17 accepted papers
Informally, a model is calibrated if its predictions are correct with a probability that matches the confidence of the prediction. By far the most common method in the literature for measuring calibration is the expected calibration error (ECE). Recent work, however, has pointed out drawbacks of ECE…
We consider the problem of sampling text from an energy-based model. This arises, for example, when sampling text from a neural language model subject to soft constraints. Although the target distribution is discrete, the internal computations of the energy function (given by the language model) are…
The use of guidance in diffusion models was originally motivated by the premise that the guidance-modified score is that of the data distribution tilted by a conditional likelihood raised to some power. In this work we clarify this misconception by rigorously proving that guidance fails to sample fr…
A language model may be viewed as a 𝛴-valued stochastic process for some alphabet 𝛴.However, in some pathological situations, such a stochastic process may “leak” probability mass onto the set of infinite strings and hence is not equivalent to the conventional view of a language model as a distribut…
Recently, researchers have found that representations learned by large-scale pre-trained language models are useful in various downstream tasks. However, there is little theoretical understanding of how pre-training performance is related to downstream task performance. In this paper, we analyze how…
We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small $L^2$ error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoot…
Noise Contrastive Estimation (NCE) is a popular approach for learning probability density functions parameterized up to a constant of proportionality. The main idea is to design a classification problem for distinguishing training data from samples from an (easy-to-sample) noise distribution $q$, in…
Score matching is an alternative to maximum likelihood (ML) for estimating a probability distribution parametrized up to a constant of proportionality. By fitting the ''score'' of the distribution, it sidesteps the need to compute this constant of proportionality (which is often intractable). While…
We provide the first polynomial-time convergence guarantees for the probabilistic flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining such guarantees for the SDE-based implementation (i.e., d…
Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM: drawing samples from a probability density $p$ given a score…
Recently, many reinforcement learning techniques have been shown to have provable guarantees in the simple case of linear dynamics, especially in problems like linear quadratic regulators. However, in practice many tasks require learning a policy from rich, high-dimensional features such as images,…
Normalizing flows are a widely used class of latent-variable generative models with a tractable likelihood. Affine-coupling models [Dinh et al., 2014, 2016] are a particularly common type of normalizing flows, for which the Jacobian of the latent-to-observable-variable transformation is triangular,…
Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima---at least those discovered by gradient-based optimization---turn out to be connected by simple paths on which the loss function is almost constant. Often, these paths can be chosen to be piece-wise linear, with…
Given a sequence of convex functions $f_0, f_1, \ldots, f_T$, we study the problem of sampling from the Gibbs distribution $\pi_t \propto e^{-\sum_{k=0}^t f_k}$ for each epoch $t$ in an {\em online} manner. Interest in this problem derives from applications in machine learning, Bayesian statistics,…
A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions, such as latent-variable generative models. However sampli…
We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix. The algorithm extends the recently introduced technique of spectral filtering, previously applied on…
We study the control of symmetric linear dynamical systems with unknown dynamics and a hidden state. Using a recent spectral filtering technique for concisely representing such systems in a linear basis, we formulate optimal control in this setting as a convex program. This approach eliminates the n…