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arXiv2026

Neural Logic, Invariance, and the Retina---McCulloch and Pitts

This chapter reconstructs the McCulloch-Pitts program as a physics of neural computation rather than the familiar cartoon of a binary neuron. The 1943 logical calculus is developed in both directions: given a net, characterize the propositions realized by its activity; given an admissible logical expression, construct a net that realizes it. We recover the original distinction between thresholded excitatory summation and absolute inhibitory veto-one the weighted-threshold form cannot preserve for arbitrarily large excitatory inputs-and read unit-time delay as the physical realization of logical depth. Recurrence is treated exactly: an autonomous, deterministic network of finitely many binary units has a finite state space, so every trajectory eventually enters a periodic orbit-a fact about finite-state dynamics, not unbounded Turing computation. A single threshold element realizes only linearly separable Boolean functions, whereas finite feedforward networks of them synthesize any Boolean function on a finite domain. We then follows McCulloch and Pitts beyond threshold logic. The 1945 heterarchy paper turns cyclic preference into an obstruction to representation by a scalar utility. The 1947 work on universals asks how a physical network can identify inputs related by nuisance transformations, developed here via group averaging and feedback canonicalization. The 1959 frog-retina study makes the adequate-stimulus question experimental, revealing parallel invariant operations before the brain proper. Spike-triggered analysis shows how a nonlinearly driven neuron can have a vanishing first-order average while second-order statistics recover its hidden selectivity: methodological failure can masquerade as physiological absence. Modern mathematical tools are used without projecting their notation onto the historical papers, and limitations of the idealization are stated explicitly.

q-bio.NC↗
arXiv2026

Stochastic Estimation of Transduced Language Models

Transduced language models (TLMs) compose a pretrained \emph{source} language model with a functional finite-state transducer to induce a language model over \emph{target} strings. Computing the probability of a target prefix under a TLM amounts to summing the source-model probabilities of all source strings that the transducer maps to target strings beginning with that prefix. This set can be exponentially large or infinite. Prior work uses a computational shortcut based on source prefix probabilities, then approximates the resulting sum with threshold-pruned beam summing. This produces a lower bound with unknown error. Instead, we resample source prefixes without replacement and reweight each selected prefix by the inverse of its inclusion probability. We show that applying this correction recursively gives an unbiased estimator of the target prefix probability and lets us estimate the mass lost by threshold pruning. Our beam-summing algorithm extends the retained source prefixes and samples which prefixes to keep, reducing their number as more probability mass is added to the running estimate. This can save computation and guarantees that the run halts with probability one. We evaluate the method on encyclopedic text and DNA against sequential Monte Carlo baselines that resample with replacement. It achieves a better compute--variance tradeoff on text and lower error at the same maximum number of particles on DNA. On a DNA-to-amino-acid transduction, it reduces runtime by several orders of magnitude relative to threshold-pruned beam summing and makes estimating prefix probabilities for long target strings feasible. Replacing threshold pruning with unbiased sampling in a published reading-time analysis substantially lowers the estimated corpus surprisal but leaves the published conclusions unchanged.

cs.CL↗
arXiv2026

Federated Learning for MRI-based BrainAGE: a multicenter study on post-stroke functional outcome prediction

$\textbf{Objective:}$ Brain-predicted age difference (BrainAGE) is a neuroimaging biomarker reflecting brain health. However, training robust BrainAGE models requires large datasets, often restricted by privacy concerns. This study evaluates the performance of federated learning (FL) for BrainAGE estimation in ischemic stroke patients treated with mechanical thrombectomy, and investigates its association with clinical phenotypes and functional outcomes. $\textbf{Methods:}$ We used FLAIR brain images from 1674 stroke patients across 16 hospital centers. We implemented standard machine learning and deep learning models for BrainAGE estimates under three data management strategies: centralized learning (pooled data), FL (local training at each site), and single-site learning. We reported prediction errors and examined associations between BrainAGE and vascular risk factors (e.g., diabetes mellitus, hypertension, smoking), as well as functional outcomes at three months post-stroke. Logistic regression evaluated BrainAGE's predictive value for these outcomes, adjusting for age, sex, vascular risk factors, stroke severity, time between MRI and arterial puncture, prior intravenous thrombolysis, and recanalisation outcome. $\textbf{Results:}$ While centralized learning yielded the most accurate predictions, FL consistently outperformed single-site models. BrainAGE was significantly higher in patients with diabetes mellitus across all models. Comparisons between patients with good and poor functional outcomes, and multivariate predictions of these outcomes showed the significance of the association between BrainAGE and post-stroke recovery. $\textbf{Conclusion:}$ FL enables accurate age predictions without data centralization. The strong association between BrainAGE, vascular risk factors, and post-stroke recovery highlights its potential for prognostic modeling in stroke care.

cs.LG↗
arXiv2026

"More Is Different'' in Neural Circuits: Algebraic Emergence of Effective Theories in Canonical Recurrent Motifs of Biological Neuronal Networks

Canonical neural circuit motifs are usually described functionally: divisive normalization rescales population activity by a pooled signal, and winner-take-all competition selects one pattern through recurrent excitation and shared inhibition. We represent them, and their compositions, algebraically as finite transformation systems and analyze the transition monoids generated by their input-conditioned updates, distinguishing structure already present in a generator from structure that appears only through composition, and, on a joint state space, structure inherited from one factor from structure that lives on a joint configuration. Individually aperiodic updates can generate non-aperiodic monoids. In the WTA, every frozen-drive generator collapses to fixed points, yet short input sequences create local cycles of winner-dependent inhibitory gating: globally dissipative dynamics with a reversible action. The strongest result arises in WTA-to-DN composition. The composed monoid then contains a genuinely composite local cycle in which normalization state and the winner's gating state change together, although every primitive generator is aperiodic. Holonomy analysis certifies this as a group component of the Krohn-Rhodes cascade rather than an incidental cycle, and finds most group-carrying image sets on joint configurations, whereas the uncoupled product has none. An exhaustive interface sweep shows that the composite cycle is a property of the coupling rather than of a chosen map. If motifs are building blocks of neural computation, composing them is a form of programming: one chooses primitives and interfaces so that the generated algebra has the intended repertoire. The transition monoid is that repertoire - what a primitive presents to any later construction. Recurrent circuits are compositional transformation systems; their algebra constrains what they can be programmed to compute.

q-bio.NC↗
arXiv2026

A Unary-to-Nonunary Transition in the Accepting-State Spectrum of Right Quotient for Permutation Automata

This paper resolves the open larger-alphabet quotient case in the accepting-state complexity theory of permutation automata. Rauch and Holzer showed that, in the unary setting, the attainable right-quotient accepting-state complexities are exactly $[1,mn]$. We prove that over arbitrary alphabets the exact spectrum is $g^{\operatorname{asc}}_{-1,\mathrm{PFA}}(m,n)=\{0\}$ if $m=0$ or $n=0$, and $g^{\operatorname{asc}}_{-1,\mathrm{PFA}}(m,n)=\mathbb{N}_{>0}$ if $m,n\ge 1$. Thus, once both input languages are nonempty, every positive accepting-state complexity is attainable for right quotient, and $0$ is the only unavoidable magic value. The proof has two parts. First, we show that if $m,n\ge 1$, then the quotient language $KL^{-1}$ cannot be empty when $K$ and $L$ are accepted by permutation automata with $\operatorname{asc}(K)=m$ and $\operatorname{asc}(L)=n$; this follows from the bijectivity of the transition action. Second, for every $m,n\ge 1$ and every $α\ge m$, we construct a ternary witness pair $(A^{\mathrm{q}}_{m,α},B^{\mathrm{q}}_{n,α})$ such that $\operatorname{asc}(L(A^{\mathrm{q}}_{m,α}))=m$, $\operatorname{asc}(L(B^{\mathrm{q}}_{n,α}))=n$, and $\operatorname{asc}(L(A^{\mathrm{q}}_{m,α})L(B^{\mathrm{q}}_{n,α})^{-1})=α$. The high-range construction is group-theoretic: the words accepted by $B^{\mathrm{q}}_{n,α}$ induce exactly a point stabilizer in a symmetric group, and the standard quotient construction then saturates the original final set of $A^{\mathrm{q}}_{m,α}$ to a full orbit, yielding a minimal quotient automaton with exactly $α$ final states. Combined with the known unary interval $[1,mn]$, this yields the complete spectrum and resolves the larger-alphabet right-quotient case for permutation automata.

cs.FL↗
arXiv2026

A Computational Obstruction to Swapping Area and Dinv: An Automata-Theoretic View of the $q,t$-Catalan Symmetry

Algebraic combinatorics often seeks bijections that explain identities between distributions object by object. Encoding combinatorial objects as words lets automata theory study such a bijection as a word-to-word computation and measure its memory, input access, and control of output order. This refines existence questions by asking which computational mechanisms a bijection requires. We develop this viewpoint for Dyck paths. Our motivating example is the $q,t$-Catalan polynomial. Let $D_n$ be the set of Dyck paths of semilength $n$, let $D=\bigcup_{n\ge 0}D_n$, and let $area, dinv, bounce \colon D\to\mathbb{N}$ be the standard statistics. Then, \[ C_n(q,t)=\sum_{P\in D_n}q^{area(P)}t^{bounce(P)} =\sum_{P\in D_n}q^{dinv(P)}t^{area(P)}. \] Haglund's zeta map $ζ\colon D\to D$ gives a bijective proof: it preserves semilength and sends $(dinv,area)$ to $(area,bounce)$. By contrast, the full symmetry $C_n(q,t)=C_n(t,q)$ still lacks a direct explanation: no explicit, uniform, semilength-preserving bijection is known that swaps area and dinv on every Dyck path. Polyregular maps from automata theory provide a natural computational starting point, but we prove that neither $ζ$ nor the classical height-sweep bijection witnessing Narayana symmetry is polyregular. The missing mechanism is global ordering by numerical levels whose range grows with the input. We call this a \emph{rank sort} and introduce \emph{weighted-rank polyregular maps} (WRP), extending polyregular maps by one such sort and containing both bijections. Nevertheless, WRP is a proper subclass of deterministic logspace. We prove that $ζ^{-1}$ lies outside WRP and that no WRP map can realise a semilength-preserving area-dinv swap. Thus the rank-sorting strategy behind $ζ$ cannot be extended within WRP to exchange the two statistics.

math.CO↗
arXiv2026

Exponential Gaps Between Intuitionistic Linear Extended Frege Systems

In this paper, we establish exponential separations between Extended Frege systems for a range of intuitionistic substructural and linear logics. More precisely, for any logic $L$ below the intuitionistic logic obtained by extending $\mathbf{ILL}$ with structural rules, and any logic $M$ not contained in $L$, we construct a family of $\mathsf{FL_e}$-provable formulas that have short proofs in $M$-Frege but require proofs of exponential size in $L$-Extended Frege. The same result holds in the $!$-free settings, using $\mathbf{IMALL}$ and $\mathbf{FL_e}$ in place of $\mathbf{ILL}$. The key ingredient in proving these separations is a variant of the feasible disjunction property for $L$-Frege, which may be of independent interest.

cs.LO↗
arXiv2026

The $\mathsf{AC}^0$-Complexity Of Visibly Pushdown Languages

We study the question of which visibly pushdown languages (VPLs) are in the complexity class $\mathsf{AC}^0$ and how to effectively decide this question. Our contribution is to introduce a particular subclass of one-turn VPLs, called intermediate VPLs, for which the raised question is entirely unclear: to the best of our knowledge our research community is unaware of containment or non-containment in $\mathsf{AC}^0$ for any language in our newly introduced class. Our main result states that there is an algorithm that, given a visibly pushdown automaton, correctly outputs exactly one of the following: that its language $L$ is in $\mathsf{AC}^0$, some $m\geq 2$ such that $L$ is $\mathsf{ACC}^0(m)$-hard (implying that $L$ is not in $\mathsf{AC}^0$), or a finite disjoint union of intermediate VPLs that $L$ is constant-depth equivalent to. In the latter of the three cases one can moreover effectively compute $k,l\in\mathbb{N}_{>0}$ with $k\not=l$ such that the concrete intermediate VPL $L(S\rightarrow \varepsilon\mid a c^{k-1} S b_1\mid ac^{l-1}Sb_2)$ is constant-depth reducible to the language $L$. Due to their particular nature we conjecture that either all intermediate VPLs are in $\mathsf{AC}^0$ or all are not. As a corollary of our main result we obtain that in case the input language is a visibly counter language our algorithm can effectively determine if it is in $\mathsf{AC}^0$ - hence our main result generalizes a result by Krebs et al. stating that it is decidable if a given visibly counter language is in $\mathsf{AC}^0$ (when restricted to well-matched words). For our proofs we revisit so-called Ext-algebras (introduced by Czarnetzki et al.), which are closely related to forest algebras (introduced by Bojańczyk and Walukiewicz), and use Green's relations.

cs.FL↗
arXiv2026

H-FedSN: Personalized Sparse Networks for Efficient and Accurate Hierarchical Federated Learning for IoT Applications

With the rapid development of the Internet of Things (IoT), federated learning (FL) has gained increasing attention for its privacy-preserving use of distributed data. However, conventional two-tier FL architectures are poorly suited to the hierarchical and heterogeneous nature of real-world IoT systems. Hierarchical Federated Learning (HFL) introduces multi-layer aggregation to better match IoT environments, but still suffers from communication inefficiencies and performance limitations caused by large data transfers, non-IID data distributions, and uneven device participation. These challenges hinder the realization of low-latency and high-accuracy training in practical IoT deployments. To address these limitations, we propose H-FedSN for practical IoT environments. H-FedSN leverages a binary mask mechanism with shared and personalized layers to reduce communication overhead by creating a sparse network without altering original weights. To tackle data heterogeneity and imbalanced device distribution, H-FedSN incorporates personalized layers for local data adaptation and employs Bayesian aggregation with cumulative Beta distribution updates at edge and cloud levels, effectively balancing contributions from diverse client groups. Experiments on three real-world IoT datasets and MNIST under non-IID conditions show that H-FedSN reduces communication costs by up to 477 times compared to baseline methods while maintaining high accuracy, making it well-suited for hierarchical FL in IoT deployments.

cs.LG↗
arXiv2026

Initialization Is Critical: Advancing Federated Short-Term Load Forecasting under Load Heterogeneity via Model Initialization

Short-term load forecasting (STLF) provides essential information for numerous applications in modern power systems. However, accurate STLF often relies on fine-grained smart-meter data from distributed users, raising increasing concerns about data privacy. Federated learning (FL) has therefore emerged as a promising privacy-preserving paradigm for STLF. Nevertheless, this paper reveals structured heterogeneity in clients' load data. Specifically, clients exhibit different responses to exogenous factors and distinct temporal load profiles, which can degrade forecasting performance in FL. To mitigate these issues, this paper studies the role of model initialization in federated STLF, and proposes two initialization strategies from global and local perspectives. For global model initialization, when auxiliary public load data are available, a pretrained initialization strategy is developed to initialize the global model before federated training, thereby reducing client drift during the training process. For local model initialization, we propose SLIAvg, a sequential local initialization strategy that promotes a more consistent training process by allowing participating clients to start from progressively adapted models within each communication round. Since the proposed strategies only modify the initialization process, they are compatible with most existing FL frameworks and privacy-enhancing techniques. Experiments on real smart-meter data with two representative forecasting architectures demonstrate that the proposed strategies effectively improve forecasting performance, as evidenced by reduced client drift, improved convergence behavior, and lower forecasting errors.

cs.LG↗
arXiv2026

Dictionary-Guided Mutation Operators for Automated HDL Repair

Automated repair of Hardware Description Language (HDL) designs remains challenging due to the large search space of candidate repairs and the strict syntactic and semantic constraints imposed by HDL grammars. Generic mutation strategies overwhelmingly generate syntactically invalid candidates that waste compilation and simulation budget, while synthesis-driven and template-based approaches impose their own constraints on generality and portability. In this paper, we propose a dictionary-guided HDL repair system that combines ANTLR-derived DUT-specific mutation vocabularies with a simulation-divergence fault localization (FL) module. The mutation operator applies category-constrained token substitutions, insertions, and deletions directly to Verilog source via regex-based matching, without requiring AST manipulation or synthesis. The FL module identifies diverging output wires from a single simulation run and scores source lines by structural proximity to those signals, directing the mutation search toward high-suspicion regions. A deterministic targeted sweep exhausts all dictionary mutations on the highest-scored lines before falling back to a genetic programming (GP) search. Evaluated on the CirFix benchmark suite across six design under test (DUT) families, the proposed approach produces correct oracle-passing repairs on 14 bug variants, including a 6-edit multi-bug instance that CirFix cannot repair, and achieves an 18x speedup over CirFix on a two-edit benchmark variant. These results indicate that dictionary-constrained mutation operators, combined with lightweight simulation-divergence FL, are a practical and competitive approach to automated HDL repair for common bug classes without formal analysis or synthesis dependencies.

cs.ET↗
arXiv2026

CACTUS: Mask-Guided Semantic Clean-Label Backdoors in Decentralized Federated Learning

Semantic triggers in federated learning (FL) can be less conspicuous than synthetic patches, but sample-dependent placement may weaken backdoor implantation across aggregation rounds. This challenge is compounded in decentralized FL (DFL), where topology-dependent peer aggregation repeatedly mixes local models. CACTUS converts label-consistent semantic pairs into target-directed representation shifts. Mask-guided, modality-specific operators isolate trigger effects, couple them across samples, and apply the shifts counterfactually to clean non-target embeddings before peer aggregation. Experiments cover speech, text, tabular, and image tasks under nine aggregation rules. With 30\% malicious nodes, CACTUS reaches a nine-rule mean attack success rate (ASR) of 51.2\% on Speech Commands and the highest nine-rule mean ASR among evaluated attacks on three of four modalities. Sensitivity analyses show that ASR varies with network topology and increases with the malicious-node ratio. These results indicate that CACTUS can propagate backdoors through repeated DFL aggregation.

cs.LG↗
arXiv2026

FlexP-SFT: A Flexible Aggregation-Free Framework for On-Device Personalized Split Federated Fine-Tuning of LLMs

To fine-tune large language models (LLMs) over private data, federated learning (FL) has emerged as a promising paradigm. However, the prohibitive memory and communication demands of LLMs render standard FL impractical for resource-constrained edge devices. While split federated learning (SFL) alleviates the computing burdens via model partitioning, existing frameworks still suffer from communication bottlenecks and straggler problem due to the parameter aggregation process. To address these challenges, we propose FlexP-SFT, a novel aggregation-free framework for personalized split federated fine-tuning, which fundamentally eliminates the client-side aggregation process. Crucially, to ensure robust training in the absence of global synchronization, we introduce a layer-flexible alignment strategy to balance personalization and generalization capabilities. We further formulate split-ratio selection as a resource-aware discrete optimization problem that jointly accounts for personalization accuracy and system cost. Our proposed scheme simultaneously enhances personalized performance, reduces communication overhead, and resolves the straggler problem. Extensive results show that FlexP-SFT substantially outperforms baselines in both accuracy and latency, and that the optimized split ratio achieves a better resource-accuracy trade-off than static or memory-only choices.

cs.DC↗
arXiv2026

Improving Federated Graph Recommendation with Semantic Guidance

Graph-based recommendation models effectively capture high-order collaborative signals from user--item interaction graphs. Federated learning (FL) enables privacy-preserving training across distributed clients. However, directly aggregating graph representations under FL is challenging: locally learned structural embeddings are not globally aligned under non-IID data distributions, and naive parameter averaging fails to recover cross-client relational structure. Existing federated graph-based approaches primarily rely on structural aggregation, yet overlook the global semantic knowledge encoded in large language models (LLMs). In this work, we propose a semantic--structural federated graph recommendation framework that leverages LLM embeddings to guide cross-client alignment. Each client learns user representations from its local interaction graph and summarizes typical interaction patterns into compact semantic vectors using a frozen LLM encoder. These vectors are sent to the server, which identifies semantically related patterns across different clients and combines their structural representations accordingly. The updated representations are then returned to clients to refine subsequent local training. This design enables collaboration guided by shared semantic understanding without exposing raw interaction data, preserving both recommendation accuracy and privacy. Experiments on benchmark datasets demonstrate consistent improvements over existing federated graph-based baselines.

cs.IR↗
arXiv2026

FedEHR-Agents: Federated Agentic Optimization for Automated EHR Modeling

Recent advances in large language models are enabling autonomous clinical agents to perform increasingly complex electronic health record (EHR) modeling workflows. However, agents deployed at individual hospitals remain constrained by institution-specific data and modeling environments, while direct cross-hospital collaboration is restricted by the sensitivity of patient-level EHR data. Although federated learning (FL) provides a natural foundation for privacy-preserving collaboration, existing approaches remain predominantly model-centric, limiting federation to prediction models or their updates while overlooking the richer modeling experience accumulated by autonomous agents. To address this limitation, we propose FedEHR-Agents, an experience-centric federated agentic optimization framework for automated EHR modeling. Each hospital deploys an autonomous clinical EHR agent that performs data preprocessing and model development while refining local clinical modeling experience through historical memory, task-specific evaluation, and TextGrad-based prompt refinement. The federated server performs evidence-guided experience aggregation to integrate reliable and complementary modeling experience across heterogeneous hospitals and distills the aggregated experience into global meta-prompts for subsequent local refinement. Extensive experiments on real-world multi-hospital EHR benchmarks demonstrate that FedEHR-Agents consistently outperforms local and federated baselines across diverse clinical prediction tasks and remains robust across different federation scales and LLM backbones. These results establish clinical modeling experience as a promising collaborative object beyond conventional parameter-centric FL and point toward federated autonomous clinical intelligence.

cs.LG↗
arXiv2026

RegionFed: Federated Learning for Personalized Query Understanding in Heterogeneous Retail Environments

Retail search systems serve diverse geographic regions with distinct query patterns, vocabularies, and product preferences, creating significant data heterogeneity that challenges both privacy-preserving training and model personalization. Federated learning offers a natural solution for privacy, but standard FL methods produce global models that sacrifice regional performance, while existing personalized FL approaches operate at the parameter level and catastrophically collapse on modern transformers (below 10\% accuracy on T5) due to tied embeddings and LayerNorm interactions. We introduce RegionFed, an \textit{architecture-robust} federated learning framework that sidesteps this failure by operating entirely at the gradient level. RegionFed uses the $\ell_2$ conflict between regional and global gradients as a unified signal that (i) diagnoses heterogeneity, (ii) routes each region to the cheapest sufficient personalization strategy, and (iii) adaptively controls personalization strength. Because it treats models as differentiable black boxes, RegionFed deploys on T5-Small, T5-3B, RoBERTa, and CNN with zero code changes, providing large gains on transformers (where parameter-level methods collapse) and consistent improvements on CNNs. Across three public datasets (Amazon ESCI, Amazon Reviews, LEAF-FEMNIST) and four architectures, RegionFed-Meta achieves 92.27\%, closing the gap to the privacy-violating centralized upper bound (Centralized + Regional Weighting: 92.04\%, $Δ$=0.23pp, within 1$σ$) while providing $(ε{\approx}0.60)$-differential privacy and $\mathcal{O}(1/\sqrt{T})$ convergence.

cs.LG↗
arXiv2026

Privacy-Enhanced Zero-Order Federated Learning via xMK-CKKS over Wireless Channels

Homomorphic encryption (HE) enables privacy-preserving aggregation in federated learning (FL) by allowing the server to operate on encrypted data without decryption. Existing HE-over-the-air (OTA) methods mainly rely on single-key HE schemes and require channel estimation or pre-equalization to compensate for wireless fading. However, single-key HE remains vulnerable to honest-but-curious (HBC) clients holding the shared secret key, while multi-key HE provides stronger client-level security by assigning each device its own secret key. We propose a four-phase protocol that enables the aggregation of xMK-CKKS over a shared wireless channel without channel estimation. The protocol retransmits partial public keys and ciphertexts through the same channel realization, so that the dominant large-modulus encryption terms cancel algebraically during decryption. We integrate this protocol with zero-order FL over slowly varying LoS-dominant channels, where each device transmits a single encrypted scalar per round and the communication/encryption overhead is independent of the model dimension. We show that the residual noise induced by encryption and wireless aggregation preserves the standard convergence rate \(O(1/\sqrt{K})\) up to a negligible noise floor, where $K$ is the number of communication rounds. The protocol assumes a non-trusted server and is secure against HBC clients, preventing any client from recovering the local updates of other participants. Numerical results on MNIST and CIFAR-10 validate the theoretical analysis.

cs.CR↗
arXiv2026

Federated Attack Campaign Detection via Contrastive Encoding of Threat Indicators in Gradient Updates

Detecting orchestrated cyberattack campaigns that span multiple organizations traditionally requires sharing sensitive telemetry and threat intelligence across institutional boundaries and country borders, a barrier that Federated Learning removes by training shared threat detectors directly on local data. We propose FedIoC, a modular framework in which clients fold locally available structured threat indicators into their gradient updates; we instantiate the client-side encoder with a supervised contrastive loss over IoC-matched flows. Within each training batch, flows that match any known indicator pattern form the positive set; the contrastive objective pulls their learned embeddings together and pushes non-IoC embeddings away, so that campaign-relevant structure is, by design, expressed in the gradient direction. Clients sharing indicators for the same attack campaign then produce aligned gradient components, which the server clusters by the cosine similarity of their updates to recover global campaign patterns without any direct IoC transmission. We evaluate FedIoC on two public threat-detection benchmarks distributed across FL clients that each observe only a fragment of every active campaign and hold disjoint indicator sets derived from their local telemetry. In this regime the FL server recovers cross-organizational campaign cohorts directly from gradient geometry. We contribute FedIoC as a modular framework for this setting, and use it to pinpoint the non-IID gradient structure as the main driver of recovery and to define the open problem of designing encoders that improve on it.

cs.LG↗