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 modeled 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). The Teacher, an auxiliary behavior model, is trained to sample high-loss 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. Source code is available at https://github.com/alstn12088/adaptive-teacher.

As trajectories sampled by policies used by reinforcement learning (RL) and generative flow networks (GFlowNets) grow longer, credit assignment and exploration become more challenging, and the long planning horizon hinders mode discovery and generalization. The challenge is particularly pronounced in entropy-seeking RL methods, such as generative flow networks, where the agent must learn to sample from a structured distribution and discover multiple high-reward states, each of which take many steps to reach. To tackle this challenge, we propose an approach to incorporate the discovery of action abstractions, or high-level actions, into the policy optimization process. Our approach involves iteratively extracting action subsequences commonly used across many high-reward trajectories and `chunking' them into a single action that is added to the action space. In empirical evaluation on synthetic and real-world environments, our approach demonstrates improved sample efficiency performance in discovering diverse high-reward objects, especially on harder exploration problems. We also observe that the abstracted high-order actions are potentially interpretable, capturing the latent structure of the reward landscape of the action space. This work provides a cognitively motivated approach to action abstraction in RL and is the first demonstration of hierarchical planning in amortized sequential sampling.

Generative models see increasing use in computer-aided drug design. However, while performing well at capturing distributions of molecular motifs, they often produce synthetically inaccessible molecules. To address this, we introduce SynFlowNet, a GFlowNet model whose action space uses chemical reactions and buyable reactants to sequentially build new molecules. By incorporating forward synthesis as an explicit constraint of the generative mechanism, we aim at bridging the gap between in silico molecular generation and real world synthesis capabilities. We evaluate our approach using synthetic accessibility scores and an independent retrosynthesis tool to assess the synthesizability of our compounds, and motivate the choice of GFlowNets through considerable improvement in sample diversity compared to baselines. Additionally, we identify challenges with reaction encodings that can complicate traversal of the MDP in the backward direction. To address this, we introduce various strategies for learning the GFlowNet backward policy and thus demonstrate how additional constraints can be integrated into the GFlowNet MDP framework. This approach enables our model to successfully identify synthesis pathways for previously unseen molecules.

Exploration is a key factor for the success of an active learning agent, especially when dealing with sparse extrinsic terminal rewards and long trajectories. We introduce Sibling Augmented Generative Flow Networks (SA-GFN), a novel framework designed to enhance exploration and training efficiency of Generative Flow Networks (GFlowNets). SA-GFN uses a decoupled dual network architecture, comprising of a main Behavior Network and an exploratory Sibling Network, to enable a diverse exploration of the underlying distribution using intrinsic rewards. Inspired by the ideas on exploration from reinforcement learning, SA-GFN provides a general-purpose exploration and learning paradigm that integrates with multiple GFlowNet training objectives and is especially helpful for exploration over a wide range of sparse or low reward distributions and task structures. An extensive set of experiments across a diverse range of tasks, reward structures and trajectory lengths, along with a thorough set of ablations, demonstrate the superior performance of SA-GFN in terms of exploration efficacy and convergence speed as compared to the existing methods. In addition, SA-GFN's versatility and compatibility with different GFlowNet training objectives and intrinsic reward methods underscores its broad applicability in various problem domains.

In drug discovery, highly automated high-throughput laboratories are used to screen a large number of compounds in search of effective drugs. These experiments are expensive, so one might hope to reduce their cost by only experimenting on a subset of the compounds, and predicting the outcomes of the remaining experiments. In this work, we model this scenario as a sequential subset selection problem: we aim to select the smallest set of candidates in order to achieve some desired level of accuracy for the system as a whole. Our key observation is that, if there is heterogeneity in the difficulty of the prediction problem across the input space, selectively obtaining the labels for the hardest examples in the acquisition pool will leave only the relatively easy examples to remain in the inference set, leading to better overall system performance. We call this mechanism inference set design, and propose the use of a confidence-based active learning solution to prune out these challenging examples. Our algorithm includes an explicit stopping criterion that interrupts the acquisition loop when it is sufficiently confident that the system has reached the target performance. Our empirical studies on image and molecular datasets, as well as a real-world large-scale biological assay, show that active learning for inference set design leads to significant reduction in experimental cost while retaining high system performance.

The Generative Flow Network (GFlowNet) is a probabilistic framework in which an agent learns a stochastic policy and flow functions to sample objects with probability proportional to an unnormalized reward function. GFlowNets share a strong connection with reinforcement learning (RL) that typically aims to maximize reward. A number of recent works explored connections between GFlowNets and maximum entropy (MaxEnt) RL, which incorporates entropy regularization into the standard RL objective. However, the relationship between GFlowNets and standard RL remains largely unexplored, despite the inherent similarities in their sequential decision-making nature. While GFlowNets can discover diverse solutions through specialized flow-matching objectives, connecting them to standard RL can simplify their implementation through well-established RL principles and also improve RL’s capabilities in diverse solution discovery (a critical requirement in many real-world applications), and bridging this gap can further unlock the potential of both fields. In this paper, we bridge this gap by revealing a fundamental connection between GFlowNets and one of the most basic components of RL – policy evaluation. Surprisingly, we find that the value function obtained from evaluating a uniform policy is closely associated with the flow functions in GFlowNets. Building upon these insights, we introduce a rectified random policy evaluation (RPE) algorithm, which achieves the same reward-matching effect as GFlowNets based on simply evaluating a fixed random policy, offering a new perspective. Empirical results across extensive benchmarks demonstrate that RPE achieves competitive results compared to previous approaches, shedding light on the previously overlooked connection between (non-MaxEnt) RL and GFlowNets.

Designing biological sequences with desired properties is challenging due to vast search spaces and limited evaluation budgets. Although reinforcement learning methods use proxy models for rapid reward evaluation, insufficient training data can cause proxy misspecification on out-of-distribution inputs. To address this, we propose a novel off-policy search, $\delta$-Conservative Search, that enhances robustness by restricting policy exploration to reliable regions. Starting from high-score offline sequences, we inject noise by randomly masking tokens with probability $\delta$, then denoise them using our policy. We further adapt $\delta$ based on proxy uncertainty on each data point, aligning the level of conservativeness with model confidence. Experimental results show that our conservative search consistently enhances the off-policy training, outperforming existing machine learning methods in discovering high-score sequences across diverse tasks, including DNA, RNA, protein, and peptide design.

Generative Flow Networks (GFlowNets) have recently emerged as a suitable framework for generating diverse and high-quality molecular structures by learning from rewards treated as unnormalized distributions. Previous works in this framework often restrict exploration by using predefined molecular fragments as building blocks, limiting the chemical space that can be accessed. In this work, we introduce Atomic GFlowNets (A-GFNs), a foundational generative model leveraging individual atoms as building blocks to explore drug-like chemical space more comprehensively. We propose an unsupervised pre-training approach using drug-like molecule datasets, which teaches A-GFNs about inexpensive yet informative molecular descriptors such as drug-likeliness, topological polar surface area, and synthetic accessibility scores. These properties serve as proxy rewards, guiding A-GFNs towards regions of chemical space that exhibit desirable pharmacological properties. We further implement a goal-conditioned finetuning process, which adapts A-GFNs to optimize for specific target properties. In this work, we pretrain A-GFN on a subset of ZINC dataset, and by employing robust evaluation metrics we show the effectiveness of our approach when compared to other relevant baseline methods for a wide range of drug design tasks. The code is accessible at https://github.com/diamondspark/AGFN.

Generative Flow Networks (GFNs) have emerged as a powerful tool for sampling discrete objects from unnormalized distributions, offering a scalable alternative to Markov Chain Monte Carlo (MCMC) methods. While GFNs draw inspiration from maximum entropy reinforcement learning (RL), the connection between the two has largely been unclear and seemingly applicable only in specific cases. This paper addresses the connection by constructing an appropriate reward function, thereby establishing an exact relationship between GFNs and maximum entropy RL. This construction allows us to introduce maximum entropy GFNs, which achieve the maximum entropy attainable by GFNs without constraints on the state space, in contrast to GFNs with uniform backward policy.

Generative Flow Networks (GFlowNets) are amortized sampling methods that learn a distribution over discrete objects proportional to their rewards. GFlowNets exhibit a remarkable ability to generate diverse samples, yet occasionally struggle to consistently produce samples with high rewards due to over-exploration on wide sample space. This paper proposes to train GFlowNets with local search, which focuses on exploiting high-rewarded sample space to resolve this issue. Our main idea is to explore the local neighborhood via backtracking and reconstruction guided by backward and forward policies, respectively. This allows biasing the samples toward high-reward solutions, which is not possible for a typical GFlowNet solution generation scheme, which uses the forward policy to generate the solution from scratch. Extensive experiments demonstrate a remarkable performance improvement in several biochemical tasks. Source code is available: \url{https://github.com/dbsxodud-11/ls_gfn}.

GFlowNets are probabilistic models that sequentially generate compositional structures through a stochastic policy. Among GFlowNets, temperature-conditional GFlowNets can introduce temperature-based controllability for exploration and exploitation. We propose Logit-scaling GFlowNets (Logit-GFN), a novel architectural design that greatly accelerates the training of temperature-conditional GFlowNets. It is based on the idea that previously proposed approaches introduced numerical challenges in the deep network training, since different temperatures may give rise to very different gradient profiles as well as magnitudes of the policy’s logits. We find that the challenge is greatly reduced if a learned function of the temperature is used to scale the policy’s logits directly. Also, using Logit-GFN, GFlowNets can be improved by having better generalization capabilities in offline learning and mode discovery capabilities in online learning, which is empirically verified in various biological and chemical tasks. Our code is available at https://github.com/dbsxodud-11/logit-gfn

Generative Flow Networks (GFlowNets; GFNs) are a family of energy-based generative methods for combinatorial objects, capable of generating diverse and high-utility samples. However, consistently biasing GFNs towards producing high-utility samples is non-trivial. In this work, we leverage connections between GFNs and reinforcement learning (RL) and propose to combine the GFN policy with an action-value estimate, $Q$, to create greedier sampling policies which can be controlled by a mixing parameter. We show that several variants of the proposed method, QGFN, are able to improve on the number of high-reward samples generated in a variety of tasks without sacrificing diversity.

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. Code is available at [this link](https://github.com/GFNOrg/diffusion-finetuning).

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.

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.

Generative flow networks (GFlowNets) are a family of algorithms that learn a generative policy to sample discrete objects $x$ with non-negative reward $R(x)$. Learning objectives guarantee the GFlowNet samples $x$ from the target distribution $p^*(x) \propto R(x)$ when loss is globally minimized over all states or trajectories, but it is unclear how well they perform with practical limits on training resources. We introduce an efficient evaluation strategy to compare the learned sampling distribution to the target reward distribution. As flows can be underdetermined given training data, we clarify the importance of learned flows to generalization and matching $p^*(x)$ in practice. We investigate how to learn better flows, and propose (i) prioritized replay training of high-reward $x$, (ii) relative edge flow policy parametrization, and (iii) a novel guided trajectory balance objective, and show how it can solve a substructure credit assignment problem. We substantially improve sample efficiency on biochemical design tasks.

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context, with a training objective that makes them approximately sample in proportion to a given reward function. In this paper, we show a number of additional theoretical properties of GFlowNets, including a new local and efficient training objective called detailed balance for the analogy with MCMC. GFlowNets can be used to estimate joint probability distributions and the corresponding marginal distributions where some variables are unspecified and, of particular interest, can represent distributions over composite objects like sets and graphs. GFlowNets amortize the work typically done by computationally expensive MCMC methods in a single but trained generative pass. They could also be used to estimate partition functions and free energies, conditional probabilities of supersets (supergraphs) given a subset (subgraph), as well as marginal distributions over all supersets (supergraphs) of a given set (graph). We introduce variations enabling the estimation of entropy and mutual information, continuous actions and modular energy functions.

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.

Generative flow networks (GFlowNets) are a method for learning a stochastic policy for generating compositional objects, such as graphs or strings, from a given unnormalized density by sequences of actions, where many possible action sequences may lead to the same object. We find previously proposed learning objectives for GFlowNets, flow matching and detailed balance, which are analogous to temporal difference learning, to be prone to inefficient credit propagation across long action sequences. We thus propose a new learning objective for GFlowNets, trajectory balance, as a more efficient alternative to previously used objectives. We prove that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution. In experiments on four distinct domains, we empirically demonstrate the benefits of the trajectory balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequences and large action spaces.

This paper is about the problem of learning a stochastic policy for generating an object (like a molecular graph) from a sequence of actions, such that the probability of generating an object is proportional to a given positive reward for that object. Whereas standard return maximization tends to converge to a single return-maximizing sequence, there are cases where we would like to sample a diverse set of high-return solutions. These arise, for example, in black-box function optimization when few rounds are possible, each with large batches of queries, where the batches should be diverse, e.g., in the design of new molecules. One can also see this as a problem of approximately converting an energy function to a generative distribution. While MCMC methods can achieve that, they are expensive and generally only perform local exploration. Instead, training a generative policy amortizes the cost of search during training and yields to fast generation. Using insights from Temporal Difference learning, we propose GFlowNet, based on a view of the generative process as a flow network, making it possible to handle the tricky case where different trajectories can yield the same final state, e.g., there are many ways to sequentially add atoms to generate some molecular graph. We cast the set of trajectories as a flow and convert the flow consistency equations into a learning objective, akin to the casting of the Bellman equations into Temporal Difference methods. We prove that any global minimum of the proposed objectives yields a policy which samples from the desired distribution, and demonstrate the improved performance and diversity of GFlowNet on a simple domain where there are many modes to the reward function, and on a molecule synthesis task.

We study the link between generalization and interference in temporal-difference (TD) learning. Interference is defined as the inner product of two different gradients, representing their alignment; this quantity emerges as being of interest from a variety of observations about neural networks, parameter sharing and the dynamics of learning. We find that TD easily leads to low-interference, under-generalizing parameters, while the effect seems reversed in supervised learning. We hypothesize that the cause can be traced back to the interplay between the dynamics of interference and bootstrapping. This is supported empirically by several observations: the negative relationship between the generalization gap and interference in TD, the negative effect of bootstrapping on interference and the local coherence of targets, and the contrast between the propagation rate of information in TD(0) versus TD($\lambda$) and regression tasks such as Monte-Carlo policy evaluation. We hope that these new findings can guide the future discovery of better bootstrapping methods.

Humans interpret texts with respect to some background information, or world knowledge, and we would like to develop automatic reading comprehension systems that can do the same.In this paper, we introduce a task and several models to drive progress towards this goal.In particular, we propose the task of rare entity prediction: given a web document with several entities removed, models are tasked with predicting the correct missing entities conditioned on the document context and the lexical resources.This task is challenging due to the diversity of language styles and the extremely large number of rare entities.We propose two recurrent neural network architectures which make use of external knowledge in the form of entity descriptions.Our experiments show that our hierarchical LSTM model performs significantly better at the rare entity prediction task than those that do not make use of external resources.

We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While deep networks are capable of memorizing noise data, our results suggest that they tend to prioritize learning simple patterns first. In our experiments, we expose qualitative differences in gradient-based optimization of deep neural networks (DNNs) on noise vs.~real data. We also demonstrate that for appropriately tuned explicit regularization (e.g.,~dropout) we can degrade DNN training performance on noise datasets without compromising generalization on real data. Our analysis suggests that the notions of effective capacity which are dataset independent are unlikely to explain the generalization performance of deep networks when trained with gradient based methods because training data itself plays an important role in determining the degree of memorization.

In this paper we present the techniques used for the University of Montréal's team submissions to the 2013 Emotion Recognition in the Wild Challenge. The challenge is to classify the emotions expressed by the primary human subject in short video clips extracted from feature length movies. This involves the analysis of video clips of acted scenes lasting approximately one-two seconds, including the audio track which may contain human voices as well as background music. Our approach combines multiple deep neural networks for different data modalities, including: (1) a deep convolutional neural network for the analysis of facial expressions within video frames; (2) a deep belief net to capture audio information; (3) a deep autoencoder to model the spatio-temporal information produced by the human actions depicted within the entire scene; and (4) a shallow network architecture focused on extracted features of the mouth of the primary human subject in the scene. We discuss each of these techniques, their performance characteristics and different strategies to aggregate their predictions. Our best single model was a convolutional neural network trained to predict emotions from static frames using two large data sets, the Toronto Face Database and our own set of faces images harvested from Google image search, followed by a per frame aggregation strategy that used the challenge training data. This yielded a test set accuracy of 35.58%. Using our best strategy for aggregating our top performing models into a single predictor we were able to produce an accuracy of 41.03% on the challenge test set. These compare favorably to the challenge baseline test set accuracy of 27.56%.