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Generative modeling of discrete data underlies important applications spanning text-based agents like ChatGPT to the design of the very building blocks of life in protein sequences. However, application domains need to exert control over the generated data by steering the generative process - typically via RLHF - to satisfy a specified property, reward, or affinity metric. In this paper, we study the problem of steering Masked Diffusion Models (MDMs), a recent class of discrete diffusion models that offer a compelling alternative to traditional autoregressive models. We introduce Discrete Denoising Posterior Prediction (DDPP), a novel framework that casts the task of steering pre-trained MDMs as a problem of probabilistic inference by learning to sample from a target Bayesian posterior. Our DDPP framework leads to a family of three novel objectives that are all simulation-free, and thus scalable while applying to general non-differentiable reward functions. Empirically, we instantiate DDPP by steering MDMs to perform class-conditional pixel-level image modeling, RLHF-based alignment of MDMs using text-based rewards, and finetuning protein language models to generate more diverse secondary structures and shorter proteins. We substantiate our designs via wet-lab validation, where we observe transient expression of reward-optimized protein sequences.

Amortized inference is the task of training a parametric model, such as a neural network, to approximate a distribution with a given unnormalized density where exact sampling is intractable. When sampling is implemented as a sequential decision-making process, reinforcement learning (RL) methods, such as generative flow networks, can be used to train the sampling policy. Off-policy RL training facilitates the discovery of diverse, high-reward candidates, but existing methods still face challenges in efficient exploration. We propose to use an adaptive training distribution (the Teacher) to guide the training of the primary amortized sampler (the Student) by prioritizing high-loss regions. The Teacher, an auxiliary behavior model, is trained to sample high-error regions of the Student and can generalize across unexplored modes, thereby enhancing mode coverage by providing an efficient training curriculum. We validate the effectiveness of this approach in a synthetic environment designed to present an exploration challenge, two diffusion-based sampling tasks, and four biochemical discovery tasks demonstrating its ability to improve sample efficiency and mode coverage., Comment: 26 pages, 12 figures

The AAS Strategic Plan for 2021-26 called for the creation of a task force to identify how the AAS can meet the goals of the Paris Agreement. The AAS and its membership recognize the danger climate change represents to humanity and our world, and to astronomy -- as a profession, a hobby, and a cultural good. Our profession in general -- and the AAS in particular -- should work to make it possible for all astronomers to have an equal opportunity to be successful without needing to incur high carbon emissions, and to preserve astronomy for future generations. A study was completed of the carbon emissions associated with the AAS, finding that 84% of total AAS-related emissions are from in-person conferences. We also conducted a survey of AAS members to determine their attitudes about climate change. Respondents overwhelmingly (97%) think that the AAS should reduce its carbon footprint. Our task force created a list of fourteen recommendations, with two ranked as top priorities: The AAS should not schedule additional in-person meetings before 2030 and it should work to innovate the AAS conference model. Based upon our analysis it is clear that online interaction is the only way to increase participation while meaningfully decreasing emissions. Our recommendations are aligned with the Astro2020 Decadal Survey as well as AAS values to disseminate our scientific understanding of the universe, and to do our work in an ethically responsible way. Because of their other benefits -- particularly in making our society more welcoming to those who traditionally have been excluded -- we feel that these are sound decisions, worthy of implementation even if the AAS wasn't trying to reduce its carbon footprint. They simply make sense as steps towards a professional society that better serves a broader membership, as our profession evolves to be greener, more inclusive, and more productive., Comment: 46 pages

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized sampling of the posterior over data, $\mathbf{x}\sim p^{\rm post}(\mathbf{x})\propto p(\mathbf{x})r(\mathbf{x})$, in a model that consists of a diffusion generative model prior $p(\mathbf{x})$ and a black-box constraint or likelihood function $r(\mathbf{x})$. We state and prove the asymptotic correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from this posterior, a problem that existing methods solve only approximately or in restricted cases. Relative trajectory balance arises from the generative flow network perspective on diffusion models, which allows the use of deep reinforcement learning techniques to improve mode coverage. Experiments illustrate the broad potential of unbiased inference of arbitrary posteriors under diffusion priors: in vision (classifier guidance), language (infilling under a discrete diffusion LLM), and multimodal data (text-to-image generation). Beyond generative modeling, we apply relative trajectory balance to the problem of continuous control with a score-based behavior prior, achieving state-of-the-art results on benchmarks in offline reinforcement learning., Comment: Code: https://github.com/GFNOrg/diffusion-finetuning

Proteins are essential for almost all biological processes and derive their diverse functions from complex 3D structures, which are in turn determined by their amino acid sequences. In this paper, we exploit the rich biological inductive bias of amino acid sequences and introduce FoldFlow-2, a novel sequence-conditioned SE(3)-equivariant flow matching model for protein structure generation. FoldFlow-2 presents substantial new architectural features over the previous FoldFlow family of models including a protein large language model to encode sequence, a new multi-modal fusion trunk that combines structure and sequence representations, and a geometric transformer based decoder. To increase diversity and novelty of generated samples -- crucial for de-novo drug design -- we train FoldFlow-2 at scale on a new dataset that is an order of magnitude larger than PDB datasets of prior works, containing both known proteins in PDB and high-quality synthetic structures achieved through filtering. We further demonstrate the ability to align FoldFlow-2 to arbitrary rewards, e.g. increasing secondary structures diversity, by introducing a Reinforced Finetuning (ReFT) objective. We empirically observe that FoldFlow-2 outperforms previous state-of-the-art protein structure-based generative models, improving over RFDiffusion in terms of unconditional generation across all metrics including designability, diversity, and novelty across all protein lengths, as well as exhibiting generalization on the task of equilibrium conformation sampling. Finally, we demonstrate that a fine-tuned FoldFlow-2 makes progress on challenging conditional design tasks such as designing scaffolds for the VHH nanobody., Comment: Presented at NeurIPS 2024

Despite substantial progress in machine learning for scientific discovery in recent years, truly de novo design of small molecules which exhibit a property of interest remains a significant challenge. We introduce LambdaZero, a generative active learning approach to search for synthesizable molecules. Powered by deep reinforcement learning, LambdaZero learns to search over the vast space of molecules to discover candidates with a desired property. We apply LambdaZero with molecular docking to design novel small molecules that inhibit the enzyme soluble Epoxide Hydrolase 2 (sEH), while enforcing constraints on synthesizability and drug-likeliness. LambdaZero provides an exponential speedup in terms of the number of calls to the expensive molecular docking oracle, and LambdaZero de novo designed molecules reach docking scores that would otherwise require the virtual screening of a hundred billion molecules. Importantly, LambdaZero discovers novel scaffolds of synthesizable, drug-like inhibitors for sEH. In in vitro experimental validation, a series of ligands from a generated quinazoline-based scaffold were synthesized, and the lead inhibitor N-(4,6-di(pyrrolidin-1-yl)quinazolin-2-yl)-N-methylbenzamide (UM0152893) displayed sub-micromolar enzyme inhibition of sEH.

Travel to academic conferences -- where international flights are the norm -- is responsible for a sizeable fraction of the greenhouse gas (GHG) emissions associated with academic work. In order to provide a benchmark for comparison with other fields, as well as for future reduction strategies and assessments, we estimate the CO2-equivalent emissions for conference travel in the field of astronomy for the prepandemic year 2019. The GHG emission of the international astronomical community's 362 conferences and schools in 2019 amounted to 42,500 tCO2e, assuming a radiative-forcing index factor of 1.95 for air travel. This equates to an average of 1.0 $\pm$ 0.6 tCO2e per participant per meeting. The total travel distance adds up to roughly 1.5 Astronomical Units, that is, 1.5 times the distance between the Earth and the Sun. We present scenarios for the reduction of this value, for instance with virtual conferencing or hub models, while still prioritizing the benefits conferences bring to the scientific community., Comment: Supplementary material is available at PNAS Nexus online: https://academic.oup.com/pnasnexus/article/3/5/pgae143/7659884

Converting a three-dimensional medical image into a 3D mesh that satisfies both the quality and fidelity constraints of predictive simulations and image-guided surgical procedures remains a critical problem. Presented is an image-to-mesh conversion method called CBC3D. It first discretizes a segmented image by generating an adaptive Body-Centered Cubic (BCC) mesh of high-quality elements. Next, the tetrahedral mesh is converted into a mixed-element mesh of tetrahedra, pentahedra, and hexahedra to decrease element count while maintaining quality. Finally, the mesh surfaces are deformed to their corresponding physical image boundaries, improving the mesh's fidelity. The deformation scheme builds upon the ITK open-source library and is based on the concept of energy minimization, relying on a multi-material point-based registration. It uses non-connectivity patterns to implicitly control the number of extracted feature points needed for the registration and, thus, adjusts the trade-off between the achieved mesh fidelity and the deformation speed. We compare CBC3D with four widely used and state-of-the-art homegrown image-to-mesh conversion methods from industry and academia. Results indicate that the CBC3D meshes (i) achieve high fidelity, (ii) keep the element count reasonably low, and (iii) exhibit good element quality., Comment: 37 pages, 26 figures

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant $n$-body particle systems. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5\times$ faster, which allows it to be the first method to train using energy on the challenging $55$-particle Lennard-Jones system., Comment: Published at ICML 2024. Code for iDEM is available at https://github.com/jarridrb/dem

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference., Comment: 24 pages; changed title from v2; code: https://github.com/GFNOrg/gfn-diffusion

The computational design of novel protein structures has the potential to impact numerous scientific disciplines greatly. Toward this goal, we introduce FoldFlow, a series of novel generative models of increasing modeling power based on the flow-matching paradigm over $3\mathrm{D}$ rigid motions -- i.e. the group $\text{SE}(3)$ -- enabling accurate modeling of protein backbones. We first introduce FoldFlow-Base, a simulation-free approach to learning deterministic continuous-time dynamics and matching invariant target distributions on $\text{SE}(3)$. We next accelerate training by incorporating Riemannian optimal transport to create FoldFlow-OT, leading to the construction of both more simple and stable flows. Finally, we design FoldFlow-SFM, coupling both Riemannian OT and simulation-free training to learn stochastic continuous-time dynamics over $\text{SE}(3)$. Our family of FoldFlow, generative models offers several key advantages over previous approaches to the generative modeling of proteins: they are more stable and faster to train than diffusion-based approaches, and our models enjoy the ability to map any invariant source distribution to any invariant target distribution over $\text{SE}(3)$. Empirically, we validate FoldFlow, on protein backbone generation of up to $300$ amino acids leading to high-quality designable, diverse, and novel samples., Comment: ICLR 2024 Spotlight

Generative flow networks (GFlowNets) are amortized variational inference algorithms that treat sampling from a distribution over compositional objects as a sequential decision-making problem with a learnable action policy. Unlike other algorithms for hierarchical sampling that optimize a variational bound, GFlowNet algorithms can stably run off-policy, which can be advantageous for discovering modes of the target distribution. Despite this flexibility in the choice of behaviour policy, the optimal way of efficiently selecting trajectories for training has not yet been systematically explored. In this paper, we view the choice of trajectories for training as an active learning problem and approach it using Bayesian techniques inspired by methods for multi-armed bandits. The proposed algorithm, Thompson sampling GFlowNets (TS-GFN), maintains an approximate posterior distribution over policies and samples trajectories from this posterior for training. We show in two domains that TS-GFN yields improved exploration and thus faster convergence to the target distribution than the off-policy exploration strategies used in past work., Comment: Structured Probabilistic Inference and Generative Modeling (SPIGM) workshop @ ICML 2023

Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their simulation-based maximum likelihood training. We introduce the generalized conditional flow matching (CFM) technique, a family of simulation-free training objectives for CNFs. CFM features a stable regression objective like that used to train the stochastic flow in diffusion models but enjoys the efficient inference of deterministic flow models. In contrast to both diffusion models and prior CNF training algorithms, CFM does not require the source distribution to be Gaussian or require evaluation of its density. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference, as evaluated in our experiments. Furthermore, we show that when the true OT plan is available, our OT-CFM method approximates dynamic OT. Training CNFs with CFM improves results on a variety of conditional and unconditional generation tasks, such as inferring single cell dynamics, unsupervised image translation, and Schr\"odinger bridge inference., Comment: TMLR. Code: https://github.com/atong01/conditional-flow-matching

We study the problem of generating diverse candidates in the context of Multi-Objective Optimization. In many applications of machine learning such as drug discovery and material design, the goal is to generate candidates which simultaneously optimize a set of potentially conflicting objectives. Moreover, these objectives are often imperfect evaluations of some underlying property of interest, making it important to generate diverse candidates to have multiple options for expensive downstream evaluations. We propose Multi-Objective GFlowNets (MOGFNs), a novel method for generating diverse Pareto optimal solutions, based on GFlowNets. We introduce two variants of MOGFNs: MOGFN-PC, which models a family of independent sub-problems defined by a scalarization function, with reward-conditional GFlowNets, and MOGFN-AL, which solves a sequence of sub-problems defined by an acquisition function in an active learning loop. Our experiments on wide variety of synthetic and benchmark tasks demonstrate advantages of the proposed methods in terms of the Pareto performance and importantly, improved candidate diversity, which is the main contribution of this work., Comment: 23 pages, 8 figures. ICML 2023. Code at: https://github.com/GFNOrg/multi-objective-gfn

Generative flow networks (GFlowNets) are a family of algorithms for training a sequential sampler of discrete objects under an unnormalized target density and have been successfully used for various probabilistic modeling tasks. Existing training objectives for GFlowNets are either local to states or transitions, or propagate a reward signal over an entire sampling trajectory. We argue that these alternatives represent opposite ends of a gradient bias-variance tradeoff and propose a way to exploit this tradeoff to mitigate its harmful effects. Inspired by the TD($\lambda$) algorithm in reinforcement learning, we introduce subtrajectory balance or SubTB($\lambda$), a GFlowNet training objective that can learn from partial action subsequences of varying lengths. We show that SubTB($\lambda$) accelerates sampler convergence in previously studied and new environments and enables training GFlowNets in environments with longer action sequences and sparser reward landscapes than what was possible before. We also perform a comparative analysis of stochastic gradient dynamics, shedding light on the bias-variance tradeoff in GFlowNet training and the advantages of subtrajectory balance., Comment: ICML 2023

A long-term (1995-2016) survey for novae in the nearby Andromeda galaxy (M31) was conducted as part of the Research-Based Science Education initiative. During the course of the survey 180 nights of observation were completed at Kitt Peak, Arizona. A total of 262 novae were either discovered or confirmed, 40 of which have not been previously reported. Of these, 203 novae form a spatially-complete sample detected by the KPNO/WIYN 0.9-m telescope within a $20'\times20'$ field centered on the nucleus of M31. An additional 50 novae are part of a spatially-complete sample detected by the KPNO 4-m telescope within a larger $36'\times36'$ field. Consistent with previous studies, it is found that the spatial distribution of novae in both surveys follows the bulge light of M31 somewhat more closely than the overall background light of the galaxy. After correcting for the limiting magnitude and the spatial and temporal coverage of the surveys, a final nova rate in M31 is found to be $R=40^{+5}_{-4}$ yr$^{-1}$, which is considerably lower than recent estimates. When normalized to the $K$-band luminosity of M31, this value yields a luminosity-specific nova rate, $\nu_K = 3.3\pm0.4$ yr$^{-1} [10^{10} L_{\odot,K}]^{-1}$. By scaling the M31 nova rate using the relative infrared luminosities of M31 and our Galaxy, a nova rate of $R_\mathrm{G}=28^{+5}_{-4}$ is found for the Milky Way., Comment: 20 pages, 15 figures. Accepted by ApJ

Design of de novo biological sequences with desired properties, like protein and DNA sequences, often involves an active loop with several rounds of molecule ideation and expensive wet-lab evaluations. These experiments can consist of multiple stages, with increasing levels of precision and cost of evaluation, where candidates are filtered. This makes the diversity of proposed candidates a key consideration in the ideation phase. In this work, we propose an active learning algorithm leveraging epistemic uncertainty estimation and the recently proposed GFlowNets as a generator of diverse candidate solutions, with the objective to obtain a diverse batch of useful (as defined by some utility function, for example, the predicted anti-microbial activity of a peptide) and informative candidates after each round. We also propose a scheme to incorporate existing labeled datasets of candidates, in addition to a reward function, to speed up learning in GFlowNets. We present empirical results on several biological sequence design tasks, and we find that our method generates more diverse and novel batches with high scoring candidates compared to existing approaches., Comment: ICML 2022. 15 pages, 3 figures. Code available at: https://github.com/MJ10/BioSeq-GFN-AL. Updated GFP results

For large libraries of small molecules, exhaustive combinatorial chemical screens become infeasible to perform when considering a range of disease models, assay conditions, and dose ranges. Deep learning models have achieved state of the art results in silico for the prediction of synergy scores. However, databases of drug combinations are biased towards synergistic agents and these results do not necessarily generalise out of distribution. We employ a sequential model optimization search utilising a deep learning model to quickly discover synergistic drug combinations active against a cancer cell line, requiring substantially less screening than an exhaustive evaluation. Our small scale wet lab experiments only account for evaluation of ~5% of the total search space. After only 3 rounds of ML-guided in vitro experimentation (including a calibration round), we find that the set of drug pairs queried is enriched for highly synergistic combinations; two additional rounds of ML-guided experiments were performed to ensure reproducibility of trends. Remarkably, we rediscover drug combinations later confirmed to be under study within clinical trials. Moreover, we find that drug embeddings generated using only structural information begin to reflect mechanisms of action. Prior in silico benchmarking suggests we can enrich search queries by a factor of ~5-10x for highly synergistic drug combinations by using sequential rounds of evaluation when compared to random selection, or by a factor of >3x when using a pretrained model selecting all drug combinations at a single time point.