Eli Sennesh

Eli Sennesh, Hao Wu, Tommaso Salvatori

Unexpected stimuli induce "error" or "surprise" signals in the brain. The theory of predictive coding promises to explain these observations in terms of Bayesian inference by suggesting that the cortex implements variational inference in a probabilistic graphical model. However, when applied to machine learning tasks, this family of algorithms has yet to perform on par with other variational approaches in high-dimensional, structured inference problems. To address this, we introduce a novel predictive coding algorithm for structured generative models, that we call divide-and-conquer predictive coding (DCPC). DCPC differs from other formulations of predictive coding, as it respects the correlation structure of the generative model and provably performs maximum-likelihood updates of model parameters, all without sacrificing biological plausibility. Empirically, DCPC achieves better numerical performance than competing algorithms and provides accurate inference in a number of problems not previously addressed with predictive coding. We provide an open implementation of DCPC in Pyro on Github.

Eli Sennesh, Tom Xu, Yoshihiro Maruyama

Applied category theory has recently developed libraries for computing with morphisms in interesting categories, while machine learning has developed ways of learning programs in interesting languages. Taking the analogy between categories and languages seriously, this paper defines a probabilistic generative model of morphisms in free monoidal categories over domain-specific generating objects and morphisms. The paper shows how acyclic directed wiring diagrams can model specifications for morphisms, which the model can use to generate morphisms. Amortized variational inference in the generative model then enables learning of parameters (by maximum likelihood) and inference of latent variables (by Bayesian inversion). A concrete experiment shows that the free category prior achieves competitive reconstruction performance on the Omniglot dataset.

Eli Sennesh, Tom Xu, Yoshihiro Maruyama

Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been pursued recently, and yet there is still a gap between abstract mathematical foundations and concrete applications to machine learning tasks. In this paper we introduce DisCoPyro as a categorical structure learning framework, which combines categorical structures (such as symmetric monoidal categories and operads) with amortized variational inference, and can be applied, e.g., in program learning for variational autoencoders. We provide both mathematical foundations and concrete applications together with comparison of experimental performance with other models (e.g., neuro-symbolic models). We speculate that DisCoPyro could ultimately contribute to the development of artificial general intelligence.

Eli Sennesh, Maxwell Ramstead

AI alignment is a field of research that aims to develop methods to ensure that agents always behave in a manner aligned with (i.e. consistently with) the goals and values of their human operators, no matter their level of capability. This paper proposes an affectivist approach to the alignment problem, re-framing the concepts of goals and values in terms of affective taxis, and explaining the emergence of affective valence by appealing to recent work in evolutionary-developmental and computational neuroscience. We review the state of the art and, building on this work, we propose a computational model of affect based on taxis navigation. We discuss evidence in a tractable model organism that our model reflects aspects of biological taxis navigation. We conclude with a discussion of the role of affective taxis in AI alignment.

Michael Ibrahim, Hanqi Zhao, Eli Sennesh et al.

Poisson-distributed latent variable models are widely used in computational neuroscience, but differentiating through discrete stochastic samples remains challenging. Two approaches address this: Exponential Arrival Time (EAT) simulation and Gumbel-SoftMax (GSM) relaxation. We provide the first systematic comparison of these methods, along with practical guidance for practitioners. Our main technical contribution is a modification to the EAT method that theoretically guarantees an unbiased first moment (exactly matching the firing rate), and reduces second-moment bias. We evaluate these methods on their distributional fidelity, gradient quality, and performance on two tasks: (1) variational autoencoders with Poisson latents, and (2) partially observable generalized linear models, where latent neural connectivity must be inferred from observed spike trains. Across all metrics, our modified EAT method exhibits better overall performance (often comparable to exact gradients), and substantially higher robustness to hyperparameter choices. Together, our results clarify the trade-offs between these methods and offer concrete recommendations for practitioners working with Poisson latent variable models.

Eli Sennesh, Jan-Willem van de Meent

A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a joint probability density over a set of random variables, and exhibit sparse structure that can be used to reason about causation and conditional independence. This work builds on recent work on Markov categories of probabilistic mappings to define a category whose morphisms combine a joint density, factorized over each sample space, with a deterministic mapping from samples to return values. This is a step towards closing the gap between recent category-theoretic descriptions of probability measures, and the operational definitions of factorized densities that are commonly employed in probabilistic programming and causal inference.

Sam Stites, Heiko Zimmermann, Hao Wu et al.

We develop operators for construction of proposals in probabilistic programs, which we refer to as inference combinators. Inference combinators define a grammar over importance samplers that compose primitive operations such as application of a transition kernel and importance resampling. Proposals in these samplers can be parameterized using neural networks, which in turn can be trained by optimizing variational objectives. The result is a framework for user-programmable variational methods that are correct by construction and can be tailored to specific models. We demonstrate the flexibility of this framework by implementing advanced variational methods based on amortized Gibbs sampling and annealing.

Eli Sennesh

Humans surpass the cognitive abilities of most other animals in our ability to "chunk" concepts into words, and then combine the words to combine the concepts. In this process, we make "infinite use of finite means", enabling us to learn new concepts quickly and nest concepts within each-other. While program induction and synthesis remain at the heart of foundational theories of artificial intelligence, only recently has the community moved forward in attempting to use program learning as a benchmark task itself. The cognitive science community has thus often assumed that if the brain has simulation and reasoning capabilities equivalent to a universal computer, then it must employ a serialized, symbolic representation. Here we confront that assumption, and provide a counterexample in which compositionality is expressed via network structure: the free category prior over programs. We show how our formalism allows neural networks to serve as primitives in probabilistic programs. We learn both program structure and model parameters end-to-end.

Hao Wu, Heiko Zimmermann, Eli Sennesh et al.

We develop amortized population Gibbs (APG) samplers, a class of scalable methods that frames structured variational inference as adaptive importance sampling. APG samplers construct high-dimensional proposals by iterating over updates to lower-dimensional blocks of variables. We train each conditional proposal by minimizing the inclusive KL divergence with respect to the conditional posterior. To appropriately account for the size of the input data, we develop a new parameterization in terms of neural sufficient statistics. Experiments show that APG samplers can train highly structured deep generative models in an unsupervised manner, and achieve substantial improvements in inference accuracy relative to standard autoencoding variational methods.

Eli Sennesh, Zulqarnain Khan, Yiyu Wang et al.

Neuroimaging studies produce gigabytes of spatio-temporal data for a small number of participants and stimuli. Rarely do researchers attempt to model and examine how individual participants vary from each other -- a question that should be addressable even in small samples given the right statistical tools. We propose Neural Topographic Factor Analysis (NTFA), a probabilistic factor analysis model that infers embeddings for participants and stimuli. These embeddings allow us to reason about differences between participants and stimuli as signal rather than noise. We evaluate NTFA on data from an in-house pilot experiment, as well as two publicly available datasets. We demonstrate that inferring representations for participants and stimuli improves predictive generalization to unseen data when compared to previous topographic methods. We also demonstrate that the inferred latent factor representations are useful for downstream tasks such as multivoxel pattern analysis and functional connectivity.

Eli Sennesh, Adam Ścibior, Hao Wu et al.

Probabilistic programs with dynamic computation graphs can define measures over sample spaces with unbounded dimensionality, which constitute programmatic analogues to Bayesian nonparametrics. Owing to the generality of this model class, inference relies on `black-box' Monte Carlo methods that are often not able to take advantage of conditional independence and exchangeability, which have historically been the cornerstones of efficient inference. We here seek to develop a `middle ground' between probabilistic models with fully dynamic and fully static computation graphs. To this end, we introduce a combinator library for the Probabilistic Torch framework. Combinators are functions that accept models and return transformed models. We assume that models are dynamic, but that model composition is static, in the sense that combinator application takes place prior to evaluating the model on data. Combinators provide primitives for both model and inference composition. Model combinators take the form of classic functional programming constructs such as map and reduce. These constructs define a computation graph at a coarsened level of representation, in which nodes correspond to models, rather than individual variables. Inference combinators implement operations such as importance resampling and application of a transition kernel, which alter the evaluation strategy for a model whilst preserving proper weighting. Owing to this property, models defined using combinators can be trained using stochastic methods that optimize either variational or wake-sleep style objectives. As a validation of this principle, we use combinators to implement black box inference for hidden Markov models.