A Theory of Cheap Control in Embodied Systems.

We present a framework for designing cheap control architectures of embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

Universal approximation depth and errors of narrow belief networks with discrete units.

We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily well. We relax the setting of binary units (Sutskever & Hinton, 2008 ; Le Roux & Bengio, 2008 , 2010 ; Montúfar & Ay, 2011 ) to units with arbitrary finite state spaces and the vanishing approximation error to an arbitrary approximation error tolerance. For example, we show that a q-ary deep belief network with L > or = 2 + (q[m-delta]-1 / (q-1)) layers of width n < or = + log(q) (m) + 1 for some [Formula : see text] can approximate any probability distribution on {0, 1, ... , q-1}n without exceeding a Kullback-Leibler divergence of delta. Our analysis covers discrete restricted Boltzmann machines and naive Bayes models as special cases.

Geometry and convergence of natural policy gradient methods.

We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that the trajectories in state-action space are solutions of gradient flows with respect to Hessian geometries, based on which we obtain global convergence guarantees and convergence rates. In particular, we show linear convergence for unregularized and regularized NPG flows with the metrics proposed by Kakade and Morimura and co-authors by observing that these arise from the Hessian geometries of conditional entropy and entropy respectively. Further, we obtain sublinear convergence rates for Hessian geometries arising from other convex functions like log-barriers. Finally, we interpret the discrete-time NPG methods with regularized rewards as inexact Newton methods if the NPG is defined with respect to the Hessian geometry of the regularizer. This yields local quadratic convergence rates of these methods for step size equal to the inverse penalization strength.

Cell graph neural networks enable the precise prediction of patient survival in gastric cancer.

Gastric cancer is one of the deadliest cancers worldwide. An accurate prognosis is essential for effective clinical assessment and treatment. Spatial patterns in the tumor microenvironment (TME) are conceptually indicative of the staging and progression of gastric cancer patients. Using spatial patterns of the TME by integrating and transforming the multiplexed immunohistochemistry (mIHC) images as Cell-Graphs, we propose a graph neural network-based approach, termed Cell-Graph Signature or CGSignature, powered by artificial intelligence, for the digital staging of TME and precise prediction of patient survival in gastric cancer. In this study, patient survival prediction is formulated as either a binary (short-term and long-term) or ternary (short-term, medium-term, and long-term) classification task. Extensive benchmarking experiments demonstrate that the CGSignature achieves outstanding model performance, with Area Under the Receiver Operating Characteristic curve of 0.960 ± 0.01, and 0.771 ± 0.024 to 0.904 ± 0.012 for the binary- and ternary-classification, respectively. Moreover, Kaplan-Meier survival analysis indicates that the "digital grade" cancer staging produced by CGSignature provides a remarkable capability in discriminating both binary and ternary classes with statistical significance (P value < 0.0001), significantly outperforming the AJCC 8th edition Tumor Node Metastasis staging system. Using Cell-Graphs extracted from mIHC images, CGSignature improves the assessment of the link between the TME spatial patterns and patient prognosis. Our study suggests the feasibility and benefits of such an artificial intelligence-powered digital staging system in diagnostic pathology and precision oncology.

Refinements of universal approximation results for deep belief networks and restricted Boltzmann machines.

We improve recently published results about resources of restricted Boltzmann machines (RBM) and deep belief networks (DBN)required to make them universal approximators. We show that any distribution pon the set {0,1}(n) of binary vectors of length n can be arbitrarily well approximated by an RBM with k-1 hidden units, where k is the minimal number of pairs of binary vectors differing in only one entry such that their union contains the support set of p. In important cases this number is half the cardinality of the support set of p (given in Le Roux & Bengio, 2008). We construct a DBN with 2n/ 2(n-b) , b ∼ log n, hidden layers of width n that is capable of approximating any distribution on {0,1}(n) arbitrarily well. This confirms a conjecture presented in Le Roux and Bengio (2010).