Error Correction

Can an attacker turn influence over an artificial intelligence (AI) adviser into a harmful quantum error-correction update? We identify an ambiguity in passive syndrome records that obstructs recovery selection, then show how additional calibration measurements support certified recovery updates under uncertainty and drift. In an odd-distance square toric code with error-free preparation, syndrome measurements, and recovery operations, opposite coherent $X$ rotations produce identical passive syndrome-history distributions. Yet a fixed phase correction can help at one sign and harm at the other. A terminal logical measurement on known encoded calibration states supplies the missing sign information. A separate evaluator accepts an update only when calibration uncertainty and a justified drift bound certify improvement over the current recovery, without assuming that the adviser recommends correctly. In simulated advice attacks, calibration-confidence checks reject harmful proposals while retaining beneficial updates under honest advice. We derive sufficient limits on calibration age that require improvement through deployment. In matched simulations, a validated channel-specific bound retains more beneficial updates than the general bound after accounting for evaluation time, while preventing the tested harmful activations under the stated drift assumption. A separate surface-code experiment includes stochastic circuit faults and noise changing during acquisition. Deterministic controllers achieve at least as many beneficial updates with the same observations. Violating the drift assumption permits harmful acceptance in the toric experiment. The results identify information required for recovery selection, establish conditional guarantees against harmful updates, and quantify the recovery improvements forgone through conservative acceptance.

We study a practical question: can a small correction module fix errors in a frozen language model's outputs without degrading its base capabilities? We propose CRN v2, a lightweight logit-level correction module (~34M trainable parameters, 0.73% of the 4.65B text module) that sits atop a fully frozen Gemma 4 E2B model. The base model is never updated; only the correction module learns, via supervised fine-tuning followed by reference-free DPO on 83,400 error-correction pairs. On a 60-question domain exam (CEHRI: Certified Human-Robot Intelligence, covering facts, arithmetic, and implicit-goal reasoning), CRN v2 corrects 53.3% of base-model errors (reworded variant: 43.3%) while showing no degradation on tested capability benchmarks (MMLU/BoolQ N=200; car-wash N=8). A LoRA baseline at the matched CRN v1 budget (6.6M params, rank 19) achieves 83.3% correction but suffers 30-75% capability loss on the same benchmarks -- the correction-capability tradeoff. An ablation shows that the KL preservation term (lambda=0.1) is critical: lowering it to 0.01 degrades correction to 35.0%. A hidden-state injection variant at earlier layers (1.6M params, SFT-only) reaches 50.0%/55.8% but does not exceed logit correction; shallower injection (layer 4) drops to 30.0%/28.3%; multi-depth logit correction (~35M) reaches only 40%; and longer training (5,000 SFT + 2,000 DPO) stays at 53.3% -- none of the alternative configurations we tested exceeded the rank-128 logit result, consistent with a best-achieved result of ~53% rather than a floor. This is a study of a design principle (frozen base + logit correction + KL anchoring), not a claim of architectural novelty. All code, main-result weights, and evaluation scripts are released (deep variant as code only -- no trained deep checkpoints).

A key subtask of quantum error correction is to extract a syndrome that, if nontrivial, signals an error. The number of possible ways to extract a syndrome grows exponentially with the syndrome size, and these implementations vary greatly in fault tolerance, as measured by their logical error rates. This creates a natural search problem: find an implementation with a low logical error rate. Previous work solves this problem but sacrifices either solution quality or scalability. In this paper, we use reinforcement learning and importance sampling to outperform previous work at all scales. Compared with the state of the art automatic scheduling tools AlphaSyndrome and PropHunt, our tool reduces the logical error rate by 25.9% and 71.7% on average, respectively, culminating with a reduction of 97.8% for a surface code with distance 15.

We present a machine-checked Lean~4 formalization of Dong and Yang's classification of optimal finite-length $(n,4)$ binary block codes for binary symmetric channels. The formalization was developed mainly by feeding the paper's proofs to an AI tool. To establish correctness, the authors verified the main theorem statements in Lean and the accepted axioms. This note discusses the corrections and simplifications made to the AI-generated formalization, and records discrepancies found in the paper during the formalization. The Lean code is available at https://github.com/shhyang/n4code_lean.

Federated learning shares model updates rather than raw data, yet these updates can be inverted to reconstruct the clients' training data. Analytic reconstruction attacks, which invert a gradient in closed form, degrade as the batch grows: prior single-round attacks recover only about half of a batch of size $100$ even when the attacker fully controls the network parameters, and known upper bounds limit what any such method can recover. We establish a connection between gradient inversion and the theory of erasure-correcting codes, and use it to construct attacks that exceed these bounds. Our attacks recover batches exactly, together with every sample's label, from a single FedSGD round, and certify each recovery without ground-truth data. On eight image and tabular benchmarks they outperform prior single-round attacks by a wide margin. Even a passive attacker who only observes an honestly trained network recovers $94$--$100\%$ of ImageNet batches at sizes up to $128$, more than prior single-round attacks achieve even with active manipulation of the model, and in the active setting more than $90\%$ is recovered at batch sizes of several hundred. These results show that the privacy leakage of federated learning has been underestimated.

Automatic Speech Recognition (ASR) technology is fundamental to customer service automation and large-scale transcription. However, even advanced ASR models exhibit inevitable errors in complex real-world environments such as call center conversations. When privacy restrictions preclude audio access, error correction must rely on text-based post-editing. Existing text-only approaches face significant challenges in low-resource languages, mainly due to a critical scarcity of annotated corpora and tailored correction methodologies. For Korean, this resource gap is particularly pronounced, as existing resources are predominantly designed for ASR training rather than text-based error correction. To address this, we introduce DasanCallDial, the first large-scale Korean benchmark dataset specifically curated for dialogue-level ASR error correction. Derived from genuine call center interactions, it comprises 1,974 dialogues with 115,460 utterances. Leveraging this resource, we propose Detector-Gated Contextual Span Correction (DCSC), a text-only post-editing framework for error-sparse Korean speech recognition transcripts. DCSC combines an encoder-based detector that first performs token-level error detection, followed by a language model-based corrector trained to rectify fine-grained span-level errors. Additionally, we employ dialogue-level context augmentation to enable the model to leverage discourse history for disambiguation. By employing multi-level granularity, our method achieves state-of-the-art performance, effectively overcoming the limitations of general LLMs in low-resource settings.

Feedback-based coding schemes have demonstrated substantial performance gains over today's open-loop coding schemes. Unfortunately, these gains are usually achieved in idealized settings with perfect feedback. Over the last few years, machine learning-based schemes have been shown to be promising solutions for implementing feedback-based codes, particularly when combined with short-block-length open-loop error correcting codes (ECCs) in a concatenated coding structure. However, existing ML-based feedback schemes remain agnostic to the outer code's structure, potentially misallocating feedback resources on error patterns already correctable by the outer ECC. To address this, we propose MaskCode, a Transformer-based inner feedback code for concatenated coding systems, which explicitly incorporates structural knowledge of the outer linear block code into the inner feedback encoder design via two synergistic mechanisms: 1) a soft syndrome-based input that informs the encoder about potential parity constraint violations, and 2) a code-aware attention mask derived from the Tanner graph. We further show that end-to-end training with a differentiable belief propagation (BP) decoder offers no additional gain, as MaskCode's structure-aware design already internalizes the structural knowledge of the outer code; in fact, backpropagation through the iterative BP decoder introduces gradient explosion, which degrades rather than improves performance. Extensive evaluations on BCH and LDPC outer codes demonstrate that MaskCode consistently outperforms all baselines, achieving up to 1.5 dB SNR gain.

The exact Shannon capacity is unknown for every odd cycle beyond the five-cycle $C_5$, making odd cycles a central open problem in zero-error information theory. Improving the known lower bounds requires constructing large independent sets in strong powers of these graphs. Recent AI-assisted work has produced a rapid sequence of improvements: building on the construction of Itty et al., Gao developed a recursive product construction for combining structured independent sets, and Buys, Polak, and Zuiddam (BPZ) subsequently strengthened this through a richer recursion framework. We continue this line of AI-assisted exploration and introduce a heterogeneous refinement of these constructions. The central observation is that the usefulness of an intermediate construction depends not only on the size of its current main independent set, but also on the auxiliary structure it carries into subsequent recursion. Consequently, different parts of that auxiliary structure need not use the same independent set, and different occurrences in a recursion need not use the same intermediate representation. We formalize this for Gao's binary product and derive explicit propagation rules showing how heterogeneous choices strengthen the resulting gadget while leaving its current code size unchanged, then extend the principle to the more general BPZ framework, tailoring constructions to the distinct roles they play within the recursion. Applying these refinements to the seven-cycle $C_7$, we obtain an independent set in $C_7^{\boxtimes 500}$ yielding $Θ(C_7)\ge 3.25883262\ldots$, improving the best known lower bound. Beyond the numerical gain, the results illustrate a general principle for recursive zero-error constructions: intermediate structures with the same dimension and current code size can have different downstream value depending on where and how they are used in the recursion.

Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution. We introduce RECAST (Recurrent Error Correction And Super-resolution of coarse-grid Trajectories), a machine-learning framework designed to restore this lost accuracy while retaining coarse-grid evolution. RECAST combines learned correction within the numerical time-stepping loop with reconstruction of the corresponding fine-grid state from the corrected coarse history. We evaluate the framework on six one-dimensional PDE systems spanning transport, diffusion, dispersion, reaction, and wave dynamics, using spatial grids coarsened by factors of 8-16 and 1000-step closed-loop rollouts from unseen initial conditions. Across the test cases, RECAST remains closely aligned with the fine-grid reference solutions and reduces time-averaged relative error by approximately 50-92% compared with the corresponding uncorrected coarse-grid solvers. Additional tests show generalization to unseen PDE parameter values, while comparison with a contemporary coarse-correction architecture shows that RECAST achieves lower error and better long-horizon agreement with the fine-grid reference over 5000-step rollouts. These results demonstrate that the learned correction and reconstruction capabilities of RECAST can enable substantially coarser PDE evolution without the corresponding loss of solution fidelity, providing a proof-of-concept route toward machine-learning acceleration of higher-dimensional numerical simulations across science and engineering.

Multimodal LLMs that recognise events reliably still fail to say when they happen. Prompted for timestamps, strong VLMs reach as little as $3.8\%$ R@0.5 on Charades-STA, and $77$ to $80\%$ of their wrong predictions carry low output entropy: the models are confidently wrong, and entropy-based error detection stays below a random classifier. We show that this failure lives in the task interface, not in perception. Holding the weights fixed, replacing timestamp regression with a coarse-to-fine scan of binary questions, whose first-token probabilities are consumed only as a ranking, raises R@0.5 by $28$ to $50$ points across four frozen backbones. The residual failures decompose into two measurable axes: a perception axis that moves with the backbone, and a geometry axis that is analytically predictable from the ratio of the output-window and event widths. FV-Action, the training-free method built on this analysis, reaches $56.8\%$ R@0.5 on Charades-STA, above the same backbone's native grounding pipeline and the strongest training-free result on this benchmark; it surpasses every TVG-trained model evaluated zero-shot on TACoS, and improves over direct prediction on ActivityNet Captions and QVHighlights, with no temporal supervision at any stage.

Quantum error correction protects logical information only when every physical operation remains below the fault-tolerance threshold, a condition that must be maintained continuously rather than only at the initial calibration. In practice, however, analog control parameters inevitably drift because of environmental fluctuations. As future fault-tolerant quantum computations are expected to run for days or even months, interrupting computation for repeated recalibration becomes fundamentally impractical. A promising alternative is to integrate calibration directly into computation by repurposing syndrome measurements as a calibration signal (Sivak et al, Nature 2026), but whether such self-calibration can be achieved with provable efficiency remains an open question. Here we establish a theoretical framework for self-calibrating quantum fault tolerance. We prove that, for a broad class of control-induced errors, the detection rate defines a locally strongly convex surrogate objective for analog calibration with high probability. This geometric property enables efficient online optimization using only syndrome measurements collected during normal error correction. We prove convergence to an $\varepsilon$ detection rate within $O(1/\varepsilon^2)$ epochs for time-independent drifts and also establish guarantees for time-dependent drifts. We further show that the convergence rate is independent of the code distance for quantum low-density parity-check (LDPC) codes. Pulse-level simulations of neutral-atom arrays and large-scale circuit-level Clifford simulations confirm these theoretical predictions. Our results establish self-calibrating fault tolerance as a provably efficient paradigm in which the same syndrome measurements simultaneously protect logical information and stabilize the underlying hardware.

Diffusion models have revolutionized generative tasks but incur high latency due to iterative denoising. While cache-based strategies accelerate inference by reusing intermediate features, they largely rely on static, sample-agnostic schedules. We argue that this rigidity overlooks two facts empirically validated in this paper: (i) generation difficulty varies across prompts, requiring adaptive resource allocation--complex inputs demand more computation while simpler ones require less; (ii) error sensitivity fluctuates across timesteps, where static policies may cache high-error steps or waste computation on low-error ones. We therefore propose OnlineCache, a dynamic caching framework that jointly learns when to cache and how to correct approximation errors. We leverage policy gradient to train a lightweight network for adaptive speed-quality trade-offs, and incorporate a learnable corrector to mitigate caching-induced errors. Both modules are jointly optimized under a bilevel optimization framework, with the policy targeting global generation quality and the corrector minimizing local errors. Our method automatically allocates computational resources across both samples and timesteps, improving overall generation quality. Extensive experiments demonstrate clear superiority. On FLUX.1-dev model, OnlineCache achieves nearly 3 speedup while preserving generation fidelity. On DiT and CogVideoX, it similarly delivers competitive acceleration without compromising quality; across all scenarios, it consistently outperforms existing cache-based acceleration baselines.

Fault-tolerant quantum computing (FTQC) relies on quantum error correction to suppress physical errors and preserve logical information at scale. In practice, however, performance is constrained not only by physical noise but also by the latency of classical decoders processing rapidly generated syndrome data. This challenge is exacerbated by hardware noise that is strong, heterogeneous, and nonstationary, as well as by the simulation-to-hardware distribution shift that can substantially degrade fixed neural decoders. We present QAdapt, a noise-adaptive neural pre-decoding framework for surface-code quantum error correction. QAdapt captures local spatiotemporal correlations in syndrome data, sequentially adapts to evolving noise conditions while mitigating catastrophic forgetting, and forwards the residual syndrome to a conventional global decoder. Across 110 synthetic out-of-distribution noise configurations for rotated surface-code memory circuits, QAdapt consistently reduces the logical error rate relative to the neural pre-decoding baseline. On Google's Willow benchmark data, without target-domain fine-tuning, it achieves reductions of up to 5.79 percent in logical error rate and 9.32 percent in backend decoding latency on the residual syndrome. These results demonstrate that QAdapt provides a practical and decoder-compatible approach to improving the robustness and backend decoding efficiency of quantum error correction under evolving hardware noise.

We present Voice Memory, a inference-only scheme for agentic speech recognition: at stream time, a frozen corrector reads a single per-domain memory.md and decides per utterance whether to act on the hypothesis or abstain and keep the 1-best. Asynchronously, a score-gated optimizer revises that file through bounded edits, accepting an edit only when it strictly improves a held-out score. Extended from classical ASR-LM framework, we refer this split the listener-thinker architecture; the two roles are coupled only through the memory, so no weights change and the learned skill stays auditable and portable. Restraint turns out to be the operative skill this loop discovers: unconstrained generative error correction (GER) over-corrects, breaking correct tokens on up to 64% of its edits on financial news, and Voice Memory, reduces this rate to 35%. Across ten HyPoradise domains with an open corrector, Voice Memory, lowers weighted word error rate from 8.36% to 7.52% (7.47% with three added in-context examples) without regressing any dataset below its 1-best baseline; gains concentrate where recoverable headroom is largest, including air-travel commands (8.40% to 3.40%) and noisy far-field speech (CHiME-4, 12.69% to 10.46%). The memory transfers across corrector families and adds zero parameters to the inference path. A demo and example code are provided for future studies.

Quantum error correction (QEC) is indispensable for scalable fault-tolerant quantum computing. However, discovering QEC codes that remain effective is challenging, as logical performance depends on the interplay between code structure, hardware, syndrome extraction, and decoding, which often impose competing requirements. Here we introduce OmniQEC, an efficient AI scientist for discovering QEC codes suited to deployment on modern quantum processors. OmniQEC formulates QEC design as an iterative discovery process in which an orchestrator, implemented by advanced large language models (LLMs), coordinates code generation, code-level screening, syndrome-extraction synthesis, and decoder-based circuit evaluation. At its core, OmniQEC combines a self-evolving reasoning mechanism with a slow--fast synergistic workflow: a fast loop explores candidates using inexpensive code-level proxies, whereas a slow loop performs physically grounded circuit-level evaluation and feeds the resulting evidence back into the search. We evaluate OmniQEC across four qLDPC construction families, three LLM backends, and $14$ total-physical-qubit budgets per backend. The discovered codes show steadily improving logical-error suppression with increasing physical-qubit budgets and outperform the BB codes with $[\![72,12,6]\!]$ and $[\![144,12,12]\!]$ under complete-implementation budgets of 98 and 240 physical qubits, respectively. The discovered codes are hardware-friendly and may be of independent interest for practical QEC implementation. These findings pave the way towards LLM-assisted QEC discovery grounded in physically informed code--circuit--decoder co-design.

Quantum error correction can be enhanced by post-selecting out runs that are likely to produce a logical failure, but the most accurate measures for that require costly decoder-level information. We introduce a practical, decoder-agnostic post-selection method that learns directly from syndrome data. The method trains a supervised classifier to distinguish between syndromes from low- and high-noise regimes, and then uses the classifier's output as an abort score for new runs, without requiring logical-error labels, correction operators, or code-specific likelihood calculations. We validate the approach in three complementary settings: circuit-level simulations of the Gross bivariate-bicycle code, code-capacity simulations of the surface code, and experimental logical magic-state distillation data from the QuEra neutral-atom processor. In the Gross and surface codes, learned syndrome post-selection reduces the conditional logical error rate at a fixed acceptance rate, with performance comparable to syndrome-weight filtering. For the surface code, the learned classifier reveals a post-selection transition distinct from the conventional decoding threshold. In the experimental data, the machine-learning score outperforms syndrome-weight post-selection and, when combined with logical-gap filtering, improves the output fidelity beyond using the logical gap alone. These results show that syndrome-only learning provides a scalable and hardware-compatible route to improving the reliability of quantum error correction.

Fringe Projection Profilometry (FPP) systems using miniaturized DOE pro-jectors often suffer from severe phase artifacts due to nonlinear projection characteristics and limited pattern controllability. We propose a ray-based phase error correction framework that models phase artifacts along projection rays from the projector pinhole, incorporating projector geometry without re-lying on image-domain processing or neighboring pixels. A projector pinhole estimation method based on a single-directional hyperbolic fringe pattern is introduced, through which projector geometry can be recovered without stereo calibration. In addition, a data-efficient strategy constructs the re-finement model from a single calibration pose. Experiments on miniaturized DOE projector-based FPP systems demonstrate significant improvements in reconstruction accuracy under nonlinear projection conditions, confirming the robustness and physical consistency of the proposed approach.

Large Language Model (LLM) agents have shown remarkable capabilities in autonomous decision-making by generating sequential trajectories of states, actions, and observations. However, in complex, long-horizon tasks, these agents frequently suffer from compounding errors and struggle to recover from failures. Existing self-correction mechanisms rely on prompt-based reflection, which is inherently brittle, incurs heavy time and API costs due to iterative trial-and-error loops, and produces task-specific memory that may be hard to generalize to new scenarios. To address this, we propose Experience Memory Graph (EMG), a framework that reformulates agent failure recovery as a graph matching problem. At training time, we convert both failed exploration trajectories and successful expert trajectories into directed action decision graphs. By matching these graphs, we extract common subgraphs (successful workflows) and graph edit paths that explicitly indicate how to correct failures (e.g., which actions to add, delete, or relabel under a given observation), and store them in a memory graph with intra-task nodes and cross-task edges. At test time, EMG retrieves relevant insights and guides the agent in a single, loop-free execution. Experiments on ALFWorld and ScienceWorld show that EMG consistently outperforms state-of-the-art reflection baselines in success rate and average reward, while requiring no test-time trial-and-error.

We propose a unified meta-decoding framework for quantum error correction that learns syndrome-to-recovery mappings across multiple stabilizer codes and noise settings, without requiring separate decoders for each configuration. The benchmark includes FiveQubit, Steane, Planar3x3, and Planar5x5 codes, four noise families, and five evaluation regimes: interpolation, unseen-p transfer, unseen-noise transfer, few-shot unseen-code adaptation, and few-shot held-out-size adaptation. We compare a classical Meta-MLP teacher-trained baseline with variational quantum circuit (VQC) meta-decoders selected through hardware-aware quantum architecture search over qubit count, circuit depth, and entangling topology. The Meta-MLP achieves teacher-label accuracies of 0.9993, 0.9118, 0.9342, 0.6304, and 0.7548 across the five regimes, while the hardware-aware VQC achieves 0.9400, 0.8495, 0.8415, 0.5678, and 0.7143. However, logical-level evaluation shows that high teacher-label accuracy alone is insufficient in the most challenging Planar5x5 setting. During interpolation, the raw logical-failure ratios relative to the teacher are 12.08 and 25.91 for the Meta-MLP and VQC, respectively, whereas confidence-gated fallback reduces them to 1.71 and 1.11. These results support confidence-aware selective recovery rather than unconditional teacher replacement.

Attributing code to the large language model that produced it is essential for provenance, licensing, and misuse accountability, yet no deployed watermark meets this need. Generation-time schemes require access to the producing model and cannot be applied to third-party code, while post-hoc schemes work on any code but carry at most 4 bits of payload, far too few to distinguish the many deployed model configurations. We present multi-channel spread-spectrum watermarking, the first post-hoc, training-free code watermark with a 24-bit payload and formal robustness guarantees. The scheme encodes bits in variable naming conventions and in eight pairs of semantically equivalent code patterns, and a keyed pseudo-random permutation maps every site to a codeword bit so that each bit receives multiple independent votes. Majority voting absorbs distributed corruption, while an outer Reed-Solomon code recovers the identifier when concentrated channel attacks defeat the vote, yielding provable robustness bounds for formatting, syntactic, and structural attacks. Across 1,750 Python files from CodeNet and from GPT-4.1 and Llama-4 generations, the watermark achieves 100% clean-detection accuracy with zero false positives. Under 17 attack types, it recovers the identifier at 97.6% accuracy under 8 variable renames and 94.1% under 10% random per-site corruption, while the strongest post-hoc baseline collapses to 0% under any single-transform attack. Embedding and detection together take under 200 ms on CPU without training data or GPU.

Real-time decoding is a major bottleneck in scaling quantum error correction (QEC) from noisy intermediate-scale quantum (NISQ) devices to fault-tolerant quantum computing. We present an adaptive confidence-gated decoding framework for the rotated surface code that treats decoding as a two-stage inference problem. A lightweight feed-forward neural network performs fast-path decoding for the majority of syndrome measurements, while only low-confidence predictions are escalated to a minimum-weight perfect matching (MWPM) refinement stage. We benchmark the framework on rotated surface codes with distances $d \in \{3,5,7,9,11\}$ under circuit-level depolarising noise using the Stim stabiliser simulator. The evaluation characterises logical accuracy, confidence-controlled accuracy-latency trade-offs, decoding throughput, per-shot latency, and decoding-graph resource scaling. Routing only 3.3%-6.2% of syndromes to the refinement stage improves logical accuracy from 99.21% for the neural-only baseline to 99.81% at a confidence threshold of 0.95 while incurring only a bounded increase in average decoding cost. Neural-decoder throughput saturates near $4.6 \times 10^{5}$ samples s$^{-1}$ at batch size 512 on commodity CPU hardware, indicating that the neural fast path is not the dominant throughput bottleneck beyond code distance $d=7$. We release the complete benchmarking pipeline, trained models, raw benchmark data, and source code, and explicitly distinguish the experimentally validated contributions from the broader hardware-aware QEC co-design roadmap, including hardware-constrained code discovery, GPU-accelerated inference, and multi-noise optimisation, which remain directions for future work.

Quantum convolutional neural networks (QCNNs) combine the power of quantum computing and classical CNN for computational speedup in classification tasks. However, noise levels on state-of-the-art quantum devices remain too high for practical QCNN execution. In addition, despite the reliable surface code providing a method for error rates below a threshold value, they have a prohibitively large qubit cost. Recently introduced bivariate bicycle (BB) codes are of particular interest for their high error threshold, constant encoding rate, and linear code distance. Through simulation with realistic hardware noise sources, we demonstrate that a 4-qubit unprotected QCNN fails to converge and exhibits a worse learning rate compared to numerical simulations. Addressing both limitations, we propose a distance-4 BB quantum error-correction (QEC) technique for QCNNs. In doing so, we validate that our low-overhead QEC technique for QCNNS represents a step toward practical QCNNs.

The rapid growth in the parameter scale of large language models (LLMs) has created a strong demand for efficient compression techniques. As a hardware-agnostic and highly compatible approach, low-rank compression has been widely adopted to reduce both memory footprint and computational cost. However, existing SVD-based methods are still largely driven by local reconstruction objectives, overlooking two critical limitations: rank budgets are often allocated without explicitly considering layer-wise loss sensitivity, and local approximation errors can propagate and accumulate through the residual stream, leading to amplified global deviations from the original model. To address these issues, we propose LACE-SVD, a Loss-Aware SVD framework with Cumulative Error correction for LLM compression. LACE-SVD first estimates the calibration negative-log-likelihood increase induced by candidate layer-wise compression ratios and solves a budget-constrained allocation problem to assign rank budgets. It then refines the compressed model with closed-form local updates and introduces a propagation-aware correction for residual-stream output modules, reducing layer-output discrepancy as a proxy for cumulative error propagation. Experimental results demonstrate that at a high compression ratio (0.6), the WikiText-2 PPL of our method on LLaMA-7B (32.57) is significantly better than that of Dobi-SVD (46.18).

Understanding the features of large language models (LLMs) is a central goal of interpretability. LLMs are commonly assumed to use superposition to represent more features than they have dimensions. They may not only represent features in superposition but also perform computation in superposition. Theory predicts that computing in superposition requires error correction that privileges feature directions over generic ones, but this prediction has not been tested empirically. We propose an empirical test of error correction in LLMs based on activation perturbations. Perturbing residual-stream activations, we find that they are robust to small perturbations--forming activation plateaus consistent with error correction--but less robust along candidate feature directions ("pure" directions, constructed from contrastive prompt pairs) than along mixtures of two such directions, indicating that the pure directions are privileged. We quantify this privilegedness by modeling the perturbation effect as a function of the $L^p$-norm of its decomposition into feature components. For $p=2$ the response is a quadratic form with at most as many nonzero eigenvalues as the residual-stream dimension, which cannot privilege the many feature directions superposition requires. $p>2$ lifts this constraint and is consistent with feature-specific error correction. We find $p>2$ for contrastive, MELBO, and SAE-decoder directions, and $p\approx2$ for random and PCA directions (controls). These results replicate across Gemma-2-9B, Qwen3-1.7B, Llama-3.1-8B, Mistral-7B-v0.3, Aya-Expanse-8B, and Yi-1.5-9B. We further validate our method on a toy model of error correction with known ground-truth features, recovering $p>2$ for true feature directions, degrading toward $2$ as we rotate away from them.

As Large Language Models (LLMs) deploy into mission-critical domains (e.g., finance, medicine, and law), output reproducibility has become a strict system requirement. While practitioners use greedy decoding to eliminate algorithmic stochasticity, empirical deployments with 16-bit precisions still exhibit catastrophic output divergence across heterogeneous GPUs. Through SASS-level profiling, we reveal that this inconsistency is fundamentally driven by truncation errors introduced during downcasting at kernel boundaries. However, achieving reproducibility via a global FP32 pipeline incurs prohibitive system penalties: bypassing 16-bit hardware accelerators hurts compute efficiency, while upcasting the KV cache doubles memory overhead. To bridge this gap, we propose Hybrid Error ALleviation (HEAL), a targeted intervention that approximates FP32 precision while resolving hardware constraints through two targeted mechanisms. First, recognizing that floating-point formats underutilize their bit-width for Q, K, V tensors, HEAL applies INT16 quantization that preserves numerical stability without expanding the KV cache footprint. Second, HEAL synthesizes high-precision matrix multiplications via an algebraic error compensation strategy, executing entirely on high-throughput 16-bit Tensor Cores. To evaluate our approach practically, we introduce MCR-Bench, a benchmark targeting reproducibility in mission-critical tasks. HEAL achieves the same level of reproducibility on downstream tasks as the FP32 baseline while reducing the performance overhead by up to 7.1x.

Time series forecasting largely benefits from combining the strengths of different models, especially using a scheme where a model corrects another model by capturing supplementary patterns from forecasting errors. Concurrently, quantum models are providing a means to augment the classical capacity, including in time series forecasting, by acting alongside classical models in hybrid architectures. In this work, we propose the first forecasting system based on error correction that jointly uses quantum and classical models. Here, quantum models first extract patterns by exploring quantum phenomena, and classical models capture the remaining patterns from the quantum errors. Compared to classical single models and classical-classical hybrid models based on error correction, the complementary capacity that emerges from this quantum-classical system provided the best results in most of the addressed problems. Therefore, this work paves the way to introduce quantum models in established hybridization schemes for time series forecasting.

The radial basis function neural network (RBFN) trained with a gradient descending algorithm provides an effective fully connected structure in both shallow and deep networks. The error correction (ErrCor), a state-of-the-art gradient-based training method, selects optimal hidden units to improve accuracy. Alternatively, as a population-based algorithm, the particle swarm optimization algorithm (PSO) uses the swarm experience to optimize RBFN parameters, offering global search and robustness to local minima. Adaptive PSO (APSO) has emerged as an improved variant of PSO. APSO algorithm improves convergence speed by dynamically adjusting swarm parameters during optimization. Both ErrCor and PSO demonstrate improved results and competitive convergence. However, with large datasets, these methods face scalability challenges such as excessive kernel computations and large hidden layer structures. A recent multi-column RBFN approach (MCRN) improves ErrCor performance by deploying small RBFNs in a parallel system. Inspired by MCRN's success, we propose two novel approaches to improve PSO performance: the multi-column RBFN with PSO (MC-PSO) and the multi-column RBFN with APSO (MC-APSO). These methods introduce parallel RBFN structures trained using evolutionary swarm methods. Each RBFN is independently trained on a specific spatial subset of the dataset using either PSO or APSO algorithms. These resulting specialist-trained RBFNs are tailored to their respective subsets. During testing, only selected RBFNs, where the test instance neighbors are located, contribute to the multi-column output. This specialization improves accuracy, while parallelism enhances speed. We evaluate the proposed methods on various benchmark datasets. The MC-PSO and MC-APSO outperform ErrCor, PSO, APSO, and MCRN in terms of accuracy and recall. They also demonstrate faster training and testing times in most experiments.

Error-correcting codes enable reliable communication, yet practical soft decoding remains challenging across code families and block lengths. We propose SB-ECC, a score-based decoder that casts decoding as continuous-time denoising. A neural denoiser defines a probability-flow ordinary differential equation (ODE) that iteratively updates the noisy channel observation toward a valid codeword, guided by parity constraints. The model is trained across noise levels without time/SNR conditioning, enabling inference without SNR estimation and supporting a direct latency accuracy trade off controlled by the ODE solver budget. We use the raw signed channel observation as input for learning a continuous denoising field. Across 42 code/SNR settings, SB-ECC achieves the best BER in 39/42 entries, with an average SNR gain of 0.17dB and a maximum gain of 0.46dB over the strongest competing baseline, we showed that swapping the solver from Euler to DPM preserves -ln(BER) while reducing end-to-end decoding time by 8.86% on average (up to 12.82%).

Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We present a general learning-based framework that, given only an encoding circuit, constructs physical implementations of logical operations while enforcing structural properties such as transversality or shallow depth. Our approach is validated by rediscovering known logical operations of standard stabilizer codes. We then extend it to a co-design procedure, dubbed variational early fault-tolerant quantum computing (VarEFTQC), which tailors non-additive encodings to a given noise model and enforces desired logical gate sets, such as transversal IQP-type families or low-depth universal sets. A software library implements the complete learning pipeline, including loss-function variants, ansatz families, and optimization routines. Together, these results position VarEFTQC as a proof-of-concept framework for discovering hardware-adapted logical gadgets for early fault-tolerant quantum computing.

Sparse autoencoders are usually trained one layer at a time, even though transformer residual stream activations are strongly coupled across depth. This creates a practical problem for multi-layer interventions: different layerwise dictionaries can spend capacity representing the same carried-forward information, and replacing several layers at once can produce interactions that are not predicted by single-layer behavior. We introduce Residualized Sparse Autoencoders (ReSAEs), which fit an affine map between selected layers and train each later-layer SAE on the unexplained residual rather than on the full activation. Reconstructions are mapped back into the original activation space through the fitted affine chain, so ReSAEs can be evaluated with the same intervention protocols as ordinary SAEs. On Pythia-1.4B and Gemma-2-9B, residualization reduces decoder redundancy and improves sparse probing and targeted perturbation in most tested settings. Despite reconstructing less of the raw activation variance, ReSAEs recover more transformer cross entropy under multi-layer replacement. This gain is clearest under teacher-forcing and at sufficient sparsity online, indicating that ReSAEs preserve the components of the activation most relevant to the model's downstream computation. These results suggest that removing linearly predictable cross-layer structure is a useful default for multi-layer SAE interventions.

Visual Autoregressive (VAR) models have emerged as a powerful paradigm for image synthesis by performing hierarchical next-scale prediction. However, VAR models are inherently prone to cascading error propagation, where subtle coarse-scale mispredictions are amplified across the hierarchy, ultimately distorting the final synthesis. To mitigate this, we propose AID-VAR, a plug-and-play framework that enhances pre-trained VARs through Adversarially Injected Diagnosis. Instead of a standard passive generation, AID-VAR introduces a proactive error-correction mechanism inspired by the adversarial feedback in GANs. We deploy a discriminator to diagnose fidelity gaps at each scale transition, coupled with a lightweight guidance injector. This module operates as a non-invasive adapter that refines the feature manifold of a frozen VAR backbone, effectively steering the generation toward the distribution of real images without destabilizing the pre-trained latent space. Furthermore, to rigorously evaluate this cross-scale progression, we introduce the Inter-Scale Consistency Score (ISCS), a novel metric that quantifies the fidelity and structural alignment between consecutive resolution scales. Experimental results across various backbones demonstrate that AID-VAR delivers sharper textural details and fewer structural distortions with negligible overhead. For instance, AID-VAR-d20 achieves a 16% improvement in FID with only a 3% increase in parameters. These results establish AID-VAR as a highly efficient and scalable pathway for upgrading large-scale VAR generators, enhancing global coherence and local detail without altering training data, base architectures, or sampling schedules. Code is available at https://github.com/bijiw515/AID-VAR.

Modern deep-learning models have achieved remarkable success in time-series forecasting. Yet, their performance degrades in long-term prediction due to error accumulation in autoregressive inference, where predictions are recursively used as inputs. While classical error correction mechanisms (ECMs) have long been used in statistical methods, their applicability to deep learning models remains limited or ineffective. In this work, we revisit the error accumulation problem in deep time-series forecasting and investigate the role and necessity of ECMs in this new context. We propose a simple, architecture-agnostic error correction model that can be integrated with any existing forecaster without requiring retraining. By explicitly decomposing predictions into trend and seasonal components and training the corrector to adjust each separately, we introduce the Universal Error Corrector with Seasonal-Trend Decomposition (UEC-STD), which significantly improves correction accuracy and robustness across 4 backbones and 10 datasets. Our findings provide a practical tool for enhancing forecasts while offering new insights into mitigating autoregressive errors in deep time-series models. Code is available at https://github.com/DA2I2-SLM/UEC-STD.

Automatic speech recognition (ASR) has improved substantially in recent years, yet performance remains limited for low-resource languages. Large language models (LLMs) have shown promise for improving ASR through generative error correction (GER), but their effectiveness in low-resource settings remains underexplored. In addition, it remains unclear to what extent data contamination influences the reported improvements in LLM-based GER. This study investigates LLM-based GER for low-resource Frisian. In addition to a public corpus, we construct and use a Frisian offline dataset with non-public texts for evaluation to control for potential data contamination. Results show that GER improves ASR performance in most settings, with the best GPT-5.1 results surpassing oracle WERs. Comparable gains on the offline dataset indicate that improvements reflect true correction ability. We further provide a detailed error analysis revealing model correction patterns.

Neural channel decoder, as a data-driven channel decoding strategy, has shown very promising improvement on error-correcting capability over the classical methods. However, the success of those deep learning-based decoder comes at the cost of drastically increased model storage and computational complexity, hindering their practical adoptions in real-world time-sensitive resource-sensitive communication and storage systems. To address this challenge, we propose an efficient variational diffusion model-based channel decoder, which effectively integrates the domain-specific belief propagation process to the modern diffusion model. By reaping the low-cost benefits of belief propagation and strong learning capability of diffusion model, our proposed neural decoder simultaneously achieves very low cost and high error-correcting performance. Experimental results show that, compared with the state-of-the-art neural channel decoders, our model provides a feasible solution for practical deployment via achieving the best decoding performance with significantly reduced computational cost and model size.

Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible decoding strategies, maximum likelihood decoding (MLD) is provably optimal, since it identifies the logical group with largest likelihood by summing over all possible errors within logical class consistent with the observed syndrome. Despite its optimality, MLD is computationally intractable in general (#P-hard), motivating a rich landscape of exact and approximate algorithms. In this topical review, we provide a unified perspective on MLD by surveying recent advances through three complementary lenses: statistical mechanics, tensor networks, and artificial intelligence. From the statistical mechanics viewpoint, the MLD problem maps onto evaluating partition functions of disordered spin models, enabling exact solutions for certain codes and noise models as well as threshold estimation via phase-transition analysis. From the tensor network perspective, approximate contraction of tensor networks on the code's factor graph yields decoders that closely approach MLD accuracy with polynomial computational cost. From the artificial intelligence perspective, neural-network-based decoders, including autoregressive generative models and recurrent transformers, learn to approximate the MLD distribution from data, achieving high accuracy with the parallelism afforded by modern hardware accelerators. We discuss the connections among these three approaches, review their application to both simulated and experimental quantum hardware, and outline open challenges including real-time decoding, scalability to large code distances, and generalization to high-rate quantum low-density parity-check codes.

Quantum error correction (QEC) is essential for building fault-tolerant quantum computers, requiring decoders that are simultaneously accurate, fast, and scalable. Most state-of-the-art neural decoders achieve high accuracy but process the full dense syndrome array of size $O(d^2 R)$regardless of the actual error rate, where d is the code distance and R is the number of measurement rounds. At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events -- yet existing decoders process the entire syndrome volume. We introduce the Sparse Mamba Decoder (SMD), a defect-centric neural decoder that processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving $O(k)$ complexity. Across depolarizing, uniform circuit-level, SI1000, and Google Sycamore experimental benchmarks, SMD reduces the MWPM logical error rate by up to 49% at $d \le 5$ under SI1000 noise, runs 95-467x faster than the Tesseract near-MLD decoder and 232-463x faster than Belief Matching, and maintains nearly constant latency (24-57 us) across d = 3-9 under uniform circuit-level noise. On the Sycamore experimental dataset, the SMD ensemble matches or slightly surpasses the dense Mamba decoder of Varbanov et al. All results are obtained on commodity NVIDIA GPUs with 7.5-16M parameters, without specialized accelerators.

Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among which neural decoders have recently emerged as a promising data-driven paradigm. Despite this progress, practical deployment remains hindered by a fundamental accuracy-latency tradeoff, often on the microsecond timescale. To address this challenge, here we revisit neural decoders for surface-code decoding under explicit accuracy-latency constraints, considering code distances up to d=9 (161 physical qubits). We unify and redesign representative neural decoders into five architectural paradigms and develop an end-to-end compression pipeline to evaluate their deployability and performance on FPGA hardware. Through systematic experiments, we reveal several previously underexplored insights: (i) near-term decoding performance is driven more by data scale than architectural complexity; (ii) appropriate inductive bias is essential for achieving high decoding accuracy; and (iii) INT4 quantization is a prerequisite for meeting microsecond-scale latency requirements on FPGAs. Together, these findings provide concrete guidance toward scalable and real-time neural QEC decoding.

Modern Deep Learning (DL) workloads are increasingly deployed in safety-critical domains, such as automotive systems and hyperscale data centers, where transient hardware faults pose a serious threat to system reliability. These workloads are highly memory-intensive, and their correct functionality strongly depends on model parameters stored in memory, which are typically protected using Error Correction Codes (ECCs). In this work, we study ECC's impact on such models and propose two lightweight alternatives to ECCs that achieve superior reliability. The first approach, MSET, selectively hardens the most vulnerable bits in CNN and ViT parameters, while the second approach, CEP, provides fine-grained protection for all parameter bits. Experimental results demonstrate that both methods significantly enhance the reliability of large CNNs and ViTs, mostly outperforming conventional Single Error Detection Double Error Correction (SECDED) ECC schemes, with no memory overhead and, in fact, with considerably lower area and delay characteristics when compared to SECDEC. Experimental results indicate that ViTs can be effectively protected by merely protecting their highest exponent bits in FP16 and FP32 representations. Furthermore, applying the CEP technique can guarantee the resilience of DNNs by up to one order of magnitude higher BERs, with a 3.5x lower area overhead and 7x faster decoder compared to SECDED ECC.

The widespread adoption of machine learning in critical applications demands techniques to mitigate high-consequence errors. Our method utilizes a dual-classifier GBDT pipeline to distinguish routine human-like errors from high-risk non-human misclassifications. Evaluated across three domains, animal breed classification, skin lesion diagnosis (ISIC 2018), and prostate histopathology (SICAPv2), our framework demonstrates robust safety improvements. To address real-world deployment concerns, our results confirm the pipeline introduces negligible inference latency (1.60% overhead for the animal dataset, 1.84% for ISIC, and 1.70% for SICAPv2) while outperforming traditional Maximum Class Probability (MCP) baselines in correction precision. Our conservative correction strategy successfully reduced dangerous non-human errors by 34.1% in ISIC and 12.57% in SICAPv2, improving super-class diagnostic safety to 90.41% and 92.13% respectively. This proves that safety-critical reliability can be substantially enhanced post-hoc without expensive model retraining. keywords: Error Analysis, Post-hoc Correction, Trustworthy AI.

Factual Error Correction (FEC) aims to revise inaccurate text into statements that are factually consistent with external evidence. Although recent methods perform well on single-hop correction, they often treat claims as atomic units and struggle with multi-hop cases that require compositional reasoning across multiple evidence sources. This challenge is further amplified by limited paired data and difficulties in locating semantic errors within complex reasoning chains. We present CECoR (Compositional Error Correction via Reasoning-aware Synthesis), a reasoning-aware framework that introduces a Decomposition and Injection paradigm for compositional error correction. CECoR decomposes multi-hop claims into interpretable reasoning steps and injects controlled perturbations to synthesize high-quality training pairs. A two-stage learning strategy combining supervised fine-tuning and reinforcement learning improves factual accuracy and robustness. Comprehensive evaluations show that CECoR achieves strong performance on multi-hop benchmarks, outperforming both distantly supervised methods and few-shot LLM baselines. It also generalizes effectively to single-hop correction and remains stable under noisy evidence, demonstrating its versatility for real-world factual correction.

Resources for Grammatical Error Correction (GEC) in non-English languages are scarce, while available spellcheckers in these languages are mostly limited to simple corrections and rules. In this paper we introduce a first GEC corpus for Romanian consisting of 10k pairs of sentences. In addition, the German version of ERRANT (ERRor ANnotation Toolkit) scorer was adapted for Romanian to analyze this corpus and extract edits needed for evaluation. Multiple neural models were experimented, together with pretraining strategies, which proved effective for GEC in low-resource settings. Our baseline consists of a small Transformer model trained only on the GEC dataset (F0.5 of 44.38), whereas the best performing model is produced by pretraining a larger Transformer model on artificially generated data, followed by finetuning on the actual corpus (F0.5 of 53.76). The proposed method for generating additional training examples is easily extensible and can be applied to any language, as it requires only a POS tagger

This paper presents a semantic-enhanced receiver framework for transmitting natural language sentences over noisy wireless channels using multiple short block codes. After ASCII encoding, the sentence is divided into segments, each independently encoded with a short block code and transmitted over an AWGN channel. At the receiver, segments are decoded in parallel, followed by a semantic error correction (SEC) model, which reconstructs corrupted segments using language model context. We further propose the semantic list decoding (SLD), which generates multiple candidate reconstructions and selects the best one via weighted Hamming distance, and a semantic confidence-guided HARQ (SHARQ) mechanism that replaces CRC-based error detection with a confidence score, enabling selective segment retransmission without CRC overhead. All modules are designed and trained using bidirectional and auto-regressive transformers (BART). Simulation results demonstrate that the proposed scheme significantly outperforms conventional capacity-approaching short codes and long codes at the same rate. Specifically, SEC provides approximately 0.4 dB BLER gain over plain short-code transmission, while SLD extends this to 0.8 dB. Compared to transmitting the entire sentence as a single long 5G LDPC codeword, our approach significantly improves semantic fidelity and reduces decoding latency by up to 90%. SHARQ further provides an additional 1.5 dB gain over conventional HARQ.

Open-ended grading is central to equitable and personalized education, yet manual grading remains time-consuming and costly, underscoring the need for automated grading systems. Although recent neural and large language model (LLM) based systems have demonstrated superior performance, they are typically black-box models whose scoring processes and rationales are difficult for educators to verify and trust. Concept bottleneck models (CBMs) have emerged as a promising approach by routing predictions through human-interpretable concepts, providing a mechanistic guarantee of transparency. However, standard CBMs are not tailored to open-ended grading: they do not explicitly model fine-grained rubric dimensions, inadequately capture the ordinal semantics of scoring scales, and neglect inherent reliability issues in human concept annotations. To address these limitations, we propose REC-CBM, a rubric-aware error-correction concept bottleneck model for trustworthy open-ended grading. REC-CBM introduces a rubric-aware concept encoder that learns concept-specific representations over responses and an ordinal pairwise calibration objective that preserves ranking structure among rubric dimensions. It further incorporates a latent concept error-correction module that denoises concept predictions before final grade prediction while preserving interpretability. Comprehensive experiments on publicly available datasets show that REC-CBM consistently improves grading performance and produces more faithful concept-level reasoning than both state-of-the-art baselines. Further analyses validate the contribution of each component and demonstrate the applicability in realistic educational settings. Overall, this work provides a practical, interpretable grading solution that enables educators to inspect, intervene in, and trust automated decisions, advancing more transparent and trustworthy education.

Achieving truly fluid interaction with robots with speech interfaces remains a hard problem, and the experience of current Human-Robot Interaction (HRI) remains laboured and frustrating. Some of the barriers to fluid interaction stem from a lack of a suitable development platform for HRI for improving interaction, even in robotic Wizard-of-Oz (WoZ) modes of operation used for data collection and prototyping. Based on previous systems, we propose the properties of interruptibility and correction (IaC), pollability, latency measurement and optimisation and time-accurate reproducibility of actions from logging data as key criteria for a fluid WoZ system to support fluid error correction. We finish by presenting a Virtual Reality (VR) HRI simulation environment for mobile manipulators which meets these criteria.

Large language models frequently commit unrecoverable reasoning errors mid-generation: once a wrong step is taken, subsequent tokens compound the mistake rather than correct it. We introduce $\textbf{Latent Phase-Shift Rollback}$ (LPSR): at each generation step, we monitor the residual stream at a critical layer lcrit, detect abrupt directional reversals (phase shifts) via a cosine-similarity $+$ entropy dual gate, and respond by rolling back the KV-cache and injecting a pre-computed steering vector. No fine-tuning, gradient computation, or additional forward passes are required. LPSR achieves $\mathbf{44.0\%}$ on MATH-500 with an 8B model versus $28.8\%$ for standard AR ($+15.2$ pp; McNemar $χ^2 = 66.96$, $p < 10^{-15}$). Critically, prompted self-correction, the most natural inference-time baseline, scores only $19.8\%$, below standard AR; LPSR exceeds it by $+24.2$ pp ($χ^2 = 89.4$, $p \approx 0$). LPSR also outperforms Best-of-16 ($+7.8$ pp) at $5.4\times$ lower token cost, and surpasses a standard 70B model ($35.2\%$) with $8.75\times$ fewer parameters at ${\sim}3\times$ the token budget. A 32-layer sweep reveals a novel \textbf{detection-correction dissociation}: error-detection AUC peaks at layer14 ($0.718$) but task accuracy peaks at layer16 ($44.0\%$ vs.\ $29.2\%$), demonstrating that optimal monitoring depth differs for detection and correction.

This paper investigates the length problem in sequence-level relative reinforcement learning. We observe that, although existing methods partially alleviate length-related phenomena, a more fundamental issue remains insufficiently characterized: the comparison units used during training lack inherent comparability. Building on this observation, we propose a new perspective: the length problem should not be viewed merely as a loss-scaling or normalization bias, but rather as a \emph{comparison unit construction} problem. We further establish a sample-construction-based training framework that, instead of applying post-hoc corrections to unequal-length responses, proactively constructs equal-length, alignable, and comparable training segments during generation. Within this framework, we propose EqLen, a concrete method applicable to group-relative comparison algorithms such as GRPO, GSPO, and RLOO. Through dual-track synchronous generation, prefix inheritance, and segment masking, EqLen efficiently collects effective equal-length training segments and enables stable

Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an optimal code sequence. We automate this choice by estimating the effective noise channel after each level and selecting the next code accordingly. In particular, we use learning-based methods to tailor small, non-additive encoders when the noise exhibits sufficient structure, then switch to standard codes once the noise is nearly uniform. In simulations, this level-wise adaptation achieves a target logical error rate with far fewer qubits than concatenating stabilizer codes alone--reducing qubit counts by up to two orders of magnitude for strongly structured noise. Therefore, this hybrid, learning-based strategy offers a promising tool for early fault-tolerant quantum computing.

Speech Large Language Models route speech encoder representations into an LLM decoder that typically accounts for over 90% of total parameters. We study how much of this decoder capacity is actually needed for speech tasks. Across two LLM families and three scales (1-8B), we show that decoder redundancy is largely inherited from the pretrained LLM: text and speech inputs yield similar redundant blocks. We then measure excess capacity by pruning decoder layers and analysing post-pruning healing to increase robustness. Our findings show that 7-8B models retain good ASR performance with only 60% of decoder layers, and the same trend extends to smaller scales with reduced pruning tolerance. We then generalise to speech translation, and show that the same blocks of layers are redundant across speech encoders, tasks and languages, indicating that a more global redundancy structure exists, enabling a single pruned and multi-tasks SpeechLLM backbone to be deployed.

The rapid emergence of new entities -- driven by cultural shifts, evolving trends, and personalized user data -- poses a significant challenge for existing Speech Large Language Models (Speech LLMs). While these models excel at general conversational tasks, their static training knowledge limits their ability to recognize domain-specific terms such as contact names, playlists, or technical jargon. Existing solutions primarily rely on prompting, which suffers from poor scalability: as the entity list grows, prompting encounters context window limitations, increased inference latency, and the "lost-in-the-middle" phenomenon. An alternative approach, Generative Error Correction (GEC), attempts to rewrite transcripts via post-processing but frequently suffers from "over-correction", introducing hallucinations of entities that were never spoken. In this work, we introduce LOGIC (Logit-Space Integration for Contextual Biasing), an efficient and robust framework that operates directly in the decoding layer. Unlike prompting, LOGIC decouples context injection from input processing, ensuring constant-time complexity relative to prompt length. Extensive experiments using the Phi-4-MM model across 11 multilingual locales demonstrate that LOGIC achieves an average 9% relative reduction in Entity WER with a negligible 0.30% increase in False Alarm Rate.