We study potential presence of statistical-computational gaps (SCG) in symmetric binary perceptrons (SBP) via a parametric utilization of \emph{fully lifted random duality theory} (fl-RDT) [96]. A structural change from decreasingly to arbitrarily ordered $c$-sequence (a key fl-RDT parametric component) is observed on the second lifting level and associated with \emph{satisfiability} ($α_c$) -- \emph{algorithmic} ($α_a$) constraints density threshold change thereby suggesting a potential existence of a nonzero computational gap $SCG=α_c-α_a$. The second level estimate is shown to match the theoretical $α_c$ whereas the $r\rightarrow \infty$ level one is proposed to correspond to $α_a$. For example, for the canonical SBP ($κ=1$ margin) we obtain $α_c\approx 1.8159$ on the second and $α_a\approx 1.6021$ (with converging tendency towards $\sim 1.59$ range) on the seventh level. Our propositions remarkably well concur with recent literature: (i) in [20] local entropy replica approach predicts $α_{LE}\approx 1.58$ as the onset of clustering defragmentation (presumed driving force behind locally improving algorithms failures); (ii) in $α\rightarrow 0$ regime we obtain on the third lifting level $κ\approx 1.2385\sqrt{\frac{α_a}{-\log\left ( α_a \right ) }}$ which qualitatively matches overlap gap property (OGP) based predictions of [43] and identically matches local entropy based predictions of [24]; (iii) $c$-sequence ordering change phenomenology mirrors the one observed in asymmetric binary perceptron (ABP) in [98] and the negative Hopfield model in [100]; and (iv) as in [98,100], we here design a CLuP based algorithm whose practical performance closely matches proposed theoretical predictions.

In this paper, we provide an in-depth study of Stochastic Backpropagation (SBP) when training deep neural networks for standard image classification and object detection tasks. During backward propagation, SBP calculates gradients by using only a subset of feature maps to save GPU memory and computational cost. We interpret SBP as an efficient way to implement stochastic gradient decent by performing backpropagation dropout, which leads to significant memory saving and training run-time reduction, with a minimal impact on the overall model accuracy. We offer best practices to apply SBP for training image recognition models, which can be adopted in learning a wide range of deep neural networks. Experiments on image classification and object detection show that SBP can save up to 40% of GPU memory with less than 1% accuracy degradation.

Given two boundary distributions, the Schr\"odinger Bridge (SB) problem seeks the ``most likely`` random evolution between them with respect to a reference process. It has revealed rich connections to recent machine learning methods for generative modeling and distribution matching. While these methods perform well in Euclidean domains, they are not directly applicable to topological domains such as graphs and simplicial complexes, which are crucial for data defined over network entities, such as node signals and edge flows. In this work, we propose the Topological Schr\"odinger Bridge problem (TSBP) for matching signal distributions on a topological domain. We set the reference process to follow some linear tractable topology-aware stochastic dynamics such as topological heat diffusion. For the case of Gaussian boundary distributions, we derive a closed-form topological SB (TSB) in terms of its time-marginal and stochastic differential. In the general case, leveraging the well-known result, we show that the optimal process follows the forward-backward topological dynamics governed by some unknowns. Building on these results, we develop TSB-based models for matching topological signals by parameterizing the unknowns in the optimal process as (topological) neural networks and learning them through likelihood training. We validate the theoretical results and demonstrate the practical applications of TSB-based models on both synthetic and real-world networks, emphasizing the role of topology. Additionally, we discuss the connections of TSB-based models to other emerging models, and outline future directions for topological signal matching.

Large language models (LLMs) demonstrate remarkable performance on many NLP tasks, yet often exhibit order dependence: simply reordering semantically identical tokens (e.g., answer choices in multiple-choice questions) can lead to inconsistent predictions. Recent work proposes Set-Based Prompting (SBP) as a way to remove order information from designated token subsets, thereby mitigating positional biases. However, applying SBP on base models induces an out-of-distribution input format, which can degrade in-distribution performance. We introduce a fine-tuning strategy that integrates SBP into the training process, "pulling" these set-formatted prompts closer to the model's training manifold. We show that SBP can be incorporated into a model via fine-tuning. Our experiments on in-distribution (MMLU) and out-of-distribution (CSQA, ARC Challenge) multiple-choice tasks show that SBP fine-tuning significantly improves accuracy and robustness to answer-order permutations, all while preserving broader language modeling capabilities. We discuss the broader implications of order-invariant modeling and outline future directions for building fairer, more consistent LLMs.

The application of reinforcement learning (RL) to dynamic resource allocation in optical networks has been the focus of intense research activity in recent years, with almost 100 peer-reviewed papers. We present a review of progress in the field, and identify significant gaps in benchmarking practices and reproducibility. To determine the strongest benchmark algorithms, we systematically evaluate several heuristics across diverse network topologies. We find that path count and sort criteria for path selection significantly affect the benchmark performance. We meticulously recreate the problems from five landmark papers and apply the improved benchmarks. Our comparisons demonstrate that simple heuristics consistently match or outperform the published RL solutions, often with an order of magnitude lower blocking probability. Furthermore, we present empirical lower bounds on network blocking using a novel defragmentation-based method, revealing that potential improvements over the benchmark heuristics are limited to 19--36\% increased traffic load for the same blocking performance in our examples. We make our simulation framework and results publicly available to promote reproducible research and standardized evaluation https://doi.org/10.5281/zenodo.12594495.

Blood pressure (BP) is a key indicator of cardiovascular health. As hypertension remains a global cause of morbidity and mortality, accurate, continuous, and non-invasive BP monitoring is therefore of paramount importance. Photoplethysmography (PPG) and electrocardiography (ECG) can potentially enable continuous BP monitoring, yet training accurate and robust machine learning (ML) models remains challenging due to variability in data quality and patient-specific factors. Recently, multiple research groups explored Electroencephalographic (EEG)--based foundation models and demonstrated their exceptional ability to learn rich temporal resolution. Considering the morphological similarities between different biosignals, the question arises of whether a model pre-trained on one modality can effectively be exploited to improve the accuracy of a different signal type. In this work, we take an initial step towards generalized biosignal foundation models by investigating whether model representations learned from abundant EEG data can effectively be transferred to ECG/PPG data solely with fine-tuning, without the need for large-scale additional pre-training, for the BP estimation task. Evaluations on the MIMIC-III and VitalDB datasets demonstrate that our approach achieves near state-of-the-art accuracy for diastolic BP (mean absolute error of 1.57 mmHg) and surpasses by 1.5x the accuracy of prior works for systolic BP (mean absolute error 2.72 mmHg). Additionally, we perform dynamic INT8 quantization, reducing the smallest model size by over 3.5x (from 13.73 MB down to 3.83 MB) while preserving performance, thereby enabling unobtrusive, real-time BP monitoring on resource-constrained wearable devices.