Aris L. Moustakas

Andreas Lolos, Theofilos Christodoulou, Aris L. Moustakas et al.

In computational pathology, weak supervision has become the standard for deep learning due to the gigapixel scale of WSIs and the scarcity of pixel-level annotations, with Multiple Instance Learning (MIL) established as the principal framework for slide-level model training. In this paper, we introduce a novel setting for MIL methods, inspired by proceedings in Neural Partial Differential Equation (PDE) Solvers. Instead of relying on complex attention-based aggregation, we propose an efficient, aggregator-agnostic framework that removes the complexity of correlation learning from the MIL aggregator. CAPRMIL produces rich context-aware patch embeddings that promote effective correlation learning on downstream tasks. By projecting patch features -- extracted using a frozen patch encoder -- into a small set of global context/morphology-aware tokens and utilizing multi-head self-attention, CAPRMIL injects global context with linear computational complexity with respect to the bag size. Paired with a simple Mean MIL aggregator, CAPRMIL matches state-of-the-art slide-level performance across multiple public pathology benchmarks, while reducing the total number of trainable parameters by 48%-92.8% versus SOTA MILs, lowering FLOPs during inference by 52%-99%, and ranking among the best models on GPU memory efficiency and training time. Our results indicate that learning rich, context-aware instance representations before aggregation is an effective and scalable alternative to complex pooling for whole-slide analysis. Our code is available at https://github.com/mandlos/CAPRMIL

Theodoros G. Tsironis, Aris L. Moustakas

We use the Kac-Rice formula and results from random matrix theory to obtain the average number of critical points of a family of high-dimensional empirical loss functions, where the data are correlated $d$-dimensional Gaussian vectors, whose number has a fixed ratio with their dimension. The correlations are introduced to model the existence of structure in the data, as is common in current Machine-Learning systems. Under a technical hypothesis, our results are exact in the large-$d$ limit, and characterize the annealed landscape complexity, namely the logarithm of the expected number of critical points at a given value of the loss. We first address in detail the landscape of the loss function of a single perceptron and then generalize it to the case where two competing data sets with different covariance matrices are present, with the perceptron seeking to discriminate between them. The latter model can be applied to understand the interplay between adversity and non-trivial data structure. For completeness, we also treat the case of a loss function used in training Generalized Linear Models in the presence of correlated input data.

Panayotis Mertikopoulos, Aris L. Moustakas, Anna Tzanakaki

Motivated by the massive deployment of power-hungry data centers for service provisioning, we examine the problem of routing in optical networks with the aim of minimizing traffic-driven power consumption. To tackle this issue, routing must take into account energy efficiency as well as capacity considerations; moreover, in rapidly-varying network environments, this must be accomplished in a real-time, distributed manner that remains robust in the presence of random disturbances and noise. In view of this, we derive a pricing scheme whose Nash equilibria coincide with the network's socially optimum states, and we propose a distributed learning method based on the Boltzmann distribution of statistical mechanics. Using tools from stochastic calculus, we show that the resulting Boltzmann routing scheme exhibits remarkable convergence properties under uncertainty: specifically, the long-term average of the network's power consumption converges within $\varepsilon$ of its minimum value in time which is at most $\tilde O(1/\varepsilon^2)$, irrespective of the fluctuations' magnitude; additionally, if the network admits a strict, non-mixing optimum state, the algorithm converges to it - again, no matter the noise level. Our analysis is supplemented by extensive numerical simulations which show that Boltzmann routing can lead to a significant decrease in power consumption over basic, shortest-path routing schemes in realistic network conditions.