arXiv:2610.29841v1 Announce Type: cross
Abstract: The mid-wave infrared (MWIR, 3-5 microns) is indispensable for thermal sensing, gas detection, long-range imaging, and free-space optical communications. Meta-optics offer a compact, lightweight, and potentially low-cost alternative to conventional refractive optics, making them attractive for size, weight, and power (SWaP)-constrained systems. However, their strong chromatic dispersion has largely restricted imaging to narrow spectral bands. Here, we demonstrate broadband imaging across the full 3-5 micron MWIR band using a single-layer silicon metasurface coupled with computational reconstruction. Remarkably, the reconstruction model is adapted using only four image captures, overcoming large training data requirements and enabling broadband image recovery despite the strongly wavelength-dependent optical response. In contrast to approaches that engineer complex, dispersion-optimized metalens profiles for broadband operation, our method leverages the wavelength-dependent information encoded by a simple 2cm diameter hyperboloid metalens. We show that this metasurface captures sufficient broadband intensity information for computational reconstruction across the entire MWIR band. These results establish a simple route toward broadband computational meta-optics without requiring broadband achromatic metalens designs, offering a promising platform for compact MWIR imaging systems.
Rose Johnson, Debabrata Mandal, Zihao Zou, Jessie Wei, Anna Wirth-Singh, Vladimir Yarmolik, Johannes Froech, Arka Majumdar, Praneeth Chakravarthula
arXiv:2610.29832v1 Announce Type: cross
Abstract: Calibrating large language models (LLMs) in open-ended generation is uniquely challenging because many distinct token sequences can express the same underlying meaning. Prior calibration techniques target either fixed-set classification confidence or the binary correctness of individual strings, making them inherently ill-suited for the dynamic, multi-string nature of open-ended semantic outcomes. To bridge this gap, we introduce S-EDL, a novel evidential method that natively optimizes LLMs for semantic calibration. By eliciting evidence from the sequence likelihoods of the model itself, S-EDL constructs a differentiable Dirichlet prior over prompt-specific semantic classes. Optimizing the evidential loss under this prior yields a calibration-aware training signal over variable semantic classes, completely bypassing the need for fixed multiple-choice options. Evaluations across four open-ended benchmarks and three models demonstrate that S-EDL substantially reduces semantic calibration error while improving accuracy. By aligning generative likelihoods with semantic correctness, this work establishes a framework for deploying trustworthy LLMs in complex, open-ended applications. Code is available at: https://github.com/sandylaker/s-edl.
Yawei Li, Jiazheng Li, David R\"ugamer, Bernd Bischl, Yulan He, Mina Rezaei
arXiv:2610.29829v2 Announce Type: cross
Abstract: General-purpose robots must handle tasks, objects and environments they were never trained on, yet zero-shot generalization remains one of the least solved problems in physical AI. In digital AI, zero-shot capability grew with the volume and, above all, the diversity of training data, much of it sourced from the crowd. Robotics instead relies on paid collection by a few well-funded teams, which yields volume without diversity. We formulate zero-shot generalization in physical AI as coverage of the deployment distribution, and show that more samples from the same collectors shrink the unseen region only slowly, while each new contributor can extend it. Building on this and on zero-shot learning, we propose a shared latent space for robot actions that combines multi-modal alignment, generative augmentation, and noisy-label learning. As a scalable source of diverse data, we propose a community of developers building applications on one standard, approachable robot, Origami. We close with a testable hypothesis and an evaluation protocol relating real-robot zero-shot success to the diversity of contributed data.
Rafael Felix, Flavia Yanase
arXiv:2610.29823v1 Announce Type: cross
Abstract: Agent memory systems such as Mem0 and Zep decide what to keep before any question arrives; coding agents keep the raw history and let the model search it with its own tools. We ask whether designed memory still helps once the model is strong enough to search for itself. On one LoCoMo conversation (419 turns, 152 questions), we run four memory methods (full context, BM25, Mem0, Zep) and three coding agents (Pi, Codex, Claude Code), each with GPT-4o-mini, GPT-6 Luna and Claude Opus 5.5, and record what every rollout costs. This is a short empirical study, with one conversation and one run per cell. Agent memory is a costly patch for a weak model: Mem0 beats full context only with GPT-4o-mini, and its build alone costs more than a whole full-context rollout. Agent memory also has a ceiling, set by the model that writes it: a stronger reader does not recover what a weaker writer left out. With Claude Opus 5.5, Pi tops the cost-accuracy frontier, scoring 99% for less than half the cost of full context; its one miss is a wrong answer key. Part of that lead comes from photo captions that only the agents could read: on the 88 questions whose evidence has no photo, Pi and full context differ by one answer.
arXiv:2610.29785v1 Announce Type: cross
Abstract: Asked what to study, which career to pursue, or what product to build, large language models (LLMs) often recommend AI-related options. We ask where this tendency comes from by comparing models before and after fine-tuning and by varying how questions are asked. First, pretrained models already include explicit AI/ML terms in the recommendations of 27% of their responses, and their released instruction-tuned versions do so in 59%. Second, fine-tuning models ourselves shows that this rise is not inevitable: general instruction tuning leaves the rate unchanged, but removing the 7% of instruction examples that concern AI cuts it by 14 percentage points, below the level of the pretrained models it starts from. Data rewarding helpfulness raise it by 9 points, while data ranked by the preferences of diverse simulated users lower it by 9. Finally, with models held fixed, asking for the "best" option or for what to do "right now" raises the rate by 8 and 18 points, whereas telling the model it is an AI advisor adds 4. Overall, the tendency starts in pretraining, and what models learn afterward, together with how a question is phrased, decides how strongly it appears.
Benaya Trabelsi, Jonathan Shaki, Sarit Kraus
arXiv:2610.29749v1 Announce Type: cross
Abstract: Large language models (LLMs) are increasingly used to generate software engineering artifacts written in domain-specific languages (DSLs). Correct DSL instances usually must comply with not only the concrete syntax but also the abstract syntax defined by a metamodel augmented with semantic well-formedness constraints. Existing constrained decoding approaches typically guarantee compliance only with concrete syntax or with a limited set of semantic constraints expressed over the generated text, making metamodel-level constraint consistency difficult to enforce during generation. We present MeMoDecode: a decoding framework that enforces a DSL's concrete syntax, abstract syntax, and well-formedness constraints jointly. Specifically, whenever the LLM generates a complete metamodel concept, MeMoDecode incrementally maps the current output to a partial model and verifies whether it can still be completed into a consistent instance. We combine MeMoDecode with a simple retry mechanism that resumes decoding from the most recent completable snapshot whenever an inconsistency is detected. Under a sound backend verifier, MeMoDecode never performs worse than grammar-constrained decoding on alignment metrics satisfying natural assumptions. Across four DSLs and six open-weight LLMs ranging from 0.6B to 70B parameters, MeMoDecode achieves the highest consistency, improving consistency by 23% on average over unconstrained decoding and by 8% on average over grammar-constrained decoding. It also improves benchmark performance while incurring only modest runtime overhead. These results show that metamodel-guided decoding is an effective approach for enforcing DSL consistency during decoding across diverse DSLs and LLM scales.
Boqi Chen, Aren A. Babikian, Jos\'e Antonio Hern\'andez L\'opez
arXiv:2610.29733v1 Announce Type: cross
Abstract: Diffusion transformers are widely used in image-editing services. To preserve both efficiency and privacy, existing systems commonly rely on cloud-device collaboration. Keeping request-specific inference on the device avoids sending personal images and prompts to the cloud. These workloads often use common templates, such as in face swapping and virtual try-on, enabling KV state to be precomputed and reused across requests. However, this reusable state is large and scales with the number of templates, making it impractical to store all of them on mobile devices. Storing them in the cloud addresses this capacity issue, but cache transfer is placed onto the inference path and can even be slower than on-device computation, especially under fluctuating mobile networks.
We introduce SAKURA, a cloud-edge architecture that delivers reusable attention state to mobile devices under a bandwidth budget. It first uses a fine-grained token-importance-aware compression method to preserve image quality under limited transfer budgets. At runtime, SAKURA adaptively selects the cache representation for each upcoming shard based on network bandwidth. To enable efficient execution, we develop a pipelined runtime that overlaps cache transfer and reconstruction with on-device execution. We evaluate SAKURA using three editing tasks and two diffusion models, using a Snapdragon 8 Elite Gen 5 phone. SAKURA reduces latency by 1.82x and 3.27x over CacheGen adapted to DiT and on-device generation, respectively. It also reduces cache storage by 3.06x over uncompressed cache, while preserving image quality.
Shuncheng Jie, Desen Sun, Ri Hong, Yuyang Tian, Hong Zhang, Sihang Liu
arXiv:2610.29725v1 Announce Type: cross
Abstract: A common application of the process mining discipline is to connect observed event data with Petri nets, which are bipartite, directed graphical process models with rich formal underpinnings. Recent work learns vector representations of Petri nets to retrieve process models and relate them to event logs, but leaves implicit two key aspects hidden within the net's structure: directed cycles (process loops) and invariants recorded by the net's incidence matrix. We expose both of these to message-passing graph neural networks, through a positional encoding built from return probabilities of directed place-transition walks (PNRWPE), and through same-type messages gated by diffusion kernels of the incidence matrix (DA-PNGNN). Our constructions raise macro balanced accuracy in predicting the generation factors of the 96 Process Discovery Contest 2023 models from 0.751 to 0.796 with PNRWPE, which nearly doubles accuracy on process loops, and to 0.830 with DA-PNGNN, which, without retuning, also improves net-to-tree retrieval top-1 accuracy on the self-supervised ProcRosetta benchmark by 4.1 to 5.9 points.
arXiv:2610.29722v1 Announce Type: cross
Abstract: Retrieval Augmented Generation (RAG) grounds large language models in external knowledge. Modern pipelines combine embedding, chunking, retrieval, reranking, query augmentation, context compression, and agentic verification, yet these techniques are typically evaluated one at a time. It remains unclear whether their isolated gains survive composition, whether retrieval quality and answer faithfulness favor the same design choices, and whether conclusions from small corpora hold at large scale. We pre-declare three hypotheses and introduce LASAGNA, an open-source framework for controlled RAG evaluation. We test 450 configurations across eight benchmarks and corpora ranging from 5K to 200K documents. Three findings emerge. First, individually strong techniques from different phases of a RAG pipeline do not necessarily compose: three retrieval techniques predict a +47% combined improvement but deliver only +17% when used together. Second, component gains stack differently for retrieval and faithfulness, and optimizing one can hurt the other. Third, the best composition changes as the corpus grows: the combination that wins on a small corpus may not remain best at large scale. These findings show that gains measured in isolation are not reliable predictors of realistic performance, and that new RAG techniques should be tested with the full surrounding stack. We call on researchers to do so and supply LASAGNA to simplify these experiments.
Ido Levy, Segev Shlomov, Leshem Choshen
arXiv:2610.29720v1 Announce Type: cross
Abstract: Spiking Neural Networks (SNNs) promise energy-efficient inference through sparse, event-driven computation, yet remain constrained on continuous, context-dependent tasks such as automatic speech recognition (ASR). A key bottleneck is the Leaky Integrate-and-Fire (LIF) neuron, whose membrane decay erases information across pauses and phonetic boundaries while it must both extract features and retain long-range context. Inspired by cortical separation of nonlinear filtering and somatic integration, we introduce the Spiking Ternary GRU (stGRU): a ternary-weight gated recurrent unit performs temporal filtering, while downstream Resonate-and-Fire (RF) neurons generate the binary spike stream driving the next block's event pathway. This makes binary event transmission a native training constraint rather than a separate deployment-time activation quantization step; together with ternary weights, learned projections avoid dense floating-point matrix MACs. Trained end-to-end on LibriSpeech-960, Small, Medium, and Large stGRUs reach 8.09%, 7.04%, and $6.44 \pm 0.17\%$ WER on test-clean without an external language model. To our knowledge, these are the first matrix-MAC-free spiking networks without a learned ANN sequence decoder to achieve single-digit WER on LibriSpeech. The architecture also achieves 10.88% test CER on Aishell-1 (9.28% on dev) when trained from scratch. Internally, trained networks develop a depth-graded hierarchy: shallow layers act as fast acoustic filters, while deep layers form slower semantic integrators whose latent representations segregate into part-of-speech manifolds and word-level spike events. Deep-layer firing rates follow lognormal distributions with a sparsity gradient, mirroring hierarchical processing observed in human cortex in vivo. Our biologically grounded architecture combines competitive ASR with favorable modeled compute and memory cost.
Pavlos Poulos, Katelyn Sadorf, Themos Stafylakis, Costas A. Anastassiou
arXiv:2610.29681v1 Announce Type: cross
Abstract: Pixel language models process text as rendered images instead of a finite vocabulary, which gives them strong cross-lingual transfer abilities. However, not much is known about how these abilities are influenced by larger-scale pretraining. In this paper, we train a family of MPIXEL models along three axes of variation: more languages, more scripts, and larger model capacity under fixed per-language compute. In evaluations on five tasks covering 83 languages, we find that scaling acts locally: each axis improves the added languages and scripts, while increased capacity mitigates the curse of multilinguality from pretraining on more languages. Transfer to unseen scripts improves with multilingual pretraining, but does not further improve with scaling. On typologically distant low-resource languages, our models outperform subword and character-level baselines across many writing systems. We also show that larger pixel models reserve more layers for visual processing, and that cross-lingual alignment weakens as more languages are added. Overall, our findings characterize how multilingual scaling improves pixel language models.
Ilker Kesen, Jenny Kunz, Kasra Malihi, Desmond Elliott
arXiv:2610.29677v1 Announce Type: cross
Abstract: Recursive self-improvement (RSI) describes a system that improves not only its behavior but also the process by which it improves. Recent digital agents test this idea by rewriting their own code and checking each version with executable tests. Bringing these mechanisms into the physical world requires learning from partial observations through costly trials, while accounting for changing operating conditions and potentially irreversible consequences. We position RSI within robot learning and trace pathways from improving robot capabilities to improving the processes that generate them. We examine how physical experience can strengthen these improvement mechanisms and when the resulting gains can support further self-improvement of the mechanisms themselves. Gains carry forward only when feedback addresses remaining learning needs, the receiving component can use the change, its value survives changes in tasks or hardware, and continued practice remains safe and affordable. Existing studies, concentrated in manipulation, support behavioral improvement, benefits to later learning, and procedure improvement. Some systems also change the improver's knowledge or tools, but the physical studies reviewed here have yet to isolate gains attributable to recursion. We synthesize these findings into evaluation principles and research directions for machines that, trial by trial, safely improve the way they improve.
Meng Luo, Zechen Bai, Shanqing Xu, Yanlin Li, Kaixin Li, Mengchen Qian, Weifeng Lu, Ran Zhang, Yingtian Zou, Ziyang Luo, Wei Chen, Hongzhan Lin
arXiv:2610.29669v1 Announce Type: cross
Abstract: LLM-generated records increasingly populate production information systems where they are treated as data assets subject to the same quality expectations as records from operational databases. A single such record can simultaneously satisfy and violate a quality rule: a grounded fact adjacent to a hallucination, a useful answer adjacent to a stereotype. Classical data cleaning cannot resolve this because the two judgments are incompatible over the same span; a single LLM judge cannot either, since it shares the training biases that produced the conflict. Existing interventions such as prompt engineering, chain-of-thought, and RLHF reduce surface error rates but provide no audit trail and cannot distinguish genuine remediation from blanket suppression. The question is whether a deterministic check over structured inter-agent records can catch the defects that referential checks alone miss. We present BiasGuard-D: two adversarial roles drawn from distinct model families exchange typed claim documents, a three-model quorum adjudicates by majority vote, and a combined referential-plus-semantic invariant validates the verdict. The semantic component fires on verdicts referential checks miss; removing the iterative loop drops invariant satisfaction sharply. The deliberation layer transfers from stereotype to hallucination remediation on HaluEval QA with only role-framing changes, raising right-answer recovery by 49 percentage points; the triage gate required a cross-family second auditor to maintain recall on objective hallucination. Every claim, vote, and instruction is stored as a typed record giving operators a provenance trail auditable under emerging AI regulations.
Kardelen Subasi, Jaros{\l}aw A. Chudziak
arXiv:2610.29663v1 Announce Type: cross
Abstract: Formulaic alpha factor mining searches for symbolic expressions that transform market data into predictive signals. Recent LLM-based evolutionary factor mining methods use large language models as semantic variation operators. Under the conventional LLM-EA paradigm, stochastic variation and fitness-based selection can leave the search weakly directed and concentrated around a narrow set of structurally similar factors. We argue that these limitations arise because current methods mainly organize search at the individual and population levels, leaving lineage-level control underused. A lineage connects successive factor variants through evolutionary descent. We propose LineageEvo, which uses lineage in two coupled forms of search control: (1) lineage-conditioned LLM variation, which distills Lineage-Scoped Search Experience into operator-specific priors and fuses them with global operator priors, providing persistent, lineage-relevant guidance for LLM generation; and (2) lineage-stratified search allocation, which balances factor quality against lineage concentration by distributing the search budget across lineages during evolutionary search. Together, these mechanisms make semantic variation more direction aware and prevent branches from dominating the evolution, thereby promoting the discovery of predictive and diverse factors. We evaluate LineageEvo on CSI 500 and S&P 500 in terms of factor predictiveness, portfolio performance, search efficiency, and lineage- and expression-level diversity. LineageEvo achieves the strongest predictive performance on both markets, while LSPS produces a more balanced lineage distribution and a structurally broader factor pool. The results support lineage as a useful intermediate unit for controlling LLM-based evolutionary factor search.
Xintong Liu, Chenkai Zhang, Yanzhao Ma, Peng Yang
arXiv:2610.29637v1 Announce Type: cross
Abstract: We present an AI-assisted mathematical addendum to Strategic Trip Planning: Striking a Balance Between Competition and Cooperation (Amar, 2018). We reconstruct selected relationships between strategic choice, cooperative stability, participant approval and enforcement. The thesis's Nash-to-core proposition is under-specified until outsider opportunities are stated. We verify two-person implications under fixed outsiders and explicit efficiency conditions. Under isolation, the original example has an empty TU core; its funded counterpart uses an explicit external subsidy. For a monotone resource model we characterize the exact financing gap. A finite negotiation procedure implemented in Lean is proved to terminate with participant approval, joint-cost non-worsening and local optimality against permitted approved moves. Supporting formalizations address bargaining geometry and regret-based efficiency. A resource-game counterinstance shows why monotonicity alone provides no uniform price-of-anarchy bound. Reproducible computations compare a documented heuristic reconstruction with the verified procedure on 44 source-based instances and 96 starting cases from four additional synthetic network families. Acceptance-matched heuristic and randomized pairwise-search controls contextualize the optimization results. The mathematical ingredients are established results; the contribution is a traceable reconstruction linking source statements, explicit assumptions, checked proofs, executable code and retained counterinstances. The study illustrates how AI-assisted investigation can turn engineering intuitions from legacy research into precise mathematical claims whose conditions and computational consequences can be inspected and reproduced.
arXiv:2610.29618v1 Announce Type: cross
Abstract: Object detection models for autonomous driving commonly experience substantial performance drops when deployed under adverse weather due to the domain shift between training data and real-world operating conditions. This degradation is especially evident when models trained on clear-weather images encounter foggy environments with reduced visibility and contrast. To address this challenge, we introduce FogTTA, an online test-time adaptation framework designed to improve the robustness of Transformer-based object detectors in fog. Using RF-DETR as the underlying object detector, FogTTA enables real-time adaptation to the streaming target domain without requiring source data or retraining. The framework follows a teacher-student design, where the deployed model serves as the teacher and generates pseudo labels from weakly augmented target inputs. These predictions are subsequently refined through non-maximum suppression and confidence filtering. The student model then learns from strongly augmented target sample using the Varifocal loss to mitigate pseudo-label noise. The teacher is updated via exponential moving averaging to ensure stable and continuous adaptation. Experiments show that FogTTA outperforms prior baselines, delivering improved detection accuracy and stability while maintaining real-time performance.
Ali Abedi, Q. M. Jonathan Wu, Ning Zhang, Shiqi Tian
arXiv:2610.29616v1 Announce Type: cross
Abstract: Early diagnosis of hepatocellular carcinoma is critical to preserve access to curative treatment options. The Liver Imaging Reporting and Data System (LI-RADS) provides a standardized framework for non-invasive diagnosis on multiphase computed tomography, based on major visual imaging features. However, these features may be difficult to assess consistently, particularly in small liver lesions. We developed dLI-RADS, an interpretable artificial intelligence method designed to estimate the probability of hepatocellular carcinoma from multiphase computed tomography images of manually segmented liver lesions, while remaining aligned with LI-RADS-related imaging concepts. dLI-RADS combines neural network-derived predictions with handcrafted quantitative imaging measurements reflecting LI-RADS major features and integrates these inputs using logistic regression. In this multicenter retrospective study, patients with multiphase computed tomography and at least one liver lesion were included, while lesions larger than 40 mm were excluded. Histology served as the reference standard for hepatocellular carcinoma, and a composite reference standard was used for non-hepatocellular carcinoma lesions. The lesion-level accuracy of dLI-RADS and LI-RADS were compared on the internal evaluation set using 10,000-repetition bootstrap non-inferiority tests, with 5% margins and significance levels. On the external test set, sensitivities were similarly compared. dLI-RADS was non-inferior to LI-RADS for lesion-level accuracy in the internal evaluation set, achieving 80% accuracy compared with 74% for LI-RADS (p = 0.04)...
Emma Sarfati, Alexandre B\^one, Pietro Gori, Sisi Yang, Marc-Michel Roh\'e, Fran\c{c}ois Nicolas, Jeong-Min Lee, Jeong Hee Yoon, Maxime Ronot, Isabelle Bloch, Christophe Aub\'e
arXiv:2610.29606v2 Announce Type: cross
Abstract: Automatic phenotype information extraction plays an important role in rare disease diagnosis, genotype-phenotype analysis, and precision medicine. However, accurately identifying phenotype concepts and determining their associations with specific patients remain challenging, particularly in full-text biomedical articles involving multiple patients and complex clinical descriptions. This paper presents an overview of CHIP 2026 Shared Task 1, which aims to promote the development of methods for patient-specific phenotype concept recognition from full-text biomedical literature. The task consists of two subtasks: full-text phenotype concept recognition and patient-specific phenotype association. For this evaluation, we used 200 annotated full-text biomedical articles from the PatientPheX dataset, containing 506 patients, 15,193 phenotype mentions, and 5,656 patient-phenotype associations. A total of 455 teams registered for the competition, with 189 and 103 valid submissions received on the Phase A and Phase B leaderboards, respectively. The best-performing system achieved an overall score of 0.7389 on the final test set, outperforming the baseline by 8.37 percentage points. The top-performing teams explored diverse approaches combining biomedical language models, large language models (LLMs), and ensemble strategies. The evaluation results highlight both the potential of these approaches and the remaining challenges in patient attribution and phenotype normalization from full-text biomedical literature. The post-evaluation phase remains open at https://tianchi.aliyun.com/competition/entrance/532512.
Xuanlyu Zhu, Feng Tian, Yang Zhong, Pengqi Zheng, Xiwen Bi, Ling Luo, Yuanyuan Sun, Jian Wang, Hongfei Lin
arXiv:2610.29605v1 Announce Type: cross
Abstract: Stochastic flow maps promise few-step sampling of stochastic differential equations (SDEs) by learning to directly jump between times along the solution path, yet training these models to learn this solution map remains difficult. The primary obstacle is the Brownian path itself: it is an infinite-dimensional object which needs to be passed to the neural network and is nowhere differentiable, which makes the implementation of derivative-based losses that power the state-of-the-art deterministic flow maps just out of reach. We identify two core design principles which address these issues: a) represent the Brownian path with a basis which carries higher-order local information, and b) train with an objective that forces the network to use the full representation of the path, not just the first order. To address this, we leverage the shifted Legendre polynomial expansion with a Wong-Zakai styled objective, unlocking derivative-based losses. Finally, we propose a recipe for fine-tuning large pre-trained flow models into strong stochastic flow maps. We ablate through this design space on several toy problems and use our findings to transform a large flow model into a strong stochastic flow map on ImageNet, achieving roughly a three-fold improvement in FD-DINOv2 over SSFM at four NFE.
Zander W. Blasingame, Antonio Franca, Raul Minan, Christian Koke, Niklas Rindtorff, Alexander Tong
arXiv:2610.29577v1 Announce Type: cross
Abstract: Many learning systems are performative: once deployed, their predictions change the data distribution on which future models are trained. In multi-agent settings, this feedback is routed through a network of interacting learners, so stability depends not only on the strength of performativity but also on who affects whom. We study repeated retraining in multi-agent performative prediction and identify a spectral threshold that separates stable learning from worst-case learning obstruction. Prior work often collapses cross-agent feedback into a scalar contraction constant, missing this network structure. We instead introduce the reflexivity matrix $\Gamma$, which records how strongly one agent's deployment can move another agent's best response, defined from per-agent gradient sensitivities and curvature parameters. The threshold occurs when the spectral radius of this matrix crosses one. Below the threshold, repeated retraining converges geometrically to a unique performatively stable equilibrium, with cumulative excess loss bounded uniformly in the time horizon. Above the threshold, we construct noisy supercritical instances in which every local-information learner incurs expected cumulative excess loss growing linearly for horizons up to order $1/(\rho(\Gamma)-1)$. Together, these results characterize the threshold behavior through upper and lower bounds and recover the single-agent scalar threshold from prior work as a special case.
Ahmed Mahrous, Roberto Di Pietro