A major challenge in AFL pertains to how DCs select and bid for DOs. Existing methods are generally static, making them ill-suited for dynamic AFL markets. To address this issue, we propose the Reinforcement Learning-based Bidding Strategy for DCs in Auction-based Federated Learning (RLB-AFL). We incorporate historical states into a Deep Q-Network to capture sequential information critical for bidding decisions. To mitigate state space sparsity, where specific states rarely reoccur for each DC during auctions, we incorporate the Gaussian Mixture Model into RLB-AFL.

A major challenge in AFL pertains to how DCs select and bid for DOs. Existing methods are generally static, making them ill-suited for dynamic AFL markets. To address this issue, we propose the R}einforcement Learning-based Bidding Strategy for DCs in Auction-based Federated Learning (RLB-AFL). We incorporate historical states into a Deep Q-Network to capture sequential information critical for bidding decisions. To mitigate state space sparsity, where specific states rarely reoccur for each DC during auctions, we incorporate the Gaussian Mixture Model into RLB-AFL.

For example, images from two different satellites may both contain RGB channels, but the remaining channels can be different for each imaging source.

B.7 Additional Details on the Running Time In this section, we provide additional details on the running time of the algorithms.

The widespread adoption of language models (LMs) has caused a huge surge in demand for GPUs. Training large LMs requires tens of thousands of GPUs and housing them in the same datacenter (DC) is a challenge due to many constraints including availability of peak power. We focus on training such models across multiple DCs connected via the Wide-Area-Network (WAN). We built Atlas that speeds up the training time using novel workload-aware temporal bandwidth sharing and other design choices. While Atlas improves the training time, it does not completely eliminate the bubbles (idle GPU cycles). We built BubbleTea that runs prefill-as-a-service (part of LM inference) during the bubbles thus improving the GPU utilization without any impact on training. Compared to state-of-the-art designs, Atlas and BubbleTea together achieve up to 17x faster training, and up to 94% GPU utilization. The code will be open-sourced.

For example, images from two different satellites may both contain RGB channels, but the remaining channels can be different for each imaging source.

B.7 Additional Details on the Running Time In this section, we provide additional details on the running time of the algorithms.

In distributed multi-agent systems, correctness is often entangled with operational policies such as scheduling, batching, or routing, which makes systems brittle since performance-driven policy evolution may break integrity guarantees. This paper introduces the Deterministic Causal Structure (DCS), a formal foundation that decouples correctness from policy. We develop a minimal axiomatic theory and prove four results: existence and uniqueness, policy-agnostic invariance, observational equivalence, and axiom minimality. These results show that DCS resolves causal ambiguities that value-centric convergence models such as CRDTs cannot address, and that removing any axiom collapses determinism into ambiguity. DCS thus emerges as a boundary principle of asynchronous computation, analogous to CAP and FLP: correctness is preserved only within the expressive power of a join-semilattice. All guarantees are established by axioms and proofs, with only minimal illustrative constructions included to aid intuition. This work establishes correctness as a fixed, policy-agnostic substrate, a Correctness-as-a-Chassis paradigm, on which distributed intelligent systems can be built modularly, safely, and evolvably.

Common evaluation paradigms for language models focus on scoring single responses through accuracy metrics or proper scoring rules, failing to capture the full richness of a model's belief state. Recent work illustrates that language models hallucinate in-part because they are optimised to be good test-takers under binary scoring schemes that reward any answer over abstention. While this insight naturally leads to penalty-based approaches, they ignore crucial distinctions in how models distribute uncertainty, for example between hedging toward incorrect answers versus hedging toward "I don't know" responses. A novel evaluation metric, the Distributional Correctness Score (DCS), is introduced to solve this problem, i.e., of not considering a model's entire probability distribution over answer choices. DCS naturally distinguishes between harmful overconfidence in wrong answers and uncertainty expressed through abstention, providing scores in an interpretable default range. Through theoretical analysis and illustrative examples, DCS is demonstrated to offer a more nuanced and aligned evaluation paradigm that incentivises models to express genuine uncertainty rather than guessing. Adapting 12 existing evaluation benchmarks to DCS's variants and measuring performance on six language models reveals that for half of the tested benchmarks scores are negative across all tested models, indicating significant tendencies towards hallucination. Evaluation of language models has commonly focused on whether they produce'correct' or desired outputs in response to given inputs or instructions, as measured using accuracy or probability-based scoring rules that account for confidence in model predictions. However, the paradigm of focusing on a single answer fundamentally misses a critical aspect of evaluating performance: how models distribute their beliefs across the space of possible responses, including the possibility of abstaining from answering in conditions of uncertainty. Recent work (Kalai et al., 2025) provides compelling evidence that language model'hallucinations' persist in-part due to the socio-technical problem of flawed evaluation metrics. Under traditional binary scoring - where correct answers receive a positive score (maximally 1 for perfect correctness), any response like "I don't know" (IDK) receives 0, and incorrect answers also receive 0 - the optimal strategy for any rational agent is to always guess rather than abstain, even when confidence in the guess is minimal. This creates a systematic bias in our evaluation paradigms toward overconfident responses and offers a socio-technical explanation for why language models persist in making confident assertions about uncertain information, i.e., 'hallucinate'.

Background: Emerging reports of "AI psychosis" are on the rise, where user-LLM interactions may exacerbate or induce psychosis or adverse psychological symptoms. Whilst the sycophantic and agreeable nature of LLMs can be beneficial, it becomes a vector for harm by reinforcing delusional beliefs in vulnerable users. Methods: Psychosis-bench is a novel benchmark designed to systematically evaluate the psychogenicity of LLMs comprises 16 structured, 12-turn conversational scenarios simulating the progression of delusional themes(Erotic Delusions, Grandiose/Messianic Delusions, Referential Delusions) and potential harms. We evaluated eight prominent LLMs for Delusion Confirmation (DCS), Harm Enablement (HES), and Safety Intervention(SIS) across explicit and implicit conversational contexts. Findings: Across 1,536 simulated conversation turns, all LLMs demonstrated psychogenic potential, showing a strong tendency to perpetuate rather than challenge delusions (mean DCS of 0.91 $\pm$0.88). Models frequently enabled harmful user requests (mean HES of 0.69 $\pm$0.84) and offered safety interventions in only roughly a third of applicable turns (mean SIS of 0.37 $\pm$0.48). 51 / 128 (39.8%) of scenarios had no safety interventions offered. Performance was significantly worse in implicit scenarios, models were more likely to confirm delusions and enable harm while offering fewer interventions (p < .001). A strong correlation was found between DCS and HES (rs = .77). Model performance varied widely, indicating that safety is not an emergent property of scale alone. Conclusion: This study establishes LLM psychogenicity as a quantifiable risk and underscores the urgent need for re-thinking how we train LLMs. We frame this issue not merely as a technical challenge but as a public health imperative requiring collaboration between developers, policymakers, and healthcare professionals.