71 research outputs found
A Super-Polynomial Separation Between Resolution and Cut-Free Sequent Calculus
We show a quadratic separation between resolution and cut-free sequent calculus width. We use this gap to get, for the first time, first, a super-polynomial separation between resolution and cut-free sequent calculus for refuting CNF formulas, and secondly, a quadratic separation between resolution width and monomial space in polynomial calculus with resolution. Our super-polynomial separation between resolution and cut-free sequent calculus only applies when clauses are seen as disjunctions of unbounded arity; our examples have linear size cut-free sequent calculus proofs writing, in a particular way, their clauses using binary disjunctions. Interestingly, this shows that the complexity of sequent calculus depends on how disjunctions are represented
Estimating Gibbs free energies via isobaric-isothermal flows
We present a machine-learning model based on normalizing flows that is
trained to sample from the isobaric-isothermal ensemble. In our approach, we
approximate the joint distribution of a fully-flexible triclinic simulation box
and particle coordinates to achieve a desired internal pressure. This novel
extension of flow-based sampling to the isobaric-isothermal ensemble yields
direct estimates of Gibbs free energies. We test our NPT-flow on monatomic
water in the cubic and hexagonal ice phases and find excellent agreement of
Gibbs free energies and other observables compared with established baselines.Comment: 19 pages, 7 figure
On Contrastive Learning for Likelihood-free Inference
Likelihood-free methods perform parameter inference in stochastic simulator
models where evaluating the likelihood is intractable but sampling synthetic
data is possible. One class of methods for this likelihood-free problem uses a
classifier to distinguish between pairs of parameter-observation samples
generated using the simulator and pairs sampled from some reference
distribution, which implicitly learns a density ratio proportional to the
likelihood. Another popular class of methods fits a conditional distribution to
the parameter posterior directly, and a particular recent variant allows for
the use of flexible neural density estimators for this task. In this work, we
show that both of these approaches can be unified under a general contrastive
learning scheme, and clarify how they should be run and compared.Comment: Appeared at ICML 202
Cubic-Spline Flows
A normalizing flow models a complex probability density as an invertible
transformation of a simple density. The invertibility means that we can
evaluate densities and generate samples from a flow. In practice,
autoregressive flow-based models are slow to invert, making either density
estimation or sample generation slow. Flows based on coupling transforms are
fast for both tasks, but have previously performed less well at density
estimation than autoregressive flows. We stack a new coupling transform, based
on monotonic cubic splines, with LU-decomposed linear layers. The resulting
cubic-spline flow retains an exact one-pass inverse, can be used to generate
high-quality images, and closes the gap with autoregressive flows on a suite of
density-estimation tasks.Comment: Appeared at the 1st Workshop on Invertible Neural Networks and
Normalizing Flows at ICML 201
Compositional Score Modeling for Simulation-based Inference
Neural Posterior Estimation methods for simulation-based inference can be
ill-suited for dealing with posterior distributions obtained by conditioning on
multiple observations, as they tend to require a large number of simulator
calls to learn accurate approximations. In contrast, Neural Likelihood
Estimation methods can handle multiple observations at inference time after
learning from individual observations, but they rely on standard inference
methods, such as MCMC or variational inference, which come with certain
performance drawbacks. We introduce a new method based on conditional score
modeling that enjoys the benefits of both approaches. We model the scores of
the (diffused) posterior distributions induced by individual observations, and
introduce a way of combining the learned scores to approximately sample from
the target posterior distribution. Our approach is sample-efficient, can
naturally aggregate multiple observations at inference time, and avoids the
drawbacks of standard inference methods
Masked Autoregressive Flow for Density Estimation
Autoregressive models are among the best performing neural density
estimators. We describe an approach for increasing the flexibility of an
autoregressive model, based on modelling the random numbers that the model uses
internally when generating data. By constructing a stack of autoregressive
models, each modelling the random numbers of the next model in the stack, we
obtain a type of normalizing flow suitable for density estimation, which we
call Masked Autoregressive Flow. This type of flow is closely related to
Inverse Autoregressive Flow and is a generalization of Real NVP. Masked
Autoregressive Flow achieves state-of-the-art performance in a range of
general-purpose density estimation tasks.Comment: section 4.3 is corrected since the previous versio
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