polarized Multi Input Multi Output (MIMO) antennas are able to improve the performance of mobile communication systems in terms of channel capacity. Especially, the implementation of MIMO configurations for automotive applications requires to consider high gain, wideband, low-profile and affordable antennas in the communication link. In this work design, simulation and measurement of a new dual-band slant-polarized MIMO antenna with HPBW (Half Power Beam Width) of around 900 are presented. Then, four replicas of the proposed antenna set are placed at four different poles (North, South, West and East) to cover 3600 around the vehicle as an omni-directional pattern. In the real world scenario, the proper antenna set is selected to communicate with the intended user. Each slant MIMO antenna set consists of two inclined (450) low band (LB: 700 to 900 MHz) and two inclined high band (HB: 1.7 to 2.7 GHz) log-periodic antennas. The measured gain of LB and HB antennas are 7 dBi and 8 dBi, respectively. Great agreement between simulation and measurement results confirms the accuracy of the design and simulation procedures of antenna system using optimization algorithm (Genetic method). The proposed antenna is also measured in the field for industrial applications.

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions:(i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser ($x$-prediction) and noise-prediction ($\epsilon$-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

This paper presents a pixelated cubic antenna design with enhanced isolation and diverse radiation pattern for vehicular applications. The design consists of four radiating patches to take advantage of a nearly omnidirectional radiation pattern with enhanced isolation and high gain. The antenna system with four patches has been pixelated and optimized simultaneously to achieve desired performance and high isolation at 5.4 GHz band. The antenna achieved measured isolation of more than -34 dB between antenna elements. The overall isolation improvement obtained by the antenna is about 18 dB compared to a configuration using standard patch antennas. Moreover, isolation improvement is achieved through patch pixelization without additional resonators or elements. The antenna achieved up to 6.9 dB realized gain in each direction. Additionally, the cubic antenna system is equipped with an E-shaped GPS antenna to facilitate connectivity with GPS satellite. Finally, the antenna performance has been investigated using a simulation model of the vehicle roof and roof rack. The reflection coefficient, isolation and radiation patterns of the antenna remains unaffected. The antenna prototype has been fabricated on Rogers substrate and measured to verify the simulation results. The measured results correlate well with the simulation results. The proposed antenna features low-profile, simple design for ease of manufacture, good radiation characteristics with multidirectional property and high isolation, which are well-suited to vehicular applications in different environments.

It is a fundamental behavior that different individuals see the world in a largely similar manner. This is an essential basis for humans' ability to cooperate and communicate. However, what are the neuronal properties that underlie these inter-subject commonalities of our visual world? Finding out what aspects of neuronal coding remain invariant across individuals' brains will shed light not only on this fundamental question but will also point to the neuronal coding scheme as the basis of visual perception. Here, we address this question by obtaining intracranial recordings from three cohorts of patients taking part in a different visual recognition task (overall 19 patients and 244 high-order visual contacts included in the analyses) and examining the neuronal coding scheme most consistent across individuals' visual cortex. Our results highlight relational coding - expressed by the set of similarity distances between profiles of pattern activations - as the most consistent representation across individuals. Alternative coding schemes, such as population vector coding or linear coding, failed to achieve similar inter-subject consistency. Our results thus support relational coding as the central neuronal code underlying individuals' shared perceptual content in the human brain.

This paper introduces aggregate Bayesian Causal Forests (aBCF), a new Bayesian model for causal inference using aggregated data. Aggregated data are common in policy evaluations where we observe individuals such as students, but participation in an intervention is determined at a higher level of aggregation, such as schools implementing a curriculum. Interventions often have millions of individuals but far fewer higher-level units, making aggregation computationally attractive. To analyze aggregated data, a model must account for heteroskedasticity and intraclass correlation (ICC). Like Bayesian Causal Forests (BCF), aBCF estimates heterogeneous treatment effects with minimal parametric assumptions, but accounts for these aggregated data features, improving estimation of average and aggregate unit-specific effects. After introducing the aBCF model, we demonstrate via simulation that aBCF improves performance for aggregated data over BCF. We anchor our simulation on an evaluation of a large-scale Medicare primary care model. We demonstrate that aBCF produces treatment effect estimates with a lower root mean squared error and narrower uncertainty intervals while achieving the same level of coverage. We show that aBCF is not sensitive to the prior distribution used and that estimation improvements relative to BCF decline as the ICC approaches one. Code is available at https://github.com/mathematica-mpr/bcf-1.

Data exploration is a challenging process in which users examine a dataset by iteratively employing a series of queries. While in some cases the user explores a new dataset to become familiar with it, more often, the exploration process is conducted with a specific analysis goal or question in mind. To assist users in exploring a new dataset, Automated Data Exploration (ADE) systems have been devised in previous work. These systems aim to auto-generate a full exploration session, containing a sequence of queries that showcase interesting elements of the data. However, existing ADE systems are often constrained by a predefined objective function, thus always generating the same session for a given dataset. Therefore, their effectiveness in goal-oriented exploration, in which users need to answer specific questions about the data, are extremely limited. To this end, this paper presents LINX, a generative system augmented with a natural language interface for goal-oriented ADE. Given an input dataset and an analytical goal described in natural language, LINX generates a personalized exploratory session that is relevant to the user's goal. LINX utilizes a Large Language Model (LLM) to interpret the input analysis goal, and then derive a set of specifications for the desired output exploration session. These specifications are then transferred to a novel, modular ADE engine based on Constrained Deep Reinforcement Learning (CDRL), which can adapt its output according to the specified instructions. To validate LINX's effectiveness, we introduce a new benchmark dataset for goal-oriented exploration and conduct an extensive user study. Our analysis underscores LINX's superior capability in producing exploratory notebooks that are significantly more relevant and beneficial than those generated by existing solutions, including ChatGPT, goal-agnostic ADE, and commercial systems.

The interstellar medium in the Milky Way's Central Molecular Zone (CMZ) is known to be strongly magnetised, but its large-scale morphology and impact on the gas dynamics are not well understood. We explore the impact and properties of magnetic fields in the CMZ using three-dimensional non-self gravitating magnetohydrodynamical simulations of gas flow in an external Milky Way barred potential. We find that: (1) The magnetic field is conveniently decomposed into a regular time-averaged component and an irregular turbulent component. The regular component aligns well with the velocity vectors of the gas everywhere, including within the bar lanes. (2) The field geometry transitions from parallel to the Galactic plane near $z=0$ to poloidal away from the plane. (3) The magneto-rotational instability (MRI) causes an in-plane inflow of matter from the CMZ gas ring towards the central few parsecs of $0.01-0.1$ M$_\odot$ yr$^{-1}$ that is absent in the unmagnetised simulations. However, the magnetic fields have no significant effect on the larger-scale bar-driven inflow that brings the gas from the Galactic disc into the CMZ. (4) A combination of bar inflow and MRI-driven turbulence can sustain a turbulent vertical velocity dispersion of $\sigma_z \simeq 5$ km s$^{-1}$ on scales of $20$ pc in the CMZ ring. The MRI alone sustains a velocity dispersion of $\sigma_z \simeq 3$ km s$^{-1}$. Both these numbers are lower than the observed velocity dispersion of gas in the CMZ, suggesting that other processes such as stellar feedback are necessary to explain the observations. (5) Dynamo action driven by differential rotation and the MRI amplifies the magnetic fields in the CMZ ring until they saturate at a value that scales with the average local density as $B \simeq 102 (n/10^3 cm^{-3})^{0.33}$ $\mu$G. Finally, we discuss the implications of our results within the observational context in the CMZ.

This paper introduces Bespoke Non-Stationary (BNS) Solvers, a solver distillation approach to improve sample efficiency of Diffusion and Flow models. BNS solvers are based on a family of non-stationary solvers that provably subsumes existing numerical ODE solvers and consequently demonstrate considerable improvement in sample approximation (PSNR) over these baselines. Compared to model distillation, BNS solvers benefit from a tiny parameter space ($<$200 parameters), fast optimization (two orders of magnitude faster), maintain diversity of samples, and in contrast to previous solver distillation approaches nearly close the gap from standard distillation methods such as Progressive Distillation in the low-medium NFE regime. For example, BNS solver achieves 45 PSNR / 1.76 FID using 16 NFE in class-conditional ImageNet-64. We experimented with BNS solvers for conditional image generation, text-to-image generation, and text-2-audio generation showing significant improvement in sample approximation (PSNR) in all.

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled generation in general. In this work we introduce D-Flow, a simple framework for controlling the generation process by differentiating through the flow, optimizing for the source (noise) point. We motivate this framework by our key observation stating that for Diffusion/FM models trained with Gaussian probability paths, differentiating through the generation process projects gradient on the data manifold, implicitly injecting the prior into the optimization process. We validate our framework on linear and non-linear controlled generation problems including: image and audio inverse problems and conditional molecule generation reaching state of the art performance across all., Comment: ICML 2024

The most common approach to implementing data analysis pipelines involves obtaining point estimates from the upstream modules and then treating these as known quantities when working with the downstream ones. This approach is straightforward, but it is likely to underestimate the overall uncertainty associated with any final estimates. An alternative approach involves estimating parameters from the modules jointly using a Bayesian hierarchical model, which has the advantage of propagating upstream uncertainty into the downstream estimates. However, when modules are misspecified, such a joint model can behave in unexpected ways. Furthermore, hierarchical models require the development of ad-hoc computational implementations that can be laborious and computationally expensive. Cut inference modifies the posterior distribution to prevent information flow between certain parameters and provides a third alternative for statistical inference in data analysis pipelines. This paper presents a unified framework that encompasses two-step, cut, and joint inference in the context of data analysis pipelines with two modules and uses two examples to illustrate the tradeoffs associated with these approaches. Our work shows that cut inference provides both some level of robustness and ease of implementation for data analysis pipelines at a lower cost in terms of statistical inference.

Spatial voting models of legislators' preferences are used in political science to test theories about their voting behavior. These models posit that legislators' ideologies as well as the ideologies reflected in votes for and against a bill or measure exist as points in some low dimensional space, and that legislators vote for positions that are close to their own ideologies. Bayesian spatial voting models have been developed to test sharp hypotheses about whether a legislator's revealed ideal point differs for two distinct sets of bills. This project extends such a model to identify covariates that explain whether legislators exhibit such differences in ideal points. We use our method to examine voting behavior on procedural versus final passage votes in the U.S. house of representatives for the 93rd through 113th congresses. The analysis provides evidence that legislators in the minority party as well as legislators with a moderate constituency are more likely to have different ideal points for procedural versus final passage votes.

Current diffusion or flow-based generative models for 3D shapes divide to two: distilling pre-trained 2D image diffusion models, and training directly on 3D shapes. When training a diffusion or flow models on 3D shapes a crucial design choice is the shape representation. An effective shape representation needs to adhere three design principles: it should allow an efficient conversion of large 3D datasets to the representation form; it should provide a good tradeoff of approximation power versus number of parameters; and it should have a simple tensorial form that is compatible with existing powerful neural architectures. While standard 3D shape representations such as volumetric grids and point clouds do not adhere to all these principles simultaneously, we advocate in this paper a new representation that does. We introduce Mosaic-SDF (M-SDF): a simple 3D shape representation that approximates the Signed Distance Function (SDF) of a given shape by using a set of local grids spread near the shape's boundary. The M-SDF representation is fast to compute for each shape individually making it readily parallelizable; it is parameter efficient as it only covers the space around the shape's boundary; and it has a simple matrix form, compatible with Transformer-based architectures. We demonstrate the efficacy of the M-SDF representation by using it to train a 3D generative flow model including class-conditioned generation with the 3D Warehouse dataset, and text-to-3D generation using a dataset of about 600k caption-shape pairs., Comment: More results and details can be found at https://lioryariv.github.io/msdf

Classifier-free guidance is a key component for enhancing the performance of conditional generative models across diverse tasks. While it has previously demonstrated remarkable improvements for the sample quality, it has only been exclusively employed for diffusion models. In this paper, we integrate classifier-free guidance into Flow Matching (FM) models, an alternative simulation-free approach that trains Continuous Normalizing Flows (CNFs) based on regressing vector fields. We explore the usage of \emph{Guided Flows} for a variety of downstream applications. We show that Guided Flows significantly improves the sample quality in conditional image generation and zero-shot text-to-speech synthesis, boasting state-of-the-art performance. Notably, we are the first to apply flow models for plan generation in the offline reinforcement learning setting, showcasing a 10x speedup in computation compared to diffusion models while maintaining comparable performance.

Diffusion or flow-based models are powerful generative paradigms that are notoriously hard to sample as samples are defined as solutions to high-dimensional Ordinary or Stochastic Differential Equations (ODEs/SDEs) which require a large Number of Function Evaluations (NFE) to approximate well. Existing methods to alleviate the costly sampling process include model distillation and designing dedicated ODE solvers. However, distillation is costly to train and sometimes can deteriorate quality, while dedicated solvers still require relatively large NFE to produce high quality samples. In this paper we introduce "Bespoke solvers", a novel framework for constructing custom ODE solvers tailored to the ODE of a given pre-trained flow model. Our approach optimizes an order consistent and parameter-efficient solver (e.g., with 80 learnable parameters), is trained for roughly 1% of the GPU time required for training the pre-trained model, and significantly improves approximation and generation quality compared to dedicated solvers. For example, a Bespoke solver for a CIFAR10 model produces samples with Fr\'echet Inception Distance (FID) of 2.73 with 10 NFE, and gets to 1% of the Ground Truth (GT) FID (2.59) for this model with only 20 NFE. On the more challenging ImageNet-64$\times$64, Bespoke samples at 2.2 FID with 10 NFE, and gets within 2% of GT FID (1.71) with 20 NFE.

Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution matching setup, where these marginals are only implicitly described as a solution to some task-specific objective function. The problem setup, known as the Generalized Schr\"odinger Bridge (GSB), appears prevalently in many scientific areas both within and without machine learning. We propose Generalized Schr\"odinger Bridge Matching (GSBM), a new matching algorithm inspired by recent advances, generalizing them beyond kinetic energy minimization and to account for task-specific state costs. We show that such a generalization can be cast as solving conditional stochastic optimal control, for which efficient variational approximations can be used, and further debiased with the aid of path integral theory. Compared to prior methods for solving GSB problems, our GSBM algorithm better preserves a feasible transport map between the boundary distributions throughout training, thereby enabling stable convergence and significantly improved scalability. We empirically validate our claims on an extensive suite of experimental setups, including crowd navigation, opinion depolarization, LiDAR manifolds, and image domain transfer. Our work brings new algorithmic opportunities for training diffusion models enhanced with task-specific optimality structures. Code available at https://github.com/facebookresearch/generalized-schrodinger-bridge-matching, Comment: ICLR 2024 Camera Ready

This paper introduces CORAE, a novel web-based open-source tool for COntinuous Retrospective Affect Evaluation, designed to capture continuous affect data about interpersonal perceptions in dyadic interactions. Grounded in behavioral ecology perspectives of emotion, this approach replaces valence as the relevant rating dimension with approach and withdrawal, reflecting the degree to which behavior is perceived as increasing or decreasing social distance. We conducted a study to experimentally validate the efficacy of our platform with 24 participants. The tool's effectiveness was tested in the context of dyadic negotiation, revealing insights about how interpersonal dynamics evolve over time. We find that the continuous affect rating method is consistent with individuals' perception of the overall interaction. This paper contributes to the growing body of research on affective computing and offers a valuable tool for researchers interested in investigating the temporal dynamics of affect and emotion in social interactions.

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the \emph{data separation function}. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to $1$ in the general case of arbitrary normalized dataset consisting of $n$ samples in $d$ dimension as $n/\sqrt{d}\rightarrow 0$. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes \emph{kinetic optimal} as $n/\sqrt{d}\rightarrow 0$. We further support this theory with empirical experiments on ImageNet.