Emergent communication, driven by generative models, enables agents to develop a shared language for describing their individual views of the same objects through interactions. Meanwhile, self-supervised learning (SSL), particularly SimSiam, uses discriminative representation learning to make representations of augmented views of the same data point closer in the representation space. Building on the prior work of VI-SimSiam, which incorporates a generative and Bayesian perspective into the SimSiam framework via variational inference (VI) interpretation, we propose SimSiam+VAE, a unified approach for both representation learning and emergent communication. SimSiam+VAE integrates a variational autoencoder (VAE) into the predictor of the SimSiam network to enhance representation learning and capture uncertainty. Experimental results show that SimSiam+VAE outperforms both SimSiam and VI-SimSiam. We further extend this model into a communication framework called the SimSiam Naming Game (SSNG), which applies the generative and Bayesian approach based on VI to develop internal representations and emergent language, while utilizing the discriminative process of SimSiam to facilitate mutual understanding between agents. In experiments with established models, despite the dynamic alternation of agent roles during interactions, SSNG demonstrates comparable performance to the referential game and slightly outperforms the Metropolis-Hastings naming game.

Authorship attribution aims to identify the origin or author of a document. Traditional approaches have heavily relied on manual features and fail to capture long-range correlations, limiting their effectiveness. Recent advancements leverage text embeddings from pre-trained language models, which require significant fine-tuning on labeled data, posing challenges in data dependency and limited interpretability. Large Language Models (LLMs), with their deep reasoning capabilities and ability to maintain long-range textual associations, offer a promising alternative. This study explores the potential of pre-trained LLMs in one-shot authorship attribution, specifically utilizing Bayesian approaches and probability outputs of LLMs. Our methodology calculates the probability that a text entails previous writings of an author, reflecting a more nuanced understanding of authorship. By utilizing only pre-trained models such as Llama-3-70B, our results on the IMDb and blog datasets show an impressive 85\% accuracy in one-shot authorship classification across ten authors. Our findings set new baselines for one-shot authorship analysis using LLMs and expand the application scope of these models in forensic linguistics. This work also includes extensive ablation studies to validate our approach.

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning models for point processes are predominantly constrained by their reliance on the characteristic intensity function, introducing an inherent trade-off between efficiency and flexibility. In this paper, we introduce Point Set Diffusion, a diffusion-based latent variable model that can represent arbitrary point processes on general metric spaces without relying on the intensity function. By directly learning to stochastically interpolate between noise and data point sets, our approach enables efficient, parallel sampling and flexible generation for complex conditional tasks defined on the metric space. Experiments on synthetic and real-world datasets demonstrate that Point Set Diffusion achieves state-of-the-art performance in unconditional and conditional generation of spatial and spatiotemporal point processes while providing up to orders of magnitude faster sampling than autoregressive baselines.

Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this paper, we propose a model-free approach for estimating such latent structures whenever they are present, without assuming they exist a priori. Given an arbitrary density $p_0$, we construct a multiscale representation of the density and propose data-driven methods for selecting representative models that capture meaningful discrete structure. Our approach uses a nonparametric maximum likelihood estimator to estimate the latent structure at different scales and we further characterize their asymptotic limits. By carrying out such a multiscale analysis, we obtain coarseto-fine structures inherent in the original distribution, which are integrated via a model selection procedure to yield an interpretable discrete representation of it. As an application, we design a clustering algorithm based on the proposed procedure and demonstrate its effectiveness in capturing a wide range of latent structures.

Patients who are undergoing physical rehabilitation, benefit from feedback that follows from reliable assessment of their cumulative performance attained at a given time. In this paper, we provide a method for the learning of the recovery trajectory of an individual patient, as they undertake exercises as part of their physical therapy towards recovery of their loss of movement ability, following a critical illness. The difference between the Movement Recovery Scores (MRSs) attained by a patient, when undertaking a given exercise routine on successive instances, is given by a statistical distance/divergence between the (posterior) probabilities of random graphs that are Bayesianly learnt using time series data on locations of 20 of the patient's joints, recorded on an e-platform as the patient exercises. This allows for the computation of the MRS on every occasion the patient undertakes this exercise, using which, the recovery trajectory is drawn. We learn each graph as a Random Geometric Graph drawn in a probabilistic metric space, and identify the closed-form marginal posterior of any edge of the graph, given the correlation structure of the multivariate time series data on joint locations. On the basis of our recovery learning, we offer recommendations on the optimal exercise routines for patients with given level of mobility impairment.

Large Language Models (LLMs) have demonstrated remarkable abilities in reasoning and planning by breaking down complex problems into sequential steps. This paper revisits LLM reasoning from an optimal control perspective, proposing a novel method, Predictive-Decoding, that leverages Model Predictive Control to enhance planning accuracy. By reweighting LLM distributions based on foresight trajectories, Predictive-Decoding aims to mitigate early errors and promote non-myopic planning. Our experiments show significant improvements across a wide range of tasks in math, coding, and agent-based scenarios. Furthermore, Predictive-Decoding demonstrates computational efficiency, outperforming search baselines while utilizing inference compute more effectively. This study provides insights into optimizing LLM planning capabilities. Code is available at this repo. Large Language Models (LLMs) are extensively pretrained on large corpus to predict the next tokens.

Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). A standard approach to FM, called conditional flow matching (CFM), exploits the fact that the marginal vector field of a CNF can be learned by fitting least-square regression to the so-called conditional vector field specified given one or both ends of the flow path. We show that viewing CFM training from a Bayesian decision theoretic perspective on parameter estimation opens the door to generalizations of CFM algorithms. We propose one such extension by introducing a CFM algorithm based on defining conditional probability paths given what we refer to as ``streams'', instances of latent stochastic paths that connect pairs of noise and observed data. Further, we advocate the modeling of these latent streams using Gaussian processes (GPs). The unique distributional properties of GPs, and in particular the fact that the velocity of a GP is still a GP, allows drawing samples from the resulting stream-augmented conditional probability path without simulating the actual streams, and hence the ``simulation-free" nature of CFM training is preserved. We show that this generalization of the CFM can substantially reduce the variance in the estimated marginal vector field at a moderate computational cost, thereby improving the quality of the generated samples under common metrics. Additionally, we show that adopting the GP on the streams allows for flexibly linking multiple related training data points (e.g., time series) and incorporating additional prior information. We empirically validate our claim through both simulations and applications to two hand-written image datasets.

Collective perception is a fundamental problem in swarm robotics, often cast as best-of-$n$ decision-making. Past studies involve robots with perfect sensing or with small numbers of faulty robots. We previously addressed these limitations by proposing an algorithm, here referred to as Minimalistic Collective Perception (MCP) [arxiv:2209.12858], to reach correct decisions despite the entire swarm having severely damaged sensors. However, this algorithm assumes that sensor accuracy is known, which may be infeasible in reality. In this paper, we eliminate this assumption to (i) investigate the decline of estimation performance and (ii) introduce an Adaptive Sensor Degradation Filter (ASDF) to mitigate the decline. We combine the MCP algorithm and a hypothesis test to enable adaptive self-calibration of robots' assumed sensor accuracy. We validate our approach across several parameters of interest. Our findings show that estimation performance by a swarm with correctly known accuracy is superior to that by a swarm unaware of its accuracy. However, the ASDF drastically mitigates the damage, even reaching the performance levels of robots aware a priori of their correct accuracy.

In a groundbreaking work, Schmidt-Hieber (2020) proved the minimax optimality of deep neural networks with ReLu activation for least-square regression estimation over a large class of functions defined by composition. In this paper, we extend these results in many directions. First, we remove the i.i.d. assumption on the observations, to allow some time dependence. The observations are assumed to be a Markov chain with a non-null pseudo-spectral gap. Then, we study a more general class of machine learning problems, which includes least-square and logistic regression as special cases. Leveraging on PAC-Bayes oracle inequalities and a version of Bernstein inequality due to Paulin (2015), we derive upper bounds on the estimation risk for a generalized Bayesian estimator. In the case of least-square regression, this bound matches (up to a logarithmic factor) the lower bound of Schmidt-Hieber (2020). We establish a similar lower bound for classification with the logistic loss, and prove that the proposed DNN estimator is optimal in the minimax sense.

Artificial General Intelligence (AGI) Agents and Robots must be able to cope with everchanging environments and tasks. They must be able to actively construct new internal causal models of their interactions with the environment when new structural changes take place in the environment. Thus, we claim that active causal structure learning with latent variables (ACSLWL) is a necessary component to build AGI agents and robots. This paper describes how a complex planning and expectation-based detour behavior can be learned by ACSLWL when, unexpectedly, and for the first time, the simulated robot encounters a sort of "transparent" barrier in its pathway towards its target. ACSWL consists of acting in the environment, discovering new causal relations, constructing new causal models, exploiting the causal models to maximize its expected utility, detecting possible latent variables when unexpected observations occur, and constructing new structures - internal causal models and optimal estimation of the associated parameters, to be able to cope efficiently with the new encountered situations. That is, the agent must be able to construct new causal internal models that transform a previously unexpected and inefficient (sub-optimal) situation, into a predictable situation with an optimal operating plan.