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arXiv2026

Polynomial Lower Bounds for Distributed Graph Sketching with Tiny Error: Connectivity and Spanning Tree Construction

We present the first polynomial lower bounds for several fundamental problems in the distributed graph sketching model in the tiny-error regime, which includes deterministic algorithms as a special case. In the graph sketching model, every node sends a single message to the referee who does not have any prior knowledge of the graph and must output the answer. While the work of Nelson and Yu (SODA 2019) and Yu (SODA 2021) showed that $Θ( \log^3n )$ is optimal for constructing a spanning forest or deciding whether the graph is connected with error at most $\frac{1}{\text{poly}(n)}$ , their approach does not yield any stronger bounds for significantly smaller error probabilities. Our main result is to show that solving either connectivity or spanning tree construction with error at most $δ$ requires messages of length $Ω( \min\{n, \log_2 \frac{1}δ\}^{1/3} )$, which implies that algorithms with exponentially small error must send messages of $Ω( n^{1/3} )$ bits in the worst case. Our results significantly narrows the current gap between the Jelani-Yu threshold of $Θ( \log^3n )$ and the trivial upper bound of sending $O(n)$ bits per node for deterministic graph sketching. We also extend our results to $k$-edge connectivity. For any $k=O(n^{1/7})$, we recover the same bound of $Ω( k )$ on the message length for algorithms with exponentially small error that was shown by Robinson and Tan (PODS 2026) only for deterministic algorithms. Finally, for $k=n^{o(1)}$, our result implies a stronger lower bound of $Ω_ε( n^ε )$ bits, for any constant $ε<\tfrac{1}{3}$.

cs.DS↗

arXiv2026

CALM: Class-wise Agreement and Label-gated Disagreement Modulation for Decentralized Federated Learning

Conventional federated learning relies on parameter averaging, which forces clients to be doubly homogeneous: all must run an identical architecture, and accuracy degrades when local data are non-IID. Decentralized federated distillation sidesteps both: each client runs its peers' model snapshots as teachers on its own local data and distills from their soft predictions, with no server, no public data, and no shared architecture. Under severe non-IID skew, however, the trustworthiness of the aggregated teacher target is a matter of degree, yet existing pipelines make hard, all-or-nothing decisions: outlier teachers are discarded by threshold, and whatever target survives is trusted in full. We propose CALM, which replaces every hard decision with a smooth trust gate at three levels: per class, teachers are weighted by agreement with the peer consensus; per sample, distillation is scaled by the teachers' divergence from that target; and a label gate scales it by how strongly the target supports the sample's true label. None of this adds communication or auxiliary data. On CIFAR-10, SVHN, OrganAMNIST, and Google Speech Commands with heterogeneous client architectures under Dirichlet label skew, CALM consistently outperforms uniform and hard-filtered distillation and matches or exceeds competing heterogeneous-FL methods.

cs.LG↗

arXiv2026

Race, Exchange, Improve: Finding high-quality MIP solutions quickly

Mixed-integer programming (MIP) is a cornerstone in applied optimization, both in industry and academia. Recently, there has been increased attention to finding strong primal solutions quickly. This is reflected, for example, in the development of the NVIDIA cuOpt solver and, most recently, in the new MIPFEAS benchmark, which has a tight time limit of 600 seconds and evaluates solvers based on how quickly they find high-quality primal solutions. This article introduces a MIP portfolio parallelization scheme, focusing on efficiently exchanging information between its workers. We present two implementations of this scheme: one built directly into the open-source MIP solver SCIP, and an external one, which we call ReXi. ReXi is currently the fastest non-commercial solver in the MIPFEAS benchmark, followed by the SCIP-integrated implementation. Moreover, we present new versions of both implementations that considerably outperform their predecessors on the MIPFEAS benchmark.

math.OC↗

arXiv2026

Poseidon: DAG-Guided Parallelism Search for LLM Pre-Training on Heterogeneous Clusters

With the rapid advancement of accelerator technologies, pre-training large language models (LLMs) on heterogeneous accelerator clusters has become increasingly crucial for maximizing hardware utilization. Existing systems, however, suffer from inaccurate training time modeling, which undermines the parallelization optimizations built upon it. Moreover, for current approaches, the vast configuration search space makes exhaustive exploration infeasible, forcing a trade-off between search time and training efficiency. To overcome these limitations, we introduce Poseidon, an efficient and scalable LLM training framework designed with heterogeneity awareness. Its core is an explicit training time model based on a directed acyclic graph. Building on this graph, Poseidon employs two efficient, theoretically grounded strategies: stage-level pruning via early stopping with partial estimation, and layer-to-stage mapping exploiting a ridge-like distribution pattern. These strategies reduce the search space without sacrificing optimal training efficiency. Experiments on heterogeneous clusters show that Poseidon improves training throughput by up to $2.76\times$ over state-of-the-art systems.

cs.DC↗

arXiv2026

FANS: Federated Adaptive Network Search Learning for Heterogeneous Devices

Heterogeneous Federated Learning (HFL) aims to train models across devices with diverse resource budgets while preserving data privacy. Existing HFL methods typically bind training to a small predefined menu of model configurations, which limits architectural coverage. To address this bottleneck, we introduce Federated Adaptive Network Search (FANS), a hypernetwork-based framework that learns a shared architecture space rather than a fixed set of client models. To optimize this shared space efficiently, we propose the Federated Parallel Scaling (FPS) algorithm, which jointly trains multiple sampled subnetworks in parallel with self-distillation so that larger sampled subnetworks can supervise smaller ones during local updates. We evaluate FANS on CIFAR-10, CIFAR-100, and MNLI using ResNet-18, DenseNet-121, and BERT-base, respectively. Across all benchmarks, FANS expands the feasible subnetwork pool by orders of magnitude (e.g., 4,680 candidates for ResNet-18 vs. 4 in existing methods) and improves the average accuracy-efficiency trade-off relative to representative HFL baselines. Device heterogeneity is emulated through resource tiers, and evaluation covers accuracy, parameter count, and MACs.

cs.LG↗

arXiv2026

Diamond Agent: Agentic Control of Federated HPC Resources as a Service

Efficiently aggregating and orchestrating computing power across heterogeneous clusters for HPC workflows faces four practical challenges: preserving workflow context across independently administered clusters, moving large datasets between sites, reasoning about site-specific environments and scheduler policies, and exploiting live queue and resource states for efficient task scheduling. To this end, we design Diamond Agent, an agentic system that enables intelligent execution of HPC workflows across heterogeneous clusters with typed skills as the interface. Diamond Agent provides an agent-facing workspace and skills that unify cross-site resource discovery, resource specification, data movement, task execution, and result retrieval. A centralized Diamond Agent instance can operate multiple supercomputers without being deployed separately on each login node. Diamond Agent translates high-level agent actions into valid site-specific executions, moves data through Globus Transfer, and uses live system capability and queue information to select feasible placements. Its event-driven continuation mechanism decouples agent actions from long-running batch jobs: persistent services monitor remote execution and resume the agent only when a result or decision-relevant event is available. We experiment with 27 hours of telemetry and 19 matched multi-site submission rounds comprising 83 jobs across four production supercomputers. Compared with a fixed-site baseline, Diamond Agent reduces the median additional completion time relative to the fastest observed placement from 42 seconds to 4 seconds, a 10.5x reduction.

cs.DC↗

arXiv2026

Minimizing Commit Rules for DAG-based Atomic Broadcast

A popular class of Byzantine fault-tolerant atomic broadcast protocols rely on directed acyclic graphs (DAGs) that represent causal relations between broadcast messages. Each process applies a protocol-specific \emph{commit rule} on its local DAG to determine which vertices can be delivered in a total order. Intuitively, commit rules that impose fewer conditions on the DAG to order its vertices imply more efficient protocols, as the broadcast messages are delivered with lower latency. In this paper, we define commit rules on an uncertified round-based DAG construction, and introduce a sub-rule relation between them: a commit rule $cr_1$ is a sub-rule of a commit rule $cr_2$ if, for any DAG, the set of vertices committed by $cr_1$ contains all vertices committed by $cr_2$. We use the sub-rule relation to determine a minimal commit rule in an eventually synchronous model and a minimal commit rule in an asynchronous model, namely, two commit rules that require the least conditions on the DAG to safely commit any set of vertices in their respective models. To the best of our knowledge, no existing DAG-based atomic broadcast protocol relies on such minimal commit rules: we introduce \emph{Minnow}, a new protocol for DAG-based atomic broadcast, which can be instantiated in both eventually synchronous (S-Minnow) and asynchronous networks (A-Minnow).

cs.DC↗

arXiv2026

A Simple Construction of Locally Checkable Problems Filling the LOCAL Complexity Gaps in Graphs with Arbitrary Large Degrees

We show that the complexity gaps in the round complexities of locally checkable labeling (LCL) problems are not due to the fact that solutions to LCL problems must be locally checkable, but solely to the fact that LCL problems are defined only for graphs of maximum degree upper bounded by some arbitrary yet constant value $Δ$. Specifically, we show that there are infinitely many locally checkable problems (i.e., problems whose solutions can be checked locally) whose round complexities belongs to the two intervals $[ω(1),o(\log\log^\star n)]$ and $[ω(\log^\star n),o(\log n)]$ whenever these problems are considered in networks with unbounded maximum degrees. This extends the previous results by Schmid (arXiv, 2026), which hold for the polynomial regime only, and by Bousquet, Feuilloley, and Pierron (OPODIS, 2025), which hold for trees only. All our upper bounds are obtained using deterministic algorithms that can be run under the port-numbering model, which is a weak variant of LOCAL, without any a priori information on the number of nodes in the network. Instead, our lower bounds apply to randomized LOCAL, and quantum LOCAL, even if nodes have identifiers in $[1,n]$, and even if they know the exact number of nodes in the network. They even hold under randomized online LOCAL, a strong variant of the LOCAL model. Finally, our lower bounds hold even for trees. Our results are obtained using two main ingredients. The first one is the analysis of a new locally checkable problem called Increasing Degree, parameterized by a function $f:\mathbb{N}\to\mathbb{N}$. Different round complexities can be obtained by tuning the function $f$ accordingly. Our second tool is a general Translation Theorem that enables to transfer results from a given range of complexities to results for a range of lower complexities.

cs.DC↗

arXiv2026

Relaxed Sender Anonymity for CBDC Interbank Settlement: A Zero-Knowledge Approach on Permissioned EVM

Central Bank Digital Currency (CBDC) interbank settlement systems operating on Distributed Ledger Technology (DLT) face a fundamental trade-off: blockchain transparency enables trustless verification but exposes commercially sensitive bilateral transaction flows to all network participants. We propose a confidential interbank settlement protocol for permissioned Ethereum-compatible networks that resolves this tension through a relaxed sender anonymity model tailored to regulatory AML/CFT requirements. In this model, the initiating institution remains publicly identifiable on-chain for accountability and compliance, while the receiving institution, transfer amount, and business payload are cryptographically obfuscated. We realize the protocol on Hyperledger Besu using QBFT consensus, combining Groth16 zero-knowledge proofs over BN254, Poseidon hash commitments in an incremental Merkle tree, multi-recipient ECIES payload encryption, and an on-chain NoteRegistry contract that stores encrypted notes as an append-only ledger log, eliminating trusted off-chain custody servers. The protocol supports shield, confidential transfer, and unshield state transitions. Experimental evaluation across a five-node network (three commercial banks, a central bank operator, and a securities depository) demonstrates end-to-end settlement in 8-16 s, proof verification overhead of about 1 ms (around 220k gas) via EVM precompiles, and client proof generation in 4-12 s on commodity ARM hardware. While receiver confidentiality is established at the protocol level, the current proof-of-concept NoteRegistry uses owner-indexed events, a trade-off addressable in production via uniform event broadcasting.

cs.CR↗

arXiv2026

Improving Progressive Compression with Adaptive Interpolation and Coefficient Decomposition

Exascale simulations generate data far faster than it can be stored or analyzed, making efficient data reduction essential. Error-controlled lossy compression offers high compression ratios under user-specified error bounds, but the target tolerance must be fixed at compression time. Progressive compression relaxes this restriction, yet existing methods still rely on fixed refactoring strategies and do not fully exploit correlations among decomposed coefficients, limiting the efficiency of progressive retrieval. In this work, we present an adaptive progressive compression framework that improves retrieval efficiency for two common targets, namely error-bound and peak Signal-to-Noise ratios. Our contributions are fourfold. (1) We propose to leverage two complementary interpolation schemes for adaptive progressive compression toward different targets, and we optimize them to achieve high efficiency. (2) We propose coefficient decomposition, a novel method that exploits the commonly overlooked spatial correlations among decorrelated data, which further improves the efficiency. (3) We develop the adaptive progressive compression workflow with automatic selection of the best-fit refactoring pipeline and tailored optimizations. (4) We evaluate the proposed framework on five real-world scientific datasets against three state-of-the-art progressive compressors. Experimental results demonstrate that the proposed framework improves the compression ratio by up to $42.3\%$ under the same requested error tolerance and up to $92.5\%$ at the same PSNR, compared with the best-performing existing methods. When transferring $512$ GB of scientific data to remote sites, the framework delivers up to $1.26\times$ speedup in the end-to-end data transfer performance. Furthermore, our method achieves the highest visualization quality while retrieving the least amount of data from storage.

cs.DC↗

arXiv2026

CIERA: Cross-Iteration Exponent Reuse for Lossless Allgather in Sharded MoE Training

In training Mixture-of-Experts (MoE) models, sharded data parallelism partitions each expert's parameters across GPUs, requiring an Allgather operation to reconstruct the full weight matrix before each layer executes. This communication often dominates iteration time. Prior work often reduces this overhead using lossy compression methods that sacrifice numerical fidelity, while existing lossless methods do not exploit cross-iteration exponent stability. In this paper, we propose Cross-Iteration Exponent Reuse Allgather (CIERA), a lossless, system-aware communication method for sharded MoE training. We observe that after a brief warmup phase, the exponent values of most weights remain unchanged across iterations. Based on this, we cache exponents locally and transmit only the sign and mantissa when exponents are unchanged. The receiver reconstructs the original weights exactly by combining the cached exponents with the received data. Since parameter matrices vary in shape across layers, compression is applied only when it yields net time savings. Moreover, the compression operation is overlapped with both Allgather communication and computation. Our real experiments and large-scale trace-driven simulator show that on OLMoE-1B-7B at 16 GPUs, CIERA achieves a 3.70x speedup over the lossless baseline and 3.68x over the lossy baseline, projected to reach 4.28x and 4.42x respectively at 128 GPUs, while preserving bitwise-exact parameter reconstruction in all evaluated runs.

cs.DC↗

arXiv2026

BF16 Component-Product Emulation of FP32 and FP64 GEMM on Intel AMX

Modern CPUs increasingly integrate high-throughput matrix engines optimized for low-precision AI workloads, while many scientific computing applications still rely on FP32 and FP64 GEMM to meet their numerical accuracy requirements. This mismatch motivates an algorithmic bridge that uses low-precision matrix products to emulate higher-precision GEMM. This paper presents a CPU-oriented method based on Intel Advanced Matrix Extensions (AMX) and BF16 matrix products. For FP32, each operand is decomposed into three BF16 components and six selected component products are evaluated, targeting FP32-level accuracy relative to oneMKL SGEMM without claiming elementwise or bitwise identity. For FP64 inputs within the supported BF16 exponent range, the method uses a simplified fixed six-slice Ozaki decomposition. Each retained BF16 product is first produced in FP32, then widened and accumulated in FP64. Four product-count settings retain 6, 10, 15, or 21 component products, exposing the accuracy--performance tradeoff relative to oneMKL DGEMM. The implementation combines precomputed packed component buffers, VNNI-packed $B$ panels, and an FP32 tile-resident operand-reuse schedule. On the tested square matrices, AMX-FP32 exceeds oneMKL SGEMM throughput. For AMX-FP64, low-product-count variants can exceed DGEMM at sufficiently large orders, while retaining more products improves accuracy at additional cost.

cs.MS↗

arXiv2026

Resilience Beyond Stationary Client Unavailability: Unlocking Efficient and Unbiased Federated Learning

Due to resource constraints or external and internal uncertainties, clients in real-world federated learning systems are often intermittently available edge devices. In highly dynamic environments, the parameter server lacks prior real-time knowledge of clients' availability, making it challenging to adapt traditional federated learning algorithms to be resilient to uncertainties in client availability. If not carefully addressed, complex client availability can introduce significant bias, potentially harming the performance of the trained model. Most prior work either fails to account for non-stationary client availability dynamics or demands significant memory and computational overhead. This paper aims to develop efficient federated learning algorithms that are provably resilient to heterogeneous and non-stationary stochastic client availability. We propose FedSWE, which admits novel algorithmic structures to (i) compensate for missed computations, (ii) stabilize and diffuse the global updates over rounds, and (iii) evenly mix the local updates through implicit gossiping, despite being agnostic to non-stationary dynamics. Compared with the standard FedAvg, FedSWE introduces light additional memory and computation overhead. We show that FedSWE converges to a stationary point of non-convex objectives while achieving the desired linear speedup property in certain special cases. We corroborate our analysis with numerical experiments over diversified client unavailability dynamics on real-world data sets.

cs.LG↗

arXiv2026

GreenPipe: Power Modeling for Containerized DNN Inference on Kubernetes Edge Nodes

Distributed DNN inference is increasingly deployed in containerized edge-cloud environments, where workloads run on-device or are exposed to remote clients over the network. Accurate online power estimation on resource-constrained ARM nodes without hardware power counters such as RAPL remains a challenge, and CPU-only models fail to capture multi-resource behavior. We present GreenPipe, an automated profiling-training-validation pipeline that builds multi-resource regression models from external power meter measurements and attributes power to containers proportionally. GreenPipe is evaluated on a Raspberry Pi 4 edge node in a K3s edge-cloud testbed, covering DNN inference with three vision models, multiple precisions, thread counts, and both local and serving scenarios. System-level MAPE is 6.3-9.4%, improving over CPU-stress and utilization-only baselines by 26.9% MAPE on average. We jointly report inference latency and energy per inference, exposing performance-energy trade-offs across workload configurations.

cs.DC↗

arXiv2026

Solution-space heterogeneity shapes federated learning dynamics across partial differential equations

Federated scientific machine learning enables institutions to train neural surrogates without centralizing local physical data, yet studies of partial differential equations (PDEs) lack a transferable definition of non-independent and identically distributed data. Existing protocols partition coordinates, coefficients, boundary conditions, or geometries according to equation-specific rules. Here, we introduce solution-space PDE-Dirichlet, a protocol that converts continuous supervised responses into reusable solution bins and quantifies the realized separation between clients through optimal transport over the geometry of these bins. We derive an exact inverse relation between population allocation heterogeneity and the Dirichlet concentration, and we establish conditions under which response heterogeneity induces gradient disagreement, local-update dispersion, and parameter divergence. Across seven controlled and public PDE tasks, three neural-operator families, and five random seeds, a lower concentration consistently increases the realized solution distance and optimization heterogeneity. The degradation in final error is task dependent: the largest effect occurs for low-viscosity Burgers, reaching 4.157 percentage points under the most heterogeneous setting, whereas additional communication or smoother dynamics can reduce the final gap despite persistent parameter separation. These results distinguish a reproducible geometric mechanism from task-dependent generalization outcomes and provide a common basis for evaluating non-IID federated PDE learning.

cs.LG↗

arXiv2026

From 80x to 385x: A Best-Matching-Unit Search at the L2 Roof, Measured Against a Symmetrically Tuned Baseline

Comparisons between GPU implementations are usually asymmetric: one side is tuned by its author, the other is run as found. I report a programme that tuned both a novel SOM algorithm (SparseBin) and the baseline algorithm it was being compared to (cuSPARSE). The best-matching-unit search that dominates self-organizing map training was tuned through four levers - tile size, tile-membership clustering, neuron-axis chunking and vectorised loads - reaching 5.6-10.1x per epoch over the previously published configuration at map sizes from 32x32 to 512x512, and lifting the margin over the CUDA implementation behind our earlier MEDLINE atlases from ~80x to ~385x. cuSPARSE, the implementation SparseBin is compared against, received every lever with an analogue on its side, and became 2-3x faster in the process. The tuned kernel pressed the L2 bandwidth roof at 77% of peak with every other unit at 40-65%, bounding any further lever at ~1.3x - a terminal result rather than a waypoint, and every untested lever was either capped by that bound by construction or measured null.

cs.LG↗

arXiv2026

Beyond Scalar Flexibility: From Eligible AI Workloads to Dependable Load Relief

Grid studies often represent data-center flexibility as a fixed percentage of load, although no public production trace has shown how much eligible load persists across event durations or co-moves across clusters. We reconstruct 4,439 hourly power observations from a 185-day trace of 155,410 GPUs and derive a workload-semantic flexibility envelope. The fleet's time-averaged Monte Carlo median facility demand is 55.8 MW, while immediate eligible curtailment averages 3.55 MW after retaining allocated-GPU idle power: 12.1% of workload power and 6.35% of median facility power. Under full realization of that eligibility, 95%-available relief falls from 2.51 MW for one hour to 2.32 MW for four hours and 1.95 MW for 24 hours; a common realizable fraction q scales every value exactly by q. A mean-calibrated scalar overstates these quantities by 17%, 25%, and 47%, while a scalar tail-calibrated at four hours understates the one-hour product by 6% and overstates the 24-hour product by 17%; the share that reproduces the surface varies by a factor of 1.6 across durations and reliability levels. Aggregating 13 clusters raises four-hour firmness from 0.38 to 0.66, but cross-cluster covariance limits the gain. The production scheduler exposes almost no additional delay-based capacity: newly deferrable arrivals average 0.008 MW and have zero 95%-available capacity. These results replace an assumed flexibility percentage with duration, reliability, portfolio, and realizability terms that can be written into interconnection and demand-response contracts.

eess.SY↗

arXiv2026

Sharpedo: Dual-Mode Uncertified DAG-Based Consensus Protocol

Mysticeti and Mahi-Mahi represent leading approaches to consensus protocols, leveraging a novel uncertified Directed Acyclic Graph data structure to achieve substantial performance benefits compared to prior work. Mysticeti and Mahi-Mahi differ in their underlying network assumptions, where the former makes assumptions about timing bounds for communication while the latter does not. Mysticeti trades robustness for lower levels of latency in ideal conditions, whereas Mahi-Mahi favours increased latency in order to ensure stronger progress guarantees in asynchronous settings. Although dual-mode protocols exist (i.e., protocols that can adapt do different network assumptions), none have been implemented to take full advantage of the novel data structure seen in the aforementioned protocols. Thus, our research project aims to trace the progression of consensus protocols, analyse how they address network assumptions constraints, and explore dual-mode protocols. Then, we present Sharpedo, the first dual-mode uncertified Directed Acyclic Graph consensus protocols which aims to achieve the best of both worlds: the high-performance of partially-synchronous protocols, while providing guarantees of progress even in asynchronous settings. Furthermore, Sharpedo integrates a novel dynamic scheduling mechanism resulting in improved system efficiency and performance optimization.

cs.DC↗