This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate inference. To do so, we define on the `syntactic' side the new notion of Bayesian lens and show that Bayesian updating composes according to the compositional lens pattern. Using Bayesian lenses, and inspired by compositional game theory, we define fibrations of statistical games and classify various problems of statistical inference as corresponding sections: the chain rule of the relative entropy is formalized as a strict section, while maximum likelihood estimation and the free energy give lax sections. In the process, we introduce a new notion of `copy-composition'. On the `semantic' side, we present a new formalization of general open dynamical systems (particularly: deterministic, stochastic, and random; and discrete- and continuous-time) as certain coalgebras of polynomial functors, which we show collect into monoidal opindexed categories (or, alternatively, into algebras for multicategories of generalized polynomial functors). We use these opindexed categories to define monoidal bicategories of cilia: dynamical systems which control lenses, and which supply the target for our functorial semantics. Accordingly, we construct functors which explain the bidirectional compositional structure of predictive coding neural circuits under the free energy principle, thereby giving a formal mathematical underpinning to the bidirectionality observed in the cortex. Along the way, we explain how to compose rate-coded neural circuits using an algebra for a multicategory of linear circuit diagrams, showing subsequently that this is subsumed by lenses and polynomial functors.
The self-rationalising capabilities of LLMs are appealing because the generated explanations can give insights into the plausibility of the predictions. However, how faithful the explanations are to the predictions is questionable, raising the need to explore the patterns behind them further. To this end, we propose a hypothesis-driven statistical framework. We use a Bayesian network to implement a hypothesis about how a task (in our example, natural language inference) is solved, and its internal states are translated into natural language with templates. Those explanations are then compared to LLM-generated free-text explanations using automatic and human evaluations. This allows us to judge how similar the LLM's and the Bayesian network's decision processes are. We demonstrate the usage of our framework with an example hypothesis and two realisations in Bayesian networks. The resulting models do not exhibit a strong similarity to GPT-3.5. We discuss the implications of this as well as the framework's potential to approximate LLM decisions better in future work.
The burgeoning fields of robot learning and embodied AI have triggered an increasing demand for large quantities of data. However, collecting sufficient unbiased data from the target domain remains a challenge due to costly data collection processes and stringent safety requirements. Consequently, researchers often resort to data from easily accessible source domains, such as simulation and laboratory environments, for cost-effective data acquisition and rapid model iteration. Nevertheless, the environments and embodiments of these source domains can be quite different from their target domain counterparts, underscoring the need for effective cross-domain policy transfer approaches. In this paper, we conduct a systematic review of existing cross-domain policy transfer methods. Through a nuanced categorization of domain gaps, we encapsulate the overarching insights and design considerations of each problem setting. We also provide a high-level discussion about the key methodologies used in cross-domain policy transfer problems. Lastly, we summarize the open challenges that lie beyond the capabilities of current paradigms and discuss potential future directions in this field.
We study the problem of fairly assigning a set of discrete tasks (or chores) among a set of agents with additive valuations. Each chore is associated with a start and finish time, and each agent can perform at most one chore at any given time. The goal is to find a fair and efficient schedule of the chores, where fairness pertains to satisfying envy-freeness up to one chore (EF1) and efficiency pertains to maximality (i.e., no unallocated chore can be feasibly assigned to any agent). Our main result is a polynomial-time algorithm for computing an EF1 and maximal schedule for two agents under monotone valuations when the conflict constraints constitute an arbitrary interval graph. The algorithm uses a coloring technique in interval graphs that may be of independent interest. For an arbitrary number of agents, we provide an algorithm for finding a fair schedule under identical dichotomous valuations when the constraints constitute a path graph. We also show that stronger fairness and efficiency properties, including envy-freeness up to any chore (EFX) along with maximality and EF1 along with Pareto optimality, cannot be achieved.
Science originates with discovering new causal knowledge from a combination of known facts and observations. Traditional causal discovery approaches mainly rely on high-quality measured variables, usually given by human experts, to find causal relations. However, the causal variables are usually unavailable in a wide range of real-world applications. The rise of large language models (LLMs) that are trained to learn rich knowledge from the massive observations of the world, provides a new opportunity to assist with discovering high-level hidden variables from the raw observational data. Therefore, we introduce COAT: Causal representatiOn AssistanT. COAT incorporates LLMs as a factor proposer that extracts the potential causal factors from unstructured data. Moreover, LLMs can also be instructed to provide additional information used to collect data values (e.g., annotation criteria) and to further parse the raw unstructured data into structured data. The annotated data will be fed to a causal learning module (e.g., the FCI algorithm) that provides both rigorous explanations of the data, as well as useful feedback to further improve the extraction of causal factors by LLMs. We verify the effectiveness of COAT in uncovering the underlying causal system with two case studies of review rating analysis and neuropathic diagnosis.
We consider the problem of model selection in a high-dimensional sparse linear regression model under privacy constraints. We propose a differentially private best subset selection method with strong utility properties by adopting the well-known exponential mechanism for selecting the best model. We propose an efficient Metropolis-Hastings algorithm and establish that it enjoys polynomial mixing time to its stationary distribution. Furthermore, we also establish approximate differential privacy for the final estimates of the Metropolis-Hastings random walk using its mixing property. Finally, we perform some illustrative experiments that show the strong utility of our algorithm.
The discourse around conspiracy theories is currently thriving amidst the rampant misinformation in online environments. Research in this field has been focused on detecting conspiracy theories on social media, often relying on limited datasets. In this study, we present a novel methodology for constructing a Twitter dataset that encompasses accounts engaged in conspiracy-related activities throughout the year 2022. Our approach centers on data collection that is independent of specific conspiracy theories and information operations. Additionally, our dataset includes a control group comprising randomly selected users who can be fairly compared to the individuals involved in conspiracy activities. This comprehensive collection effort yielded a total of 15K accounts and 37M tweets extracted from their timelines. We conduct a comparative analysis of the two groups across three dimensions: topics, profiles, and behavioral characteristics. The results indicate that conspiracy and control users exhibit similarity in terms of their profile metadata characteristics. However, they diverge significantly in terms of behavior and activity, particularly regarding the discussed topics, the terminology used, and their stance on trending subjects. In addition, we find no significant disparity in the presence of bot users between the two groups. Finally, we develop a classifier to identify conspiracy users using features borrowed from bot, troll and linguistic literature. The results demonstrate a high accuracy level (with an F1 score of 0.94), enabling us to uncover the most discriminating features associated with conspiracy-related accounts.
We investigate the problem of autonomous racing among teams of cooperative agents that are subject to realistic racing rules. Our work extends previous research on hierarchical control in head-to-head autonomous racing by considering a generalized version of the problem while maintaining the two-level hierarchical control structure. A high-level tactical planner constructs a discrete game that encodes the complex rules using simplified dynamics to produce a sequence of target waypoints. The low-level path planner uses these waypoints as a reference trajectory and computes high-resolution control inputs by solving a simplified formulation of a racing game with a simplified representation of the realistic racing rules. We explore two approaches for the low-level path planner: training a multi-agent reinforcement learning (MARL) policy and solving a linear-quadratic Nash game (LQNG) approximation. We evaluate our controllers on simple and complex tracks against three baselines: an end-to-end MARL controller, a MARL controller tracking a fixed racing line, and an LQNG controller tracking a fixed racing line. Quantitative results show our hierarchical methods outperform the baselines in terms of race wins, overall team performance, and compliance with the rules. Qualitatively, we observe the hierarchical controllers mimic actions performed by expert human drivers such as coordinated overtaking, defending against multiple opponents, and long-term planning for delayed advantages.
GFlowNets are probabilistic models that sequentially generate compositional structures through a stochastic policy. Among GFlowNets, temperature-conditional GFlowNets can introduce temperature-based controllability for exploration and exploitation. We propose \textit{Logit-scaling GFlowNets} (Logit-GFN), a novel architectural design that greatly accelerates the training of temperature-conditional GFlowNets. It is based on the idea that previously proposed approaches introduced numerical challenges in the deep network training, since different temperatures may give rise to very different gradient profiles as well as magnitudes of the policy's logits. We find that the challenge is greatly reduced if a learned function of the temperature is used to scale the policy's logits directly. Also, using Logit-GFN, GFlowNets can be improved by having better generalization capabilities in offline learning and mode discovery capabilities in online learning, which is empirically verified in various biological and chemical tasks. Our code is available at \url{//github.com/dbsxodud-11/logit-gfn}
Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.
Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.