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Federated learning (FL) enables collaborative model training without sharing raw patient data, but standard approaches such as FedAvg treat each client as a black box and provide no mechanism for isolating an adversarial contributor, auditing per-client influence, or honoring a departed participant's right to be forgotten. We present Fed-FBD (Federated Functional Block Diversification), a modular federated architecture that decomposes a ResNet backbone into six functional blocks (the stem, four residual groups, and the classification head) and maintains a warehouse of N color variants, each assembled from independently tracked and contributor-stamped blocks. Fed-FBD provides three capabilities absent in FedAvg: (i) architecturally guaranteed block-level isolation, so that an adversarial or mislabelled client cannot contaminate the clean colous; (ii) privacy-by-design, where membership inference advantage is already indistinguishable from chance before any privacy mechanism is applied; and (iii) surgical machine unlearning of a departed participant's contribution at sub-second cost and without retraining. Experiments on six MedMNIST-2D datasets, PathMNIST at 224x224, and CIFAR-10 sh

We consider the online algorithmic challenge that is faced by blockchains that have multidimensional block constraints and serve quasi-patient bidders. We first provide online approximation algorithms for the important special cases of small transactions or a small number of dimensions; this solves open problems left by [Babaioff and Nisan, EC 2025]. Second, we study multidimensional variants of Ethereum's EIP-1559 protocol. We show that if the block builders manage to approximately optimize each block's welfare myopically, then an approximation to the global offline optimal welfare is obtained. On the other hand, we show that, unlike in the single-dimensional case, EIP-1559 by itself does not guarantee any good approximation.

Modern large language models increasingly require long contexts for reasoning and multi-document tasks, but attention's quadratic complexity creates a severe computational bottleneck. We present Block-Sparse FlashAttention (BSFA), a drop-in replacement that accelerates long-context inference while preserving model quality. Unlike methods that predict importance before computing scores, BSFA computes exact query-key similarities to select the top-k most important value blocks for each query. By comparing per-block maximum scores against calibrated thresholds, we skip approximately 50% of the computation and memory transfers for pruned blocks. Our training-free approach requires only a one-time threshold calibration on a small dataset to learn the per-layer and per-head attention score distributions. We provide a CUDA kernel implementation that can be used as a drop-in replacement for FlashAttention. On Llama-3.1-8B, BSFA achieves up to 1.10x speedup on real-world reasoning benchmarks and up to 1.24x for needle-in-a-haystack retrieval tasks while maintaining above 99% baseline accuracy, with certain configurations even improving accuracy by focusing on the most relevant content, subs

This study investigates the problem of learning linear block codes optimized for Belief-Propagation decoders significantly improving performance compared to the state-of-the-art. Our previous research is extended with an enhanced system design that facilitates a more effective learning process for the parity check matrix. We simplify the input dataset, restrict the number of parameters to learn and improve the gradient back-propagation within the model. We also introduce novel optimizers specifically designed for discrete-valued weights. Based on conventional gradient computation, these optimizers provide discrete weights updates, enabling finer control and improving explainability of the learning process. Through these changes, we consistently achieve improved code performance, provided appropriately chosen hyper-parameters. To rigorously evaluate the performance of learned codes in the context of short to medium block lengths, we propose a comprehensive code performance assessment framework. This framework enables a fair comparison between our learning methodology and random search approaches, ensuring statistical significance in our results. The proposed model pave the way for a

This paper describes a framework for capturing geological structures in a 3D block model and improving its spatial fidelity given new mesh surfaces. Using surfaces that represent geological boundaries, the objectives are to identify areas where refinement is needed, increase spatial resolution to minimize surface approximation error, reduce redundancy to increase the compactness of the model and identify the geological domain on a block-by-block basis. These objectives are fulfilled by four system components which perform block-surface overlap detection, spatial structure decomposition, sub-blocks consolidation and block tagging, respectively. The main contributions are a coordinate-ascent merging algorithm and a flexible architecture for updating the spatial structure of a block model when given multiple surfaces, which emphasizes the ability to selectively retain or modify previously assigned block labels. The techniques employed include block-surface intersection analysis based on the separable axis theorem and ray-tracing for establishing the location of blocks relative to surfaces. To demonstrate the robustness and applicability of the proposed block merging strategy in a more

Detecting out-of-distribution (OOD) inputs during the inference stage is crucial for deploying neural networks in the real world. Previous methods commonly relied on the output of a network derived from the highly activated feature map. In this study, we first revealed that a norm of the feature map obtained from the other block than the last block can be a better indicator of OOD detection. Motivated by this, we propose a simple framework consisting of FeatureNorm: a norm of the feature map and NormRatio: a ratio of FeatureNorm for ID and OOD to measure the OOD detection performance of each block. In particular, to select the block that provides the largest difference between FeatureNorm of ID and FeatureNorm of OOD, we create Jigsaw puzzle images as pseudo OOD from ID training samples and calculate NormRatio, and the block with the largest value is selected. After the suitable block is selected, OOD detection with the FeatureNorm outperforms other OOD detection methods by reducing FPR95 by up to 52.77% on CIFAR10 benchmark and by up to 48.53% on ImageNet benchmark. We demonstrate that our framework can generalize to various architectures and the importance of block selection, whi

We consider financial market regime detection from the perspective of deep representation learning of the causal information geometry underpinning traded asset systems using a hierarchical correlation structure to characterise market evolution. We assess the robustness of three toy models: SPDNet, SPD-NetBN and U-SPDNet whose architectures respect the underlying Riemannian manifold of input block hierarchical SPD correlation matrices. Market phase detection for each model is carried out using three data configurations: randomised JSE Top 60 data, synthetically-generated block hierarchical SPD matrices and block-resampled chronology-preserving JSE Top 60 data. We show that using a singular performance metric is misleading in our financial market investment use cases where deep learning models overfit in learning spatio-temporal correlation dynamics.

We develop the thermal shadow formalism to study the conformal blocks decomposition in $D$-dimensional conformal field theory on $\mathbb{S}_β^{1} \times \mathbb{S}^{D-1}$, where the temperature is $T = β^{-1}$. It is demonstrated that both the 1-point thermal ($T eq 0$) conformal blocks and the 4-point plane ($T=0$) conformal blocks are defined by the same 4-point conformal integral. It is shown that up to power prefactors the 1-point thermal conformal block is given by the fourth Appell function.

Partial-order plans in AI planning facilitate execution flexibility due to their less-constrained nature. Maximizing plan flexibility has been studied through the notions of plan deordering, and plan reordering. Plan deordering removes unnecessary action orderings within a plan, while plan reordering modifies them arbitrarily to minimize action orderings. This study, in contrast with traditional plan deordering and reordering strategies, improves a plan's flexibility by substituting its subplans with actions outside the plan for a planning problem. Our methodology builds on block deordering, which eliminates orderings in a POP by encapsulating coherent actions in blocks, yielding a hierarchically structured plan termed a Block Decomposed Partial-Order (BDPO) plan. We consider the action blocks in a BDPO plan as candidate subplans for substitutions, and ensure that each successful substitution produces a plan with strictly greater flexibility. In addition, this paper employs plan reduction strategies to eliminate redundant actions within a BDPO plan. We also evaluate our approach when combined with MaxSAT-based reorderings. Our experimental result demonstrates a significant improvem

We consider the conformal block decomposition in arbitrary exchange channels of a two-dimensional conformal field theory on a torus. The channels are described by diagrams built of a closed loop with external legs (a necklace sub-diagram) and trivalent vertices forming trivalent trees attached to the necklace. Then, the $n$-point torus conformal block in any channel can be obtained by acting with a number of OPE operators on the $k$-point torus block in the necklace channel at $k=1,...,n$. Focusing on the necklace channel, we go to the large-$c$ regime, where the Virasoro algebra truncates to the $sl(2, \mathbb{R})$ subalgebra, and obtain the system of the Casimir equations for the respective $k$-point global conformal block. In the plane limit, when the torus modular parameter $q\to 0$, we explicitly find the Casimir equations on a plane which define the $(k+2)$-point global conformal block in the comb channel. Finally, we formulate the general scheme to find Casimir equations for global torus blocks in arbitrary channels.

The randomized Kaczmarz algorithm is one of the most popular approaches for solving large-scale linear systems due to its simplicity and efficiency. In this paper, we propose two classes of global randomized Kaczmarz methods for solving large-scale linear matrix equations $AXB=C$, the global randomized block Kaczmarz algorithm and global randomized average block Kaczmarz algorithm. The feature of global randomized block Kaczmarz algorithm is the fact that the current iterate is projected onto the solution space of the sketched matrix equation at each iteration, while the global randomized average block Kaczmarz approach is pseudoinverse-free and therefore can be deployed on parallel computing units to achieve significant improvements in the computational time. We prove that these two methods linearly converge in the mean square to the minimum norm solution $X_*=A^†CB^†$ of a given linear matrix equation. The convergence rates depend on the geometric properties of the data matrices and their submatrices and on the size of the blocks. Numerical results reveal that our proposed algorithms are efficient and effective for solving large-scale matrix equations. In particular, they can als

We present new results on community recovery based on the PageRank Nibble algorithm on a sparse directed stochastic block model (dSBM). Our results are based on a characterization of the local weak limit of the dSBM and the limiting PageRank distribution. This characterization allows us to estimate the probability of misclassification for any given connection kernel and any given number of seeds (vertices whose community label is known). The fact that PageRank is a local algorithm that can be efficiently computed in both a distributed and asynchronous fashion, makes it an appealing method for identifying members of a given community in very large networks where the identity of some vertices is known.

We present Block-NeRF, a variant of Neural Radiance Fields that can represent large-scale environments. Specifically, we demonstrate that when scaling NeRF to render city-scale scenes spanning multiple blocks, it is vital to decompose the scene into individually trained NeRFs. This decomposition decouples rendering time from scene size, enables rendering to scale to arbitrarily large environments, and allows per-block updates of the environment. We adopt several architectural changes to make NeRF robust to data captured over months under different environmental conditions. We add appearance embeddings, learned pose refinement, and controllable exposure to each individual NeRF, and introduce a procedure for aligning appearance between adjacent NeRFs so that they can be seamlessly combined. We build a grid of Block-NeRFs from 2.8 million images to create the largest neural scene representation to date, capable of rendering an entire neighborhood of San Francisco.

Estimating the number of communities is one of the fundamental problems in community detection. We re-examine the Bayesian paradigm for stochastic block models and propose a "corrected Bayesian information criterion",to determine the number of communities and show that the proposed estimator is consistent under mild conditions. The proposed criterion improves those used in Wang and Bickel (2016) and Saldana et al. (2017) which tend to underestimate and overestimate the number of communities, respectively. Along the way, we establish the Wilks theorem for stochastic block models. Moreover, we show that, to obtain the consistency of model selection for stochastic block models, we need a so-called "consistency condition". We also provide sufficient conditions for both homogenous networks and non-homogenous networks. The results are further extended to degree corrected stochastic block models. Numerical studies demonstrate our theoretical results.

We compute the conformal blocks of the Virasoro minimal model or its W$_N$ extension with large central charge from Wilson line networks in a Chern-Simons theory including loop corrections. In our previous work, we offered a prescription to regularize divergences from loops attached to Wilson lines. In this paper, we generalize our method with the prescription by dealing with more general operators for $N=3$ and apply it to the identity W$_3$ block. We further compute general light-light blocks and heavy-light correlators for $N=2$ with the Wilson line method and compare the results with known ones obtained using a different prescription. We briefly discuss general W$_3$ blocks.

This paper will prove that: 1. $G$ has a block only having linear ordinary characters if and only if $G$ is a $p$-nilpotent group with an abelian Sylow $p$-subgroup; 2. $G$ has a block only having linear Brauer characters if and only if $O_{p'}(G)\leq O_{p'p}(G)=HO_{p'}(G)= \textrm{Ker}(B_{0}^{*}) \leq O_{p'pp'}=G$, where $H=G^{'}O^{p'}(G), \textrm{Ker}(B_{0}^{*})=\bigcap_{λ\in \textrm{IBr}(B_{0})} \textrm{Ker}(V_λ), B_{0}$ is the principal block of $G$ and $V_λ$ is the $F[G]$-module affording the Brauer character $λ$; 3. if $G$ satisfies the conditions above, then for any block algebra $B$ of $G$, we have $$ \frac{\textrm{Dim}_{F}(B)}{|D|}= \sum_{φ\in \textrm{IBr}(B)}φ(1)^{2}$$ where $D$ is the defect group of $B$.

We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and solves typically several associated proximal subproblems that usually have a closed-form solution, until a certain progress on objective value is achieved. In contrast to the usual randomized block coordinate descent method [23,20], our method has a nonmonotone flavor and uses variable stepsizes that can partially utilize the local curvature information of the smooth component of objective function. We show that any accumulation point of the solution sequence of the method is a stationary point of the problem {\it almost surely} and the method is capable of finding an approximate stationary point with high probability. We also establish a sublinear rate of convergence for the method in terms of the minimal expected squared norm of certain proximal gradients over the iterations. When the problem under consideration is convex, we show that the expected objective values genera

An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. The model is the stochastic blockmodel (SBM) with block parameters integrated out. The resulting marginal distribution defines a posterior over the number of clusters and cluster memberships. Sampling from this posterior is simpler than from the original SBM as transdimensional MCMC can be avoided. The algorithm is based on the allocation sampler. It requires a prior to be placed on the number of clusters, thereby allowing the number of clusters to be directly estimated by the algorithm, rather than being given as an input parameter. Synthetic and real data are used to test the speed and accuracy of the model and algorithm, including the ability to estimate the number of clusters. The algorithm can scale to networks with up to ten thousand nodes and tens of millions of edges.

Iterative decoding techniques have gain popularity due to their performance and their application in most communications systems. In this paper, we present a new application of our iterative decoder on the GPCB (Generalized Parallel Concatenated Block codes) which uses cyclic permutations. We introduce a new variant of the component decoder. After extensive simulation; the obtained result is very promising compared with several existing methods. We evaluate the effects of various parameters component codes, interleaver size, block size, and the number of iterations. Three interesting results are obtained; the first one is that the performances in terms of BER (Bit Error Rate) of the new constituent decoder are relatively similar to that of original one. Secondly our turbo decoding outperforms another turbo decoder for some linear block codes. Thirdly the proposed iterative decoding of GPCB-BCH (75, 51) is about 2.1dB from its Shannon limit.