A fundamental problem in cognitive neuroscience is how humans make decisions, act, and behave in relation to other humans. Here we adopt the hypothesis that when we are in an interactive social setting, our brains perform Bayesian inference of the intentions and cooperativeness of others using probabilistic representations. We employ the framework of partially observable Markov decision processes (POMDPs) to model human decision making in a social context, focusing specifically on the volunteer's dilemma in a version of the classic Public Goods Game. We show that the POMDP model explains both the behavior of subjects as well as neural activity recorded using fMRI during the game. The decisions of subjects can be modeled across all trials using two interpretable parameters.

Recent work has documented striking heterogeneity in the performance of stateof-the-art vision language models (VLMs), including both multimodal language models and text-to-image models. These models are able to describe and generate a diverse array of complex, naturalistic images, yet they exhibit surprising failures on basic multi-object reasoning tasks - such as counting, localization, and simple forms of visual analogy - that humans perform with near perfect accuracy. To better understand this puzzling pattern of successes and failures, we turn to theoretical accounts of the binding problem in cognitive science and neuroscience, a fundamental problem that arises when a shared set of representational resources must be used to represent distinct entities (e.g., to represent multiple objects in an image), necessitating the use of serial processing to avoid interference. We find that many of the puzzling failures of state-of-the-art VLMs can be explained as arising due to the binding problem, and that these failure modes are strikingly similar to the limitations exhibited by rapid, feedforward processing in the human brain.

A basic question in learning theory is to identify if two distributions are identical when we have access only to examples sampled from the distributions. This basic task is considered, for example, in the context of Generative Adversarial Networks (GANs), where a discriminator is trained to distinguish between a reallife distribution and a synthetic distribution. Classically, we use a hypothesis class H and claim that the two distributions are distinct if for some h H the expected value on the two distributions is (significantly) different. Our starting point is the following fundamental problem: "is having the hypothesis dependent on more than a single random example beneficial". To address this challenge we define k-ary based discriminators, which have a family of Boolean k-ary functions G.

I do not completely understand (apart for some parts of the proofs) why refer to these functions as Graph-based. Boolean k-ary functions may be thought of as hyper-graphs. The definition shouldn't be unusual and it will be clarified to avoid any possible This is completely analogous to the standard empirical distribution for hypotheses classes. It might be helpful to summarise,..., some basic properties of this new notion of VC dimension......, is there a Sauer-Shelah type upper bound on the size of the class in terms of the graph VC dimension? VC dimension entail small graph VC dimension). Shelah Lemma for graph VC dimension, indeed this is noteworthy and we should discuss this in the main text.

In this paper, we study learning-augmented algorithms for the Bahncard problem. The Bahncard problem is a generalization of the ski-rental problem, where a traveler needs to irrevocably and repeatedly decide between a cheap short-term solution and an expensive long-term one with an unknown future. Even though the problem is canonical, only a primal-dual-based learning-augmented algorithm was explicitly designed for it. We develop a new learning-augmented algorithm, named PFSUM, that incorporates both history and short-term future to improve online decision making. We derive the competitive ratio of PFSUM as a function of the prediction error and conduct extensive experiments to show that PFSUM outperforms the primal-dual-based algorithm.

The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network's own one-step-ahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of the recurrent network to be the same when training the network and when sampling from the network over multiple time steps. We apply Professor Forcing to language modeling, vocal synthesis on raw waveforms, handwriting generation, and image generation. Empirically we find that Professor Forcing acts as a regularizer, improving test likelihood on character level Penn Treebank and sequential MNIST. We also find that the model qualitatively improves samples, especially when sampling for a large number of time steps.

Computer-aided synthesis planning (CASP) algorithms have demonstrated expertlevel abilities in planning retrosynthetic routes to molecules of low to moderate complexity. However, current search methods assume the sufficiency of reaching arbitrary building blocks, failing to address the common real-world constraint where using specific molecules is desired. To this end, we present a formulation of synthesis planning with starting material constraints. Under this formulation, we propose Double-Ended Synthesis Planning (DESP), a novel CASP algorithm under a bidirectional graph search scheme that interleaves expansions from the target and from the goal starting materials to ensure constraint satisfiability. The search algorithm is guided by a goal-conditioned cost network learned offline from a partially observed hypergraph of valid chemical reactions. We demonstrate the utility of DESP in improving solve rates and reducing the number of search expansions by biasing synthesis planning towards expert goals on multiple new benchmarks. DESP can make use of existing one-step retrosynthesis models, and we anticipate its performance to scale as these one-step model capabilities improve.

Markov chain Monte Carlo (MCMC) is one of the main workhorses of probabilistic inference, but it is notoriously hard to measure the quality of approximate posterior samples. This challenge is particularly salient in black box inference methods, which can hide details and obscure inference failures. In this work, we extend the recently introduced bidirectional Monte Carlo technique to evaluate MCMC-based posterior inference algorithms. By running annealed importance sampling (AIS) chains both from prior to posterior and vice versa on simulated data, we upper bound in expectation the symmetrized KL divergence between the true posterior distribution and the distribution of approximate samples. We integrate our method into two probabilistic programming languages, WebPPL and Stan, and validate it on several models and datasets.

We would like to thank all reviewers for their time and effort writing these valuable reviews. Reviewer 3 mentioned that a performance measure with other recent methods would be beneficial. The code for this paper will be released with the camera-ready version. In the following, we focus on the questions given by Reviewer 2. The presented network does not contain fewer parameters compared to the classical B-spline method for optimization. Furthermore, it is straightforward to extend for the 3D case.

Bayesian nonparametric methods based on the Dirichlet process (DP), gamma process and beta process, have proven effective in capturing aspects of various datasets arising in machine learning. However, it is now recognized that such processes have their limitations in terms of the ability to capture power law behavior. As such there is now considerable interest in models based on the Stable Processs (SP), Generalized Gamma process (GGP) and Stable-beta process (SBP). In analogy to tractable processes such as the finite-dimensional Dirichlet process, we describe a class of random processes, we call iid finite-dimensional BFRY processes, that enables one to begin to develop efficient posterior inference algorithms such as variational Bayes that readily scale to massive datasets. For illustrative purposes, we describe a simple variational Bayes algorithm for normalized SP mixture models, and demonstrate its usefulness with experiments on synthetic and real-world datasets.