arXiv subjects

Chau Yuen

Publications and source records attributed to Chau Yuen.

At least 19 recordsLinked to original sources

arXiv2026

An Efficient SIM Beamforming Scheme Based on Physical-Empowered Projected Gradient

Stacked Intelligent Metasurfaces (SIMs) have emerged as a promising technology for next-generation wireless systems. Especially in multi-input multi-output (MIMO) systems, it has the potential to realize complicated wave-domain transformations with low hardware costs and energy consumption. However, SIM-assisted MIMO systems face two major challenges in channel estimation and beamforming. As the SIM elements do not have the signal processing capability, channel estimation can only be conducted in an indirect manner, which makes it challenging. Moreover, the precoding optimization after channel estimation is non-convex and also difficult. Targeting these issues, we exploit the time-division duplex (TDD) channel reciprocity to calculate the gradient backpropagation in an over-the-air manner. Based on this structure, we propose a gradient-based optimization framework that optimizes beamforming without explicitly estimating the SIM--UE channel. The proposed method, namely the physical projected gradient descent (P2GD) method, optimizes the achievable sum rate while incorporating zero-forcing (ZF) constraints. Based on the method of incorporating the ZF restriction, we propose two variations of P2GD, namely user equipment (UE)-P2GD and base station (BS)-P2GD. We also provide a theoretical convergence analysis and projected gradient techniques to ensure physical feasibility. Simulation results show that the proposed approach can achieve suboptimal beamforming in the multi-user system within a small number of over-the-air iterations, using a per-direction signaling budget below the pilot cost of explicit SIM--UE channel estimation. The proposed method provides a low-overhead beamforming scheme for SIM systems without explicit SIM--UE channel estimation.

eess.SP↗

arXiv2026

Share the Symbol, Not the Vector: Training-Free Fact Communication Across Language Models

Multi-agent systems allow language models to solve tasks collaboratively by sharing complementary information. These systems typically communicate through text, while recent approaches also explore exchanging internal model states. However, sharing these states across architectures often requires learned translators or assumptions about model compatibility. We introduce SYNC (Symbol-Indexed Neural Communication), a word-indexed interface that connects heterogeneous models without fine-tuning or a learned translator. From descriptions only it can see, the sender selects words from a shared list and sends their indices for each object, without seeing the questions. The receiver writes the described facts into its hidden states using its own word directions, vectors fitted once from its activations. We test selective use by swapping one attribute between two objects and requiring correct answers about both changed and unchanged attributes before and after the swap, four answers in total. We choose an early write layer on four development receivers and then fix it. With three different senders and nine newer receivers from five families, four-answer success on new scenes reaches 72.0-98.3%, up to 96 percentage points above middle-layer writing, and the two largest receivers match plain text. A task-free probe predicted in advance which depths each new receiver can use (45 of 45 cases). Without retuning, messages listing every fact keep 89.6-100% success under new layouts, and sender messages reach 23.9-64.0% on a landmark task with multi-token symbols, below text but from 0% without a message. These results show that shared word indices and receiver-local directions can support selective fact use across model families without additional training.

cs.CL↗

arXiv2026

Energy Efficiency Maximization for Integrated Sensing and Communication in IoT C-RAN

Integrated sensing and communication (ISAC) with cloud radio access networks (C-RAN) unifies two foundational technologies for the Internet of Things (IoT), enabling both high-data-rate transmission and accurate environmental awareness. This paper investigates an uplink C-RAN system where multiple remote radio units (RRUs) jointly serve user equipment devices (UEs) and sense a target. We demonstrate that only a subset of RRUs is typically needed to meet sensing requirements, while energy is potentially conserved by deactivating redundant sensing RRUs. Motivated by this, we aim to improve the system's energy efficiency (EE) by jointly optimizing RRU activation, user association, and power allocation, while ensuring localization accuracy through the Cramér-Rao lower bound (CRLB). To address this problem, we propose a model-based iterative algorithm that integrates optimal user association, decision tree-based selection of sensing RRUs, and fixed-point power allocation. This algorithm is further used to train a graph neural network (GNN) framework, ISAC-GNN, to overcome scalability and computational complexity limitations. Our theoretical analysis ensures performance guarantees, while a semi-supervised training strategy enhances stability and generalization. Simulation results demonstrate that ISAC-GNN reduces inference time by 67% relative to the model-based approach, enabling real-time implementation for ISAC system resource management. In addition, ISAC-GNN allows scalable deployment across various system scenarios without retraining the model.

eess.SP↗

arXiv2026

Many Right Answers, One Training Example: Removing Responder Noise from GRPO for LLM Recommenders

A recommendation request on Reddit draws several replies, each naming different titles. When an LLM recommender is trained on such threads with reinforcement learning (RL), which replies should a generated list be rewarded against? The state-of-the-art recipe, Rank-GRPO, picks one reply per training example, so the advantage mostly records which reply was drawn (85% of its variance) rather than how good the list is. We argue that RL should train on the request, not on each answer, and propose ReMaRk: it scores every list once against the union of all replies' titles and samples each request equally. This makes RL cheaper. On seven backbones and three datasets, ReMaRk reaches the validation recall of 2,000 per-reply RL steps in 25 to 53% of the steps and leads at that budget; trained until neither improves, it is never significantly behind Rank-GRPO and in four of seven pairs reaches Rank-GRPO's best with fewer GPU-hours. The same reward helps on ProtoQA, where about 100 people answer each question, which points to a simple rule for RL with several valid human answers: reward them jointly.

cs.CL↗

arXiv2026

ErrOPD: When Does On-Policy Distillation Transfer Teacher Errors?

A distilled student can copy its teacher's mistakes along with its skills. On-policy distillation (OPD), used in recent post-training recipes, has the teacher grade every token of the student's own outputs. Which teacher errors does it pass on? We build ErrOPD, a testbed whose teachers are fine-tuned to close a JSON list one item early, an error their students almost never make. The answer depends on the KL direction: across four model families, forward-KL OPD transmits the error within the training budget (+13-23 points), while reverse-KL OPD at our reference learning rate adds under 0.05 points. A duplicated ID and, where the decision arises, two SQL errors show the same split. The reverse-KL update scales with the student's own probability of a token, and an intervention tests this: giving reverse KL forward KL's gradient magnitude at the error decision alone makes it transmit on two model pairs. Reverse-KL OPD can delay such errors rather than block them: some runs adopt the error with longer training, and Qwen3 students that already make it, even rarely, adopt it within the budget. Because greedy evaluation on Qwen3 misses the inherited error, distilled students should also be audited on sampled outputs.

cs.LG↗

arXiv2026

Cold-Atom Rydberg Array with Spatiotemporal Multiplexing for High-Sensitivity Wireless Communications

An effective Cold-Atom Rydberg Array (CoRA) architecture is investigated, which addresses the fundamental thermal noise limit in classical electromagnetics and intrinsic Doppler broadening as well as photon shot noise in conventional hot-vapor cell-based atomic receivers. However, translating the CoRA-based quantum electrometers into practical wireless communication receivers is bottlenecked by both the macroscopic readout dead-times and nonlinear binomial population counts rather than the additive-Gaussian baseband samples in conventional receivers. To address these critical challenges and facilitate the practicality of the CoRA, in this paper, a subarray scheduling-based spatiotemporal multiplexing (STM) framework is first proposed for gap-free symbol interrogation within an admitted packet. Additionally, a signal detection scheme based on a joint binomial particle smoother (JBPS) is proposed for burst-wise state and data inference. Furthermore, the weak-signal quantum-projection-noise (QPN) limit and the state-averaged finite-alphabet rate are derived for CoRA-assisted wireless communications. Numerical results demonstrate that: 1) The proposed STM-based CoRA scheme resolves the macroscopic temporal bottleneck for continuous signal sampling; 2) The proposed JBPS approach effectively mitigates the nonlinear noise amplification to achieve a lower bit error rate; and 3) Performance analysis reveals a fundamental sensitivity-sustainability tradeoff that increasing the number of atoms effectively suppresses the QPN, but simultaneously reduces the sustainable packet repetition rate.

cs.IT↗

arXiv2026

Rydberg Atomic Quantum Receivers for OFDM Systems: An Atomic-Comb Design

Rydberg atomic quantum receivers (RAQR) exhibit exceptional sensitivity to radio-frequency (RF) signals, positioning them as promising candidates for next-generation wireless systems. Extending their capabilities to orthogonal frequency-division multiplexing (OFDM), however, requires atomic responses that go beyond broadband reception and are tailored to the structured interference of multicarrier signals. To bridge this gap, we develop an atomic-comb Rydberg receiver based on six-wave mixing (SWM) transduction. In particular, injecting a multi-tone local oscillator (LO) into the RAQR generates frequency-shifted replicas of the intrinsic SWM response. By subtly tuning the amplitude and phase of each LO tone, constructive and destructive interference can be selectively induced to preserve desired response components while attenuating harmful frequency offsets. Furthermore, we harness the response-reshaping capability of the proposed atomic comb to proactively mitigate OFDM interference. More explicitly, by exploiting the discrete difference-frequency structure of both carrier-frequency-offset (CFO)-induced and phase-noise (PN)-induced inter-carrier interference (ICI), we optimize the atomic-comb response to suppress dominant ICI components directly. We further reveal an intrinsic coupling between spectral shaping and the time-domain effective channel memory, motivating a joint optimization of both ICI and inter-symbol interference (ISI), which simultaneously suppresses inter-carrier leakage and post-cyclic-prefix (CP) tail energy. Extensive simulation results validate our atomic-comb design, unveiling that the proposed atomic comb can effectively reshape the receiver response over the OFDM, while mitigating ICI, shortening the effective channel memory, and substantially lowering CP overhead.

cs.IT↗

arXiv2026

Distributed Relative Localization Based on Ultra-WideBand and LiDAR for Multi-robot with Limited Communication

Relative localization is crucial for a multi-robot system to collaboratively perform tasks, such as exploration and formation. However, this is highly challenging for homogeneous robots with similar appearance in GPS-denied and communication-limited environments. In this paper, we propose a fully distributed relative position estimation approach for a team of robots based on onboard UWB and LiDAR sensors, in which LiDAR is utilized to obtain the position of anonymous objects in Line-of-Sight (LOS), and UWB is used for ranging between robots. We construct two graphs, namely UWB connection graph and LiDAR connection graph, to represent the spatial relationship among objects (robots and obstacles) based on UWB and LiDAR measurements. Identification and relative position estimation are formulated as a common subgraph matching problem. A falsely-matched robot identification approach is designed to recognize the falsely-matched results caused by obstacle blockage in LiDAR field of view. These robots are then localized by leveraging the well-matched robots and the UWB ranging measurements in the UWB connection graph. We conducted experiments to evaluate the performance of our approach. The results show that the proposed approach is capable of achieving satisfactory positioning accuracy for a team of robots in a distributed manner with only exchanging limited information.

cs.RO↗

arXiv2026

Distributed Relative Localization for Homogeneous Multi-Robot Systems through UWB Ranging and Limited Communications

Accurate and reliable relative localization is crucial for multi-robot applications like exploration, search, and rescue missions. LiDAR-based solutions offer high accuracy in localizing surrounding objects; however, distinguishing homogeneous robots with similar appearances remains challenging due to the lack of distinctive identification features. In this paper, we propose a fully distributed relative pose estimation approach by integrating LiDAR, UWB, and odometry measurements, allowing each robot to accurately and continuously localize its teammates without external infrastructure. Specifically, potential anonymous teammate robot clusters from LiDAR scans are tracked by a dynamic tracker. We then identify teammate robots from these tracked anonymous clusters using a joint matching strategy, ensuring reliable data association between robots and clusters. Finally, by combining the corresponding LiDAR observations, UWB ranging, and odometry measurements, each robot precisely localizes others while minimizing data exchange. The system requires only odometry data exchange through onboard UWB, eliminating the need for additional communication infrastructure like WiFi routers or mesh networks. Extensive simulation and real-world experiments demonstrate the effectiveness and reliability of the proposed relative localization approach.

cs.RO↗

arXiv2026

Event-Native Immersive Communication for 6G: From Multimodal Streams to Event Beliefs

The development of multimodal sensing capabilities is crucial for realizing immersive communications and enabling rich, natural remote interactions in future sixth-generation~(6G) communications. However, transmitting high-dimensional sensory streams places substantial pressure on wireless resources and leaves a fundamental question unresolved: what information about the underlying physical process should be preserved across wireless delivery? To address this issue, we establish an event-native immersive-communication framework in which a service-relevant physical event defines the communication object, while event beliefs represent the information available to transceiver agents before and after wireless delivery. Based on this event-native framework, we further propose event-belief deficiency (EBD) to evaluate quality of experience (QoE) in immersive communications, which differs from the conventional normalized mean-squared error (NMSE), as NMSE can be insensitive to physically distinct procedures whose stream distortions lie in a similar range. For Gaussian event beliefs with mode-separable delivery over Rayleigh fading, we derive the log-det EBD, its induced received signal-to-noise ratio (SNR) threshold, the exact outage probability, and the required transmit SNR. Simulation results with a physics-driven source show that stream NMSE can remain nearly unchanged across physically distinct event procedures, whereas log-det EBD reliably reflects their event-level uncertainty. Relative to a mean-squared-error (MSE)-oriented interface, event-native delivery reduces normalized log-det EBD by up to $63.6\%$ and lowers the required average received SNR by $3.47$~dB under the evaluated outage constraint, substantiating the effectiveness of the proposed framework.

cs.IT↗

arXiv2026

Rydberg Atomic Quantum Receivers for Wireless Communications: Two-Color vs. Three-Color Excitation

An efficient three-color (3C) laser excitation-based Rydberg atomic quantum receiver (RAQR) architecture is investigated for wireless communications, utilizing a five-level (5L) electronic transition mechanism. Specifically, the conventional two-color (2C) RAQR with the four-level (4L) excitation faces three fundamental obstacles: 1) high cost and engineering challenges due to the reliance on unstable short-wavelength lasers; 2) a fundamental sensitivity limit in thermal atoms caused by residual Doppler broadening; and 3) the inability to detect low-frequency bands due to the energy-level constraint of two-photon resonance. To address these challenges, this paper analyzes a 3C5L-RAQR architecture with all-red/infrared lasers, which not only solves the engineering cost issues but also enables effective Doppler cancellation and low-frequency detection by exploiting the three-photon resonance. Bridging atomic physics and communication theory, an end-to-end equivalent baseband signal model is derived. Furthermore, the performance of different RAQR architectures is evaluated in terms of sensitivity, achievable rate and spectrum access range. Moreover, we provide an exact numerical solution for practical RAQRs by employing the Liouvillian superoperator formalism. Numerical results demonstrate that the exhibited 3C5L-RAQR achieves superior sensitivity compared to the conventional 2C4L-RAQR and a classical antenna-based radio frequency receiver for weak-signal detection. Finally, the inherent sensitivity-rate trade-off is revealed, showing that the 3C5L-RAQR is more suitable for deployment in power-limited communication scenarios demanding broad spectrum access.

cs.IT↗

arXiv2026

WirelessMathBench-XL: An Auditable Benchmark for Wireless Mathematical Reasoning

Technical-domain benchmarks constructed from arXiv papers can overlap the same public text used in LLM pretraining. Auditing this risk at training-corpus scale requires searching billions of corpus n-grams while retaining per-item evidence that users can inspect and recompute. We contribute a reverse-probe audit at a fixed 13-gram threshold: it indexes benchmark prompts, streams public pretraining corpora, and emits per-problem prompt-surface lexical-overlap metadata with memory that scales with the benchmark. We instantiate the protocol in WirelessMathBench-XL, a 4,027-problem wireless mathematical-reasoning benchmark built from 836 retained arXiv papers across 20 subfields. Against 12.9B streamed 13-grams from RedPajama-arXiv, the audit identifies a strict zero-hit view S0 covering 3,853 problems (95.7%). Filtering to S0 changes accuracy by less than 1 pp for every evaluated model; frontier calibration rows form one high-accuracy cluster between 86.5% and 91.3%, not a resolved rank order. Only 30/800 test items carry detected overlap. Under an all-flagged-correct counterfactual, their largest possible positive score inflation is 0.31-0.51 pp for the frontier rows, so full-versus-S0 is a bounded, structurally underpowered stability summary rather than a contamination-effect test or cleanliness claim. The audit channel does not cover paraphrase, target-answer, post-training, or closed-corpus exposure. The release includes source-paper identifiers, verifier-facing ground truths, audit and threshold metadata, filtered views, a paper-disjoint sensitivity view, evaluation traces, paired-bootstrap scripts, training recipes, Croissant metadata, and a Datasheet for Datasets.

cs.LG↗

arXiv2026

Stacked Intelligent Metasurface-Diffractive Deep Neural Networks for Onboard Terrain Classification from SAR Level-0 Raw Data

Real-time terrain classification directly from Level-0 raw Synthetic Aperture Radar (SAR) data remains restricted by traditional digital-centric paradigms, where the processing of noisy, high-dimensional patches is hindered by computationally intensive processors and significant downlink latency. To address these fundamental limitations, this work establishes a new research paradigm for autonomous on-board sensing by proposing a Stacked Intelligent Metasurface-Diffractive Deep Neural Network (SIM-D$^2$NN). This architecture leverages the physical wave-propagation medium to offload inference tasks from digital processors to a physical device. By executing in-wave feature mapping, the SIM-D$^2$NN facilitates a move toward an integrated `compute-while-transmitting' framework, providing an alternative to the traditional `digitize-then-process' sequence. The multi-layer metasurface is positioned at the forefront of the satellite communication module. The initial layer modulates the raw SAR data through both amplitude and phase adjustments, where a 90$^\circ$ phase rotation is introduced as a lightweight but effective augmentation strategy to enhance robustness against noise and Doppler distortions. Subsequent layers learn variable phase shifts, enabling advanced feature mapping for the classification task. The classification results at the terrestrial station can be directly obtained based on the signal amplitude received at each antenna. This design reduces reliance on downlink bandwidth and high-power terrestrial computing, achieving performance around 90% in the binary task directly from real raw SAR data in terms of accuracy, precision, recall, and F1 Score. Therefore, our method helps bridge the gap between next-generation remote sensing tasks and in-orbit processing needs, paving the way for computationally efficient remote sensing applications.

eess.SP↗

arXiv2026

Measuring Collapse and Correction in Homogeneous-Panel LLM Debate

Multi-agent large language model (LLM) debate is often evaluated by whether final answers improve, but movement is not necessarily improvement: the same discussion can rescue an initially wrong majority or destroy an initially correct one. Standard final-accuracy evaluations conflate these opposing mechanisms. We introduce an auditable protocol for homogeneous debate on multiple-choice questions (MCQs) that records each run as a transition ledger over collapse, correction, onset, and signed intervention utility. On 6,925 MMLU-Pro debates, the protocol identifies 253 collapses and a parallel correction ledger that changes how interventions should be judged. Replay experiments reveal the central tradeoff: a leave-one-model-out probe-gated freeze prevents 29 collapses but loses 108 corrections under equal weights, so collapse prevention alone can recommend the wrong policy. A compact pre-debate 8-probe screen is a triage signal: its unadjusted family-level association with conditional-collapse risk is high (G=7, Spearman rho=0.893, exact two-sided p=0.0123), but initial-majority accuracy is a close comparator (rho=0.821; family partial rho=0.767, p=0.0877), so we do not treat it as calibrated or capability-adjusted prediction. Round-level traces localize many collapses to the first debate round, where early disagreement can precede both harmful cascades and useful recovery. We release replayable schemas, coders, audits, cost cards, and zero-API rebuild scripts so future model-scaffold rows can be compared under the same denominators and signed utility ledger.

cs.CL↗

arXiv2026

Beyond Teacher Assignment: Domain-Normalized Multi-Teacher On-Policy Distillation

Reinforcement learning can turn one language model into several specialists, each excellent at a single skill such as mathematics, coding or following instructions, but users need one model with all of these skills. Multi-teacher on-policy distillation (MOPD) merges them by letting the specialists teach one student: the student answers each prompt, and the specialist for that prompt's domain gives feedback on every token. This routing decides which specialist teaches, but not how strongly its feedback moves the shared student. In Qwen3.5 models at three sizes, we find that MOPD's student does not beat one taught by the best single specialist and gains little of the mathematics specialist's advantage. The feedback is unbalanced: instruction-following feedback is several times more spread out than mathematics feedback and dominates the student's updates. We propose Domain-Normalized MOPD (DN-MOPD), which keeps the routing and rescales each domain's feedback by its measured spread. On six public benchmarks, DN-MOPD improves the average score over MOPD at every size, across three random seeds and under two answer-length limits, and recovers most of the lost mathematics gain. Controls with fixed domain weights show that the gain comes mainly from turning down instruction-following feedback rather than turning up mathematics alone, and that fixed weights close to those DN-MOPD measures perform comparably. Combining specialists therefore requires deciding not only which one teaches, but also how strongly its feedback counts.

cs.LG↗

arXiv2026

CoCurve: Cross-Module Co-Pruning Curvature for Structured LLM Pruning

Resource-constrained deployment requires sustaining large language model (LLM) capabilities as models scale under fixed memory and computation budgets. Structured pruning advances this deployment frontier with smaller dense checkpoints, yet deciding what to prune remains bottlenecked by interactions among joint removals. We introduce Cross-Module Co-Pruning Curvature (CoCurve), which formulates structured pruning as set-dependent predictive risk over a unified inventory of attention heads and feed-forward groups. A co-pruning graph built from single-unit forward ablations assigns individual risk to nodes and reinforcement or cancellation to interaction edges, conditioning each decision on the units already removed. We evaluate 6 LLMs (3B--70B) and 3 vision--language models (VLMs) across 3 perplexity corpora, 12 language tasks, and 7 multimodal benchmarks. Across the five-model 20--40% grid and the 70B 10--50% sweep, CoCurve ranks first in 53/60 corpus comparisons (15/15 at 70B); matched-quality interpolation permits 2.2--6.6 more pruning points in 9/10 cases, while CoCurve leads all 6 VLM Avg$_7$ blocks. After the same lightweight recovery, its retained structures remain strongest through 50% pruning, where the 8B checkpoint regains 10.8 Avg$_{12}$ points; physical slicing delivers $1.58\times$ dense prefill throughput with 41% lower peak memory. Mechanism analysis across 10 LLMs and 7 VLMs finds organized within- and cross-module edge structure; matched low-saliency, high-coupling removals degrade 19/20 capability groups by up to 23.7 points.

cs.LG↗

arXiv2026

State of Thought Enables Endogenous Reasoning

Test-time compute has emerged as a major approach to improving the capabilities of Large Language Models (LLMs). However, existing test-time reasoning paradigms rely heavily on externally imposed control, either through fixed reasoning programs or through costly expansion in constrained search spaces, limiting both generalization and efficiency. We propose State of Thought (SoT), a new reasoning paradigm that enables endogenous reasoning in LLMs, with the model's internal reasoning state governing how reasoning unfolds. Concretely, SoT extracts a compact dynamics-geometric state from the model's internal information transfer and uses a 582-parameter controller on frozen backbones to selectively activate historical reasoning support useful under the current reasoning state, framing reasoning as a state-conditioned process over evidence rather than an externally prescribed token chain. Across quantitative (1.34x), general (1.62x), symbolic-and-code (1.76x), and long-context (2.51x) reasoning on 3 LLMs and 16 datasets, SoT consistently improves mean-baseline accuracy while reducing generated tokens by 62.6% and end-to-end latency by 44.6%. Across 2 VLM scales and 3 reasoning tasks, it improves mean accuracy by 3.8 points over reasoning baselines, with 74.9% fewer completion tokens and 73.5% lower latency than search-based methods. Under constrained access, SoT retains 38.2%/36.5% mean accuracy gains in training-free/embedding-only settings, while trajectory-only judging reaches 84.1% agreement across 3 API models. Together, endogenous state-driven reasoning provides a generalizable and efficient alternative.

cs.CL↗

arXiv2026

Conditional Co-Ablation: Recovering Self-Repair Backups in Transformer Circuits

Mechanistic interpretability seeks to explain transformer behavior through circuits: sets of internal components that causally support a behavior. However, self-repair creates a blind spot: ablating a primary component can activate a dormant backup, so a circuit that explains behavior in the intact model can become incomplete under the intervention used to test it. We formulate this gap as conditional circuit completion: given a primary set, identify components that become causally important after its removal. We introduce conditional co-ablation (CoAx), which ranks candidates by growth in ablation effect after primary-set removal. We show that a perfectly dormant backup can be indistinguishable from an irrelevant component to per-unit intact-state scores, whereas its conditional effect change exactly aggregates all interaction orders linking it to the removed set. On GPT-2-small's Indirect Object Identification (IOI) circuit, CoAx recovers the documented backup heads at 0.941 ROC-AUC, versus 0.815 for the strongest intact-state attribution baseline and 0.758 for the matched conditional-energy control. Recovery drops to 0.40 +/- 0.13 AUC for alternative component sets matched in behavioral effect, output displacement, and depth, showing that recovery is specific to the removed circuit. Beyond recovery, the CoAx-selected heads are causally load-bearing: freezing them after primary removal sharply reduces the IOI margin, while adding them to the incomplete circuit reduces incompleteness from 0.75 to 0.21. More broadly, conditional growth aligns with intervention-derived repair in 11/12 held-out instances across 4 mechanism clusters, and CoAx completions outperform matched random completions on all 8 non-GPT-2 models spanning 6 architecture families. Together, causal explanations of self-repairing transformers must account for backup circuitry when primary components fail.

cs.LG↗