Sarthak Mittal

arxiv.org

Amortized In-Context Bayesian Posterior Estimation

N. L. Bracher

Priyank Jaini

Marcus Brubaker

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Cur… (see more)rent solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and Variational Inference (VI), which need to be re-run whenever new observations are available. Amortization, through conditional estimation, is a viable strategy to alleviate such difficulties and has been the guiding principle behind simulation-based inference, neural processes and in-context methods using pre-trained models. In this work, we conduct a thorough comparative analysis of amortized in-context Bayesian posterior estimation methods from the lens of different optimization objectives and architectural choices. Such methods train an amortized estimator to perform posterior parameter inference by conditioning on a set of data examples passed as context to a sequence model such as a transformer. In contrast to language models, we leverage permutation invariant architectures as the true posterior is invariant to the ordering of context examples. Our empirical study includes generalization to out-of-distribution tasks, cases where the assumed underlying model is misspecified, and transfer from simulated to real problems. Subsequently, it highlights the superiority of the reverse KL estimator for predictive problems, especially when combined with the transformer architecture and normalizing flows.

2025-02-09

ArXiv (preprint)

arxiv.org

Amortizing intractable inference in diffusion models for vision, language, and control

Nikolay Malkin

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors … (see more)in downstream tasks poses an intractable posterior inference problem. This paper studies amortized sampling of the posterior over data,

2024-12-09

Advances in Neural Information Processing Systems (published)

Improved off-policy training of diffusion samplers

Nikolay Malkin

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We ben… (see more)chmark 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.

2024-12-09

Advances in Neural Information Processing Systems (published)

Iterated Denoising Energy Matching for Sampling from Boltzmann Densities

Avishek Joey Bose

Cheng-Hao Liu

Nikolay Malkin

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-… (see more)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

2024-07-22

International Conference on Machine Learning (Accept (Poster))

proceedings.mlr.press

Explicit Knowledge Factorization Meets In-Context Learning: What Do We Gain?

2024-03-04

ICLR.cc/2024/Workshop/R2-FM (poster)

MixupE: Understanding and improving Mixup from directional derivative perspective

Vikas Verma

Yingtian Zou

Wai Hoh Tang

Hieu Pham

Juho Kannala

Arno Solin

Kenji Kawaguchi

2023-07-01

Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence (published)

proceedings.mlr.press

Exploring Exchangeable Dataset Amortization for Bayesian Posterior Inference

Niels Leif Bracher

Priyank Jaini

Marcus A Brubaker

Bayesian inference provides a natural way of incorporating uncertainties and different underlying theories when making predictions or analyz… (see more)ing complex systems. However, it requires computationally expensive routines for approximation, which have to be re-run when new data is observed and are thus infeasible to efficiently scale and reuse. In this work, we look at the problem from the perspective of amortized inference to obtain posterior parameter distributions for known probabilistic models. We propose a neural network-based approach that can handle exchangeable observations and amortize over datasets to convert the problem of Bayesian posterior inference into a single forward pass of a network. Our empirical analyses explore various design choices for amortized inference by comparing: (a) our proposed variational objective with forward KL minimization, (b) permutation-invariant architectures like Transformers and DeepSets, and (c) parameterizations of posterior families like diagonal Gaussian and Normalizing Flows. Through our experiments, we successfully apply amortization techniques to estimate the posterior distributions for different domains solely through inference.

2023-06-18

ICML.cc/2023/Workshop/SPIGM (poster)

Supplementary Material for MixupE

Yingtian Zou

Vikas Verma

Wai Hoh Tang

Hieu Pham

Juho Kannala

Arno Solin

Kenji Kawaguchi

We denote by z = (x,y) the input and output pair where x ∈ X ⊆ R and y ∈ Y ⊆ R . Let fθ(x) ∈ R be the output of the logits (i.e.,… (see more) the last layer before the softmax or sigmoid) of the model parameterized by θ. We use l(θ, z) = h(fθ(x)) − yfθ(x) to denote the loss function. Let g(·) be the activation function. We use x(i) to index i-th element of the vector x and xj to represent j-th variable in a set. The notation list is:

2022-12-31

(published)

www.semanticscholar.org

Is a Modular Architecture Enough?

Inspired from human cognition, machine learning systems are gradually revealing advantages of sparser and more modular architectures. Recent… (see more) work demonstrates that not only do some modular architectures generalize well, but they also lead to better out-of-distribution generalization, scaling properties, learning speed, and interpretability. A key intuition behind the success of such systems is that the data generating system for most real-world settings is considered to consist of sparsely interacting parts, and endowing models with similar inductive biases will be helpful. However, the field has been lacking in a rigorous quantitative assessment of such systems because these real-world data distributions are complex and unknown. In this work, we provide a thorough assessment of common modular architectures, through the lens of simple and known modular data distributions. We highlight the benefits of modularity and sparsity and reveal insights on the challenges faced while optimizing modular systems. In doing so, we propose evaluation metrics that highlight the benefits of modularity, the regimes in which these benefits are substantial, as well as the sub-optimality of current end-to-end learned modular systems as opposed to their claimed potential.

2022-11-28

Neural Information Processing Systems (Accept)

On Neural Architecture Inductive Biases for Relational Tasks

Current deep learning approaches have shown good in-distribution generalization performance, but struggle with out-of-distribution generaliz… (see more)ation. This is especially true in the case of tasks involving abstract relations like recognizing rules in sequences, as we find in many intelligence tests. Recent work has explored how forcing relational representations to remain distinct from sensory representations, as it seems to be the case in the brain, can help artificial systems. Building on this work, we further explore and formalize the advantages afforded by 'partitioned' representations of relations and sensory details, and how this inductive bias can help recompose learned relational structure in newly encountered settings. We introduce a simple architecture based on similarity scores which we name Compositional Relational Network (CoRelNet). Using this model, we investigate a series of inductive biases that ensure abstract relations are learned and represented distinctly from sensory data, and explore their effects on out-of-distribution generalization for a series of relational psychophysics tasks. We find that simple architectural choices can outperform existing models in out-of-distribution generalization. Together, these results show that partitioning relational representations from other information streams may be a simple way to augment existing network architectures' robustness when performing out-of-distribution relational computations.

2022-06-08

ArXiv (preprint)

arxiv.org

Compositional Attention: Disentangling Search and Retrieval

Sharath Chandra Raparthy

Irina Rish

Multi-head, key-value attention is the backbone of the widely successful Transformer model and its variants. This attention mechanism uses m… (see more)ultiple parallel key-value attention blocks (called heads), each performing two fundamental computations: (1) search - selection of a relevant entity from a set via query-key interactions, and (2) retrieval - extraction of relevant features from the selected entity via a value matrix. Importantly, standard attention heads learn a rigid mapping between search and retrieval. In this work, we first highlight how this static nature of the pairing can potentially: (a) lead to learning of redundant parameters in certain tasks, and (b) hinder generalization. To alleviate this problem, we propose a novel attention mechanism, called Compositional Attention, that replaces the standard head structure. The proposed mechanism disentangles search and retrieval and composes them in a dynamic, flexible and context-dependent manner through an additional soft competition stage between the query-key combination and value pairing. Through a series of numerical experiments, we show that it outperforms standard multi-head attention on a variety of tasks, including some out-of-distribution settings. Through our qualitative analysis, we demonstrate that Compositional Attention leads to dynamic specialization based on the type of retrieval needed. Our proposed mechanism generalizes multi-head attention, allows independent scaling of search and retrieval, and can easily be implemented in lieu of standard attention heads in any network architecture.

2022-04-24

International Conference on Learning Representations (Accept (Spotlight))