Deterministic

LLM-based memory systems increasingly maintain facts that evolve over time, where a recurring failure is conflict resolution: when a fact has multiple contradictory values, which should the agent return? MemoryAgentBench (MAB; Hu et al., 2026) makes this explicit in its FactConsolidation task: facts are numbered, the counterfactual has the higher serial, and agents are told newer facts have larger serials. Yet every published system underperforms: HippoRAG-v2 reaches 54% on single-hop (FC-SH), BM25 48%, Mem0 18%, and the temporal KG Zep/Graphiti just 7%. Multi-hop is near-unsolved (at most 7% across 22 systems). We argue the bottleneck is the assembly step: baselines leave conflict resolution to LLM-mediated retrieval or generation rather than version-aware aggregation. A matched-setup comparison (same backbone, retrieval, chunking, TOP_K) shows that replacing the LLM-judgment answer pipeline with candidate-extraction plus Python max(serial) yields +10.8 points on FC-SH (gpt-4o-mini), widening from +8 at 6K to +21 at 262K. This is a whole-pipeline effect (resolver, prompt, format, and temperature vary jointly); isolating the resolver is future work. The recipe reaches 78.0% on FC-SH (gpt-4o-mini), 94.8% (gpt-4o), and 30.2% on FC-MH (gpt-4o-mini, rising to 51.5% with gpt-4o) via a per-hop deterministic extension of Self-Ask. At matched-262K, it beats HippoRAG-v2 by +28 points and the best published FC-MH result by +20. The implication is corrective for the subfield: the bottleneck on conflict resolution is assembly (post-retrieval aggregation), not storage. A LongMemEval knowledge-update check shows the mechanism ports from max(serial) to max(timestamp) but only ties LLM judgment (57.8% vs 64.4%, n=45): deterministic aggregation is the right primitive for current-value conflicts and must be composed with question-type-aware handling for broader memory QA.

Run-level pass rate overstates retry-free coverage by up to 17.8 percentage points -- and the gap is largest precisely for mid-performing systems. We investigate this accuracy--stability relationship in large language model (LLM) evaluation for deterministic text-conditioned generation, using programming tasks as a concrete testbed. Standard code-generation benchmarks emphasize single-run accuracy or eventual success under repeated sampling, but many deployment settings also require stability: consistent outcomes across repeated invocations under the same task description. We present a repeated-run evaluation protocol with metrics for run-level accuracy, retry-free coverage, and per-problem variability. On a recency-based benchmark of 100 LeetCode-style problems, we evaluate 16 models from five provider families under two prompt templates with five repeated runs per problem, yielding 16,000 evaluation instances. Although run-level pass rate and perfect stability rate are strongly correlated (r=0.985), pass rate consistently exceeds retry-free coverage -- a gap that reaches 17.8 percentage points and reverses model rankings even among closely matched systems. Prompt effects are model-dependent rather than uniformly beneficial. These results suggest that repeated-run stability analysis is a necessary complement to conventional accuracy reporting for deterministic text-conditioned generation tasks.

Large language models (LLMs) are increasingly being used to generate health text from structured records such as wearable time series, biomarkers, vitals, and care-management logs. For recurring health outputs, fluency is not enough: systems must remain faithful to source data, ground explanatory claims in available evidence, follow stated policies, emit machine-readable outputs, and run cheaply enough for repeated use. We ask which responsibilities in structured health generation should be deterministic computation rather than runtime LLM prompting. We introduce Think Fast, Talk Smart, a sleep-health insight pipeline in which deterministic code performs recurring analysis before one bounded LLM writer call. Across 280 user-nights and six models, achieves lower numeric error, lower instruction-compliance error, and lower end-to-end cost than structured zero-shot and few-shot one-call baselines. Layer replacement reveals contract-specific failures: LLM comparison raises numeric error, LLM ranking degrades policy selection, LLM attribution increases unsupported causal language, and an LLM-generated writer interface reintroduces errors even after upstream facts are deterministic. The results support a broader design rule: let code own recurring analysis, and let LLMs express verified facts within bounded interfaces.

In safety-critical robotics applications, guaranteed and practical uncertainty quantification (UQ) in perception is vital. Many existing works either offer no formal containment guarantee, rely on restrictive modeling assumptions, or focus only on pose estimation rather than a complete SLAM pipeline. This paper presents provably guaranteed UQ algorithms for 3D-3D landmark-based SLAM. The algorithms consist of three basic UQ modules: forward UQ for mapping, backward UQ for pose tracking, and pose compound. Each module produces a certified uncertainty set; when the input uncertainty bounds are deterministic, the output sets inherit deterministic guarantees, i.e., they provably contain the true poses and landmarks. Specifically, we use polytopes to represent uncertainty sets, enabling tractable computations and a unified treatment of pose uncertainty. To enhance algorithms' practical usability, we incorporate conformal prediction to calibrate measurement uncertainty from data with prescribed probability. Simulations and experiments demonstrate that the proposed algorithms provide both strong theoretical guarantees and practical usability. The code is open-sourced at https://github.com/LIAS-CUHKSZ/Polytopic-SLAM-Uncertainty-Quantification.

We construct a binary mixed-regime process with one deterministic textual regime and one random regime governed by an unobserved latent state. Even an ideal infinite-capacity sequence predictor that exactly recovers the text-only marginal law can become overconfident when the observed prefix is compatible with the wrong latent regime. The resulting entropy difference is not an ordinary optimization error; it is a sufficiency gap caused by marginalization over an unobserved state. We then formalize retrieval, tool use, and external grounding through an auxiliary binary signal with fidelity $γ\in [1/2,1]$. The resulting Bayesian update yields a contextual dominance threshold: a corrective signal reverses the posterior odds induced by the textual history exactly when its fidelity exceeds the text-only posterior weight assigned to the misleading regime. This threshold reduces, but does not generally eliminate, the sufficiency gap; complete closure requires perfect revelation of the relevant latent state or an equivalent verification mechanism. The analysis clarifies why temperature scaling cannot restore missing context, why grounding mechanisms must be both informative and learnably usable by the model, and why autonomous sequence models require structurally decoupled observers or verifiers in high-stakes domains.

We present MobileGym, a browser-hosted, lightweight, fully controllable environment for everyday mobile use, targeting interaction fidelity without replicating proprietary backends. It enables two capabilities previously out of reach for everyday apps: verifiable outcome signals through deterministic state-based judging over structured JSON state, and scalable online RL through low-cost parallel rollouts. The full environment state is captured, configured, forked, and compared as structured JSON, and a single server can host hundreds of parallel instances, with about 400 MB memory per instance and about 3 s cold start. A layered state model and a declarative task-definition framework keep state programmability and task creation practical at scale, and a single programmatic judging mechanism delivers both deterministic evaluation verdicts and dense RL rewards. The accompanying MobileGym-Bench provides 416 parameterized task templates, including 256 test and 160 train templates, over 28 apps, with deterministic judges and a structured AnswerSheet protocol that avoids free-text matching failures. In a Sim-to-Real case study, GRPO on Qwen3-VL-4B-Instruct gains +12.8 percentage points on the 256-task test set, and on a 59-task real-device signal subset, real-device execution retains 95.1% of the simulation-side training gain. Project page: https://mobilegym.github.io.

Recent work on recursive architectures has shown that tiny neural networks can be surprisingly powerful on structured reasoning tasks. The trick is to model reasoning trajectories with a latent dynamical system. We argue that the inference-time behaviour of these architectures is best understood as approximate inference over latent reasoning trajectories, with deterministic recursion as the one-particle, zero-noise limit. We make this view operational through guided stochastic exploration: stochastic perturbations of the reasoning dynamics propose neighbouring trajectories, and the model's existing early-stopping head reweights them online. The framework yields three label-free diagnostics: local stability, guide alignment, and cloud-token entropy. These predict, from inference traces alone, whether the procedure will help and which of its outputs to trust. On Sudoku-Extreme it lifts exact-solve accuracy from $85.9\%$ to $98.0\%$ without retraining; on Maze-Hard the diagnostics flag a misaligned guide, as validation performance later confirms. The same machinery thus characterises both when recursive reasoning has room to improve at the trajectory level and when the model's internal guide can recover it.

When a structured tool agent fails mid-execution, the runtime faces a dilemma: replaying the entire task is safe but wasteful, while restoring from a local checkpoint is efficient but can leave committed downstream work tied to an upstream history that no longer exists. This tension is acute in commitment-sensitive settings, where rollback targets a single failed instance yet downstream consumers have already acted on its output. Existing recovery approaches provide mechanical rollback but no criterion for whether a local restore remains semantically valid after downstream commitment. We formalize this gap as semantic recoverability and address it in DART, a modular runtime that localizes the failed instance, certifies semantically recoverable boundaries of that instance, aligns checkpoints to those boundaries, and selects an admissible restore point that preserves committed downstream work under dependency and effect constraints-or blocks otherwise. Across three LLM-driven domains and external validation on a LangGraph-based substrate, DART correctly recovers all evaluated commitment-sensitive cases where baseline local recovery fails, and a five-domain safety audit finds no unsafe admitted rollbacks. These results show that controller legality does not imply semantic validity, and that sound local recovery requires an explicit admissibility check.

Distributed LLM agent workflows should not be monitored as if they produced a single sequential log. In an asynchronous execution, a decision can only depend on events that are causally visible to the lifeline that makes it: an event that appears earlier in some log may still be unknown locally. We extend the ZipperGen agent-workflow framework with Causal Past Logic (CPL), a small past-time temporal logic for guards in conditionals and while loops. In addition to standard past-time modalities such as previous and since, a guard can inspect the latest causally visible event of another lifeline and selected variables stored there. The formula is a source-level guard: it is evaluated online by the owner lifeline and can influence control flow at runtime. We give a vector-clock monitor with latest-value views and prove that the locally computed monitor value coincides with the denotational semantics of the guard at the current event. Thus runtime verification becomes part of the coordination language itself, rather than a post-hoc check over an execution log.

Production LLM agents combine stochastic model outputs with deterministic software systems, yet the boundary between the two is rarely treated as a first-class architectural object. This paper names that boundary the stochastic-deterministic boundary (SDB): a four-part contract among a proposer, verifier, commit step, and reject signal that specifies how an LLM output becomes a system action. We argue that the SDB is the load-bearing primitive of production agent runtimes. Around this primitive, we organize agent runtime design into three concerns: Coordination, State, and Control. We present a catalog of six runtime patterns that compose the SDB differently across conversational, autonomous, and long-horizon agents: hierarchical delegation, scatter-gather plus saga, event-driven sequencing, shared state machine, supervisor plus gate, and human in the loop. For each pattern, we trace its lineage to distributed-systems concepts and identify what changes when the worker is stochastic. The paper contributes a five-step methodology for selecting runtime patterns, a diagnostic procedure that maps production failures to pattern weaknesses, and a failure mode called replay divergence, in which LLM-based consumers of a deterministic event log produce different downstream outputs under model-version or prompt changes. A stylized reliability decomposition separates per-call model variance from architectural momentum, motivating the claim that as model variance decreases, pattern choice and SDB strength become increasingly important levers for long-run reliability. We apply the methodology to five workloads and provide one runnable reference implementation for a 90-day contract-renewal agent.

Operators of safety-critical industrial processes increasingly rely on digital twins to screen control interventions, but such simulators rarely carry certified safety guarantees. Wastewater treatment plants exemplify the gap: operators face a daily safety-efficiency trade-off where aerating too little risks effluent violations and nitrous-oxide (N2O) spikes, and aerating too much wastes energy. We develop an explainable digital twin for aeration and dosing setpoints. CCSS-IX, the simulator, is a bank of interpretable locally linear state-space "experts" adaptively mixed by a context-aware gating network, building on a continuous-time regime-switching scaffold. A runtime decision layer applies conformal risk control to abstain, reopen, or return a falsifying temporal witness for any operator-proposed action that cannot be statistically certified. The artificial-intelligence contribution is twofold: an identifiable, context-conditioned structured surrogate that retains operator-readable dynamics, and a self-falsifying decision rule with finite-sample coverage guarantees. The engineering contribution is a validated, end-to-end decision-support pipeline, tested on a 1000-step slice of the Avedøre full-scale plant (42.6% sensor missingness, 2-minute sampling), the Agtrup/BlueKolding full-scale plant in Denmark, and the Benchmark Simulation Model No. 2 (BSM2) international benchmark, under a matched ten-seed protocol. The static structured ensemble lies within 0.78% root-mean-square error of an unconstrained black-box reference, and the adaptive variant within 1.08%. The calibrated reopen rule cuts aggregate two-plant regret by 43.6% at an unsafe-action cost weight of 4 and eliminates unsafe chosen actions on the BSM2 main slice. Event-aligned temporal witnesses prevent 93 of 187 false-safe N2O approvals, about 4.65x the dyadic baseline (paired McNemar p < 1e-21).

Large language models are increasingly deployed as automated judges to evaluate the strength of arguments. As this role expands, their legitimacy depends on consistency, transparency, and the ability to separate argumentative structure from rhetorical appeal. However, we show that holistic judging - a common LLM-as-a-Judge practice where a model provides a global verdict on a debate - suffers from substantial inter-model disagreement. We argue that this instability arises from collapsing a debate's complex interaction structure into a single opaque score. To address this, we propose GRASP (Gradual Ranking with Attacks and Support Propagation), a deterministic framework that aggregates stable local interaction judgments into a global ranking via a convergent attack--defense propagation operator. We show that local interaction judgments are more reproducible than holistic rankings in LLM-as-a-Judge evaluations, allowing GRASP to produce more consistent global rankings. We further show that GRASP scores do not correlate with human "convincingness" labels, highlighting a vital sociotechnical distinction: GRASP does not measure persuasion, factuality, or rhetorical appeal, but structural sufficiency - a defense-aware notion of argument robustness over the explicit interaction graph. Overall, GRASP offers a transparent and auditable alternative to holistic LLM judging.

Physical AI is being successfully applied to data which does not follow the traditional paradigm of independent and identically distributed (i.i.d.) samples. In fact, physical AI is often trained on data which is not random at all, and is instead derived from chaotic dynamical systems like turbulence. We aim to explain the empirical success of these methods using the example of generative adversarial networks (GANs), whose statistical learning theory under the i.i.d. assumption is generally well understood. We prove that it is possible, using an infinite-dimensional model of generative adversarial learning (GAL), to learn the invariant distribution of a sufficiently chaotic dynamical system from a single deterministically evolving time series of its states or measurements thereof, and give explicit rates for the convergence to the solution in terms of the Jensen-Shannon divergence.

In this study, we explore in depth a few under-studied topics at the intersection of uncertainty estimation and segmentation. Prior work has shown that the quality of uncertainty estimates can be very sensitive to a range of variables. As one of the main uses of uncertainty estimation is to help identify and deal with prediction errors in practical scenarios, any factors that affect this must be clearly identified. For example, do more challenging domains or different datasets and architectures result in worse performance when using uncertainty estimates? Can prior frames in a video sequence in fact provide useful uncertainty estimates comparable to other approaches? Is it possible to combine uncertainty estimation approaches, taking advantage of sample diversity, to get better estimates? Finally, when might it make sense to use an ensemble-based uncertainty estimate over a deterministic network? We address these questions by creating a framework for and executing a large scale study across many variables such as datasets, backbones, and downstream tasks, for both semantic and panoptic segmentation. We find that a) the more challenging task of panoptic segmentation usually results in worse performance while high performance variance between datasets and backbones indicates that generalization is not guaranteed, b) time series samples can be useful for specific configurations, but in many cases are not worth the cost, c) sample diversity shows the most promise in the downstream task of calibration, but otherwise fails to beat simpler alternatives, d) a deterministic approach is adequate for some downstream tasks, but ensembles allow for significant improvements if the right conditions can be achieved in deployment.

Deploying machine learning in regulated financial environments -- credit risk, fraud detection, and anti-money laundering -- exposes critical vulnerabilities in algorithmic reproducibility. While early financial ML addressed statistical challenges such as backtest overfitting, deep neural networks and Generative AI have introduced mechanical nondeterminism rooted in hardware and architecture. This survey provides a systems perspective on reproducibility failures across three modalities now dominant in financial AI: tabular models (post-hoc explanation variance), graph networks (stochastic sampling and temporal asynchrony), and LLM-based agentic workflows (batch-dependent divergence and trajectory drift). We supplement the literature analysis with first-party experiments on public financial datasets -- quantifying explanation rank instability in credit scoring, prediction flip rates in GNN-based fraud detection, and tensor-parallel-induced output divergence in LLM entity extraction. We propose a layered evaluation framework linking modality-specific metrics (RBO, D_cos, TDI, PSD) to audit readiness, and empirically validate the complementarity of logit-level and semantic-level determinism measures.

Modernizing legacy COBOL systems remains difficult due to scarce expertise, large and long-lived codebases, and strict correctness requirements. Recent large language model (LLM)-based modernization systems increasingly rely on agentic workflows in which the model controls multi-step tool execution. However, it remains unclear whether delegating execution control to the LLM improves correctness, robustness, or efficiency in structured software engineering workflows. We present a controlled empirical study of deterministic and LLM-controlled orchestration for COBOL-to-Python modernization. Using a unified experimental framework, we hold the language models, prompts, tools, configurations, and source programs constant while varying only the execution control strategy. This isolates orchestration as the sole experimental variable. We evaluate both approaches using functional correctness, robustness across repeated stochastic runs, and computational efficiency. Across multiple models, deterministic orchestration achieves comparable computational accuracy to LLM-controlled orchestration while improving worst-case robustness and reducing performance variability across runs. Deterministic execution also reduces token consumption by up to 3.5x, leading to substantially lower operational cost. These results suggest that, in structured modernization workflows with explicit validation stages, fixed execution policies provide more stable and cost-efficient behavior than fully agentic orchestration without reducing translation quality.

We present the Wristband Gaussian Loss, a deterministic batch loss for Gaussianizing point embeddings without sampling, KL terms, or iterative transport. Each $x \in \mathbb{R}^d$ is mapped to a direction $u = x/\|x\|$ and a CDF-transformed radius $t = F_{χ^2_d}(\|x\|^2)$ on the wristband $S^{d-1} \times [0,1]$. We prove (and machine-verify in Lean~4) that for $d \ge 2$ the pushforward wristband map equals $σ_{d-1} \otimes \mathrm{Unif}[0,1]$ iff the source is $\mathcal{N}(0, I_d)$, and that the Neumann-reflected wristband repulsion energy is uniquely minimized at the uniform target. We compute this reflected-kernel objective in two ways: a nearest three-image pairwise truncation at $O(N^2 d)$, and a spectral Neumann path joining angular and radial Mercer modes (spherical-harmonic and cosine) at $O(N d K)$, with empirically matched gradients. A 1D Wasserstein radial term and a moment penalty serve as finite-sample accelerators with the same optimum, and Monte-Carlo null calibration turns the components into a single standardized statistic. We evaluate direct point-cloud Gaussianization with a calibrated barycentric $W_2$ score: a deterministic Gaussian reference batch is built by recursive Hungarian averaging, with each method reported as a $z$-score against same-size Gaussian batches. On the axis-uniform X benchmark, Wristband is competitive in 2D and gives the best 10D score. On a harder radial--angular-copula impostor whose Gaussian radial and angular marginals are correct but dependent, Wristband gives the best 10D and 128D scores. Coupled with learnable-key Euclidean attention and exact invertible flows, the resulting Deterministic Gaussian Autoencoder delivers a Gaussian-latent interface for counterfactual sampling with independent factors and a context/residual construction for dependent factors.

On-policy distillation (OPD) is widely used for LLM post-training. When pushed with a reward-extrapolation coefficient lambda > 1, the student can lift past the teacher in domain, but past a threshold lambda* the same step violates the output contract on structured-output tasks. In a single-position Bernoulli reduction, we derive a closed-form base-relative clip-safety threshold lambda*(p,b,c) determined by three measurable quantities: the teacher modal probability, the warm-start mass, and the importance-sampling clip strength. Above lambda*, the extrapolated fixed point exits the clip-safe region, changing training from format-preserving to format-collapsing. We extend the rule to calibrated K-ary listwise JSON tasks where a single binding equivalence class dominates the output contract and SFT retains parse headroom. On Amazon Fashion, three pre-registered tests--a fine-grid cliff interval, a budget-extension test, and a small-clip cross-prediction--fall within their locked prediction windows, with the small-clip value matching the closed-form prediction below grid resolution. Operating just below lambda*, ListOPD brings a 1.7B Qwen3 student to in-domain parity with an 8B-SFT baseline at one-fifth the parameters. The gain is driven primarily by format adherence: NDCG@1 on parsed outputs remains flat across lambda, while parse validity sharply changes at the predicted boundary. The cliff diagnostic is rubric-independent, whereas the parity claim uses a Gemini-graded rubric and inherits that evaluator's exposure.

Mazocarta is a seeded procedural tactical deckbuilder implemented in Rust, compiled to WebAssembly for browser play, and executable natively for simulation. Its primary technical contribution is not the invention of a new deckbuilding genre, but the construction of an instrumented game-development reference artifact: the same rules engine supports interactive play, native command-line simulation, automated end-to-end tests, save/load fixtures, and local-area multiplayer. This paper describes Mazocarta's architecture, deterministic run model, reproducible balance probes, and QR-mediated WebRTC pairing for local multiplayer. An evaluation snapshot over 1,000 deterministic seeds shows that the simulation pipeline can produce reproducible development signals. In the evaluated configuration, single-player and two-player autoplay win rates were 36.1% and 34.9% over 1,000 deterministic seeds, respectively. These rates are not presented as final player-facing balance metrics, but as repeatable probes for future balance shifts and regressions. Mazocarta is positioned as a playable open-source reference artifact for instrumented game development: deterministic regression checks, automated playtesting workflows, balance probes for game mechanics, and browser-native local multiplayer all exercise one shared production rules core.

Evaluating Computer Use Agents (CUAs) on interactive environments is fraught with methodological pitfalls that the field has yet to systematically address. We show that a 1MB replay script that blindly executes a recorded action sequence without ever observing the screen outperforms frontier models on prominent static benchmarks, and prove that its expected success rate is exactly equal to the source agent's pass@k in deterministic environments. We trace this and other failures to two root causes: non-principled environment design (static, unsandboxed, or unreliably verified environments) and non-principled evaluation methodology (naive aggregation and misuse of pass@k for stateful UI interactions). To address the first, we propose PRISM, five design principles for CUA environments (privileged verification, realistic environments, integrity-checked configurations, sandboxed execution, and multifactorial variability) and instantiate them in DigiWorld, a benchmark of 15 realistic sandboxed mobile applications able to evaluate agents in over 3.2 million verified unique configurations. To address the second, we develop an aggregation framework pairing Wilson score intervals with hierarchical bootstrap, producing confidence intervals that correctly account for the nested structure of CUA benchmarks, as we empirically demonstrate. All together, we show that principled environment design and rigorous evaluation methodology are not optional refinements but prerequisites for meaningful CUA research.

Robots operate under significant uncertainty, from quantifiable noise to unquantifiable unknowns, and must account for strict operational constraints, such as limited resources. In this paper, we consider the problem of synthesizing robust strategies to guide a robot's actions in fulfilling a given task, while ensuring the system never exhausts its resources. To solve this problem, we first model the robotic system as a Consumption Markov Decision Process with Set-valued Transitions(CMDPST), a unified framework modelling nondeterministic actions, quantifiable and unquantifiable uncertainty, and resource consumption. Then, we combine the CMDPST with the task specification, expressed as a Linear Temporal Logic over finite traces (LTLf ) formula. Lastly, we address the resource constrained optimal robust strategy synthesis problem, which aims to synthesize a strategy that maximizes the probability of satisfying the LTLf objective without resource exhaustion. Our solution involves two techniques: a direct unrolling-based method and a more efficient, optimized approach that leverages state-space pruning for better performance. Experiments on a warehouse transportation network show the effectiveness of the proposed solutions.

LLM agents that operate over long context depend on external memory to accumulate knowledge over time. However, existing methods typically store each observation as a single deterministic conclusion (e.g., inferring "API~X failed" from temporary errors), even though such observations are inherently partial and potentially ambiguous. By committing to one conclusion and discarding uncertainty, these methods introduce self-reinforcing error: the agent acts on the stored conclusion, never revisits alternatives, and reinforces the conclusion over time. To address this issue, we propose BeliefMem, which shifts the memory paradigm from committing to a single conclusion per observation to retaining multiple candidate conclusions with their probabilities. Concretely, BeliefMem stores the candidate conclusions as separate memory entries, each carrying a probability that is updated via Noisy-OR rules as new observations arrive. At retrieval, all candidates surface together with their probabilities, keeping alternatives visible to the agent. Since each conclusion in memory retains its probability, BeliefMem preserves the uncertainty that the deterministic paradigm discards, enabling the agent to act with high confidence on well-evidenced knowledge while retaining the capacity to update its confidence when new evidence arrives. Empirical evaluations on LoCoMo and ALFWorld benchmarks show that, even with limited data, BeliefMem achieves the best average performance, remarkably outperforming well-known baselines. More broadly, such probabilistic memory produces substantial gains and explores a new direction for agent memory in partially observable environments.

This study presents a novel deterministic optimization algorithm based on a special variant of the Linear Congruential Generator (LCG). While conventional algorithms generally operate within the search space, the introduced technique follows a two-level architecture. In particular, an external loop that adaptively balances between exploration and exploitation, while the internal loop evaluates solutions. It is motivated by the intrinsic structure of the generator, the reason behind naming it the Structured Linear Congruential Generator (S- LCG). which enjoys a number of unique characteristics as follows: 1) a memoryless scheme, which ensures non-overlapping sequences based on distinct seeds, thus ensuring no evaluation redundancy; 2) bit splitting representation, which converts LCG states into multi-dimensional points to overcome the Marsaglia lattice effect; 3) adaptive exploration-exploitation of the generator space, which leads to implicit optimization of the surrogate smooth objective function; and 4) constant information gathering speed to avoid the problem of premature convergence. Extensive testing on 26 benchmark functions across dimensions d = 2 to 30 demonstrates that S-LCG comes within 1% of the global optimum in 83.3% of 138 cases (100% at d = 2, 81.2% at d = 30) while the nearest competitor GA achieved 75.4%. Statistical validation shows that S-LCG outperforms eight cutting-edge binary algorithms. Furthermore, its practical value is confirmed by validation on three constrained engineering design problems. In the end, S-LCG offers an optimization framework that is strictly reproducible and requires only one sensitive parameter to be tuned.

Large Language Models (LLMs) have demonstrated strong capabilities in natural language understanding and reasoning. However, their ability to perform exact, deterministic computation remains unclear. In this work, we systematically evaluate multiple prompting strategies, including Chain-of-Thought (CoT), Least-to-Most decomposition, Program-of-Thought (PoT), and Self-Consistency (SC), on tasks requiring precise and error-free outputs, including binary counting, longest substring detection, and arithmetic evaluation. To support this study, we introduce a synthetic dataset with diverse natural language instructions, enabling controlled evaluation of exact computation across multiple task types. Our results show that standard prompting methods achieve only moderate accuracy on sequence-based tasks. CoT provides limited improvement, while Least-to-Most suffers from error accumulation. In contrast, PoT achieves perfect accuracy by generating executable code and delegating computation to an external interpreter. Self-Consistency improves robustness through majority voting, but incurs substantial computational overhead. We further train a small domain-specific model (CodeT5-small) to generate executable programs, which achieves perfect accuracy on held-out synthetic test data across all tasks with minimal training cost. Overall, our findings suggest that LLMs may simulate reasoning patterns rather than reliably perform exact symbolic computation. For deterministic tasks, combining LLMs with external tools or using specialized models provides a more reliable and efficient solution.

Agentic systems involved in high-stake decision-making under adversarial pressure need formal guarantees not offered by existing approaches. Motivated by the operational needs of security operations centers (SOCs) that must configure endpoint detection and response (EDR) policies under adversarial pressure, we present a tool-mediated architecture: LLM agents use deterministic tools (Stackelberg best-response, Bayesian observer updates, attack-graph primitives) and select from finite action catalogs enforced at the tool-output interface. A composite Lyapunov function machine-checked in Lean 4 with zero sorry certifies controllability, observability from asymmetric sensor data, and Input-to-State Stability (ISS) robustness under intelligent adversarial disturbance, with two corollaries extending the certificate to any controller or adversary from the catalogs. On 282 real enterprise attack graphs, the claims hold with margin. On paired offensive/defensive telemetry, a tool-mediated Claude Sonnet 4 controller reduces the attacker's expected payoff (game value) by 59% relative to a deterministic greedy baseline, with zero variance across 40 runs at four temperatures. A Claude Haiku 4.5 controller converges to suboptimal game values but stays catalog-bounded over an additional 40 runs, demonstrating that architectural stability is not dependent on the controller capability. The LLM agent's non-determinism furthers creative exploration of strategies, while the tool-mediated architecture ensures system stability.

Automated planning traditionally assumes that all aspects of a planning task (initial state, goals, and available actions) are fully specified in advance, an approach well-suited to domains with fixed rules and deterministic execution. However, real-world planning often requires flexibility, allowing for deviations from the original task parameters in response to unforeseen circumstances or to improve outcomes. This paper surveys existing works on counterfactual reasoning in automated planning, categorizing them by what elements are changed, when the reasoning is triggered, and why and how these changes are made. We conclude by discussing key findings and outlining open research questions to guide future work in this area.

The Object-Oriented Method for Requirements Authoring and Management (OOMRAM) is a requirements reuse framework that relies on exact identifier matching and rigid templates, limiting its ability to adapt specifications across diverse contexts. While Large Language Models (LLMs) offer the flexibility to overcome this bottleneck, they introduce the risk of generating structurally invalid or inconsistent requirement combinations. To address this tension, we present a neuro-symbolic multi-agent system that re-conceptualizes requirements reuse as a Model-Driven Elicitation process. In this paradigm, an LLM serves as a non-deterministic heuristic for traversing a deterministic domain model represented by a formal OOMRAM requirement lattice. A deterministic, symbolic validator enforces all structural constraints within the agent loop, effectively eliminating hallucinated requirement combinations by construction. Evaluated on an autonomous benchmark across two application families, our system achieves 100% requirement coverage and a constraint-violation rate of only 0.2%. Although the F1-score against a single gold standard is moderate (0.47-0.51), every generated specification is structurally valid and satisfies all mandatory domain requirements. The model-agnostic implementation scales to larger lattices via subgraph navigation and provides transparent audit trails for regulatory compliance.

Large language models (LLMs) accelerate software development but often exhibit instability, non-determinism, and weak adherence to development discipline in unconstrained workflows. While test-driven development (TDD) provides a structured Red-Green-Refactor process, existing LLM-based approaches typically use tests as auxiliary inputs rather than enforceable process constraints. We present an AI-native TDD framework that operationalizes classical TDD principles as structured prompt-level and workflow-level governance mechanisms. Extracted principles are formalized in a machine-readable manifesto and distributed across planning, generation, repair, and validation stages within a layered architecture that separates model proposal from deterministic engine authority. The system enforces phase ordering, bounded repair loops, validation gates, and atomic mutation control to improve stability and reproducibility. We describe architecture and discuss encoding software engineering discipline directly into prompt orchestration, which we think offers a promising direction for reliable LLM-assisted development.

Enterprise SLM deployment faces epistemic asymmetry: small models cannot self-correct reasoning errors, while frontier LLMs incur prohibitive costs and data sovereignty risks at scale. We propose Semantic Gradient Descent (SGDe), a teacher-student framework that compiles agentic workflows into discrete execution plans--DAG topologies, system prompts, and deterministic code. The trailing e distinguishes this discrete, compilation-based approach from stochastic gradient descent. Operating in discrete semantic space, a frontier teacher generates natural-language critiques that serve as directional gradients to iteratively refine the SLM's workflow artefacts. We formalise SGDe under PAC learning, establishing sample-complexity bounds that enable convergence with as few as three training examples by leveraging the teacher as a statistical prior. On an adversarially synthesized GSM-Hard test set, compiled workflows achieve 91.3% accuracy at m=5 and 99.3% at m=3--a +26.3% to +34.3% absolute gain over state-of-the-art prompt optimisers. Within harness engineering, SGDe treats deterministic code placement (which subtasks to delegate to Python versus retain as LLM calls) as a trace-driven, per-node optimisation target, generalising static whole-problem offloading in PAL and PoT. The teacher compiles two deterministic structures: capability offloading (delegating subtasks to Python when the SLM is unreliable) and structural consensus (wrapping variance-sensitive steps in fan-out/fan-in subgraphs with deterministic voting).

Large Language Models produce a controllability gap in safety-critical engineering: even low rates of undetected constraint violations render a system undeployable. Current orchestration paradigms suffer from sycophantic compliance, context attention decay, and stochastic oscillation during self-correction. We introduce the Convergent AI Agent Framework (CAAF), which transitions agentic workflows from open-loop generation to closed-loop fail-safe determinism via three pillars: (1) Recursive Atomic Decomposition with physical context firewalls; (2) Harness as an Asset, formalizing domain invariants into machine-readable registries enforced by a deterministic Unified Assertion Interface; and (3) Structured Semantic Gradients with State Locking for monotonic non-regression. This paper makes two core claims. First, an industrialization thesis: once domain invariants are formalized as an executable Harness, the Harness itself becomes a first-class enterprise asset that compounds in value as foundation models commoditize, and CAAF's ability to deliver its reliability on commodity-tier models makes fully self-hosted, on-premises deployment architecturally feasible for regulated sectors where cloud APIs are not an option. Second, an architectural claim supported by ablation: CAAF's three pillars address complementary failure surfaces and none alone closes the controllability gap at commodity cost. The paper contributes entirely at the orchestration and industrialization layer. Evidence across two complementary benchmarks, three-tier UAI ablations, multi-agent baselines, and a closed-source commodity family replicated by two independent open-weight families, is reported in the body.

Traffic forecasting is a challenging spatio-temporal modeling task and a critical component of urban transportation management. Current studies mainly focus on deterministic predictions, with limited considerations on the uncertainty and stochasticity in traffic dynamics. Therefore, this paper proposes an elegant yet universal approach that transforms existing models into probabilistic predictors by replacing only the final output layer with a novel Gaussian Mixture Model (GMM) layer. The modified model requires no changes to the training pipeline and can be trained using only the Negative Log-Likelihood (NLL) loss, without any auxiliary or regularization terms. Experiments on multiple traffic datasets show that our approach generalizes from classic to modern model architectures while preserving deterministic performance. Furthermore, we propose a systematic evaluation procedure based on cumulative distributions and confidence intervals, and demonstrate that our approach is considerably more accurate and informative than unimodal or deterministic baselines. Finally, a more detailed study on a real-world dense urban traffic network is presented to examine the impact of data quality on uncertainty quantification and to show the robustness of our approach under imperfect data conditions. Code available at https://github.com/Weijiang-Xiong/OpenSkyTraffic

Learned action policies are increasingly popular in sequential decision-making, but suffer from a lack of safety guarantees. Recent work introduced a pipeline for testing the safety of such policies under initial-state and action-outcome non-determinism. At the pipeline's core, is the problem of deciding whether a state is safe (a safe policy exists from the state) and finding faults, which are state-action pairs that transition from a safe state to an unsafe one. Their most effective algorithm for deciding safety, TarjanSafe, is effective on their benchmarks, but we show that it has exponential worst-case runtime with respect to the state space. A linear-time alternative exists, but it is slower in practice. We close this gap with a new policy-iteration algorithm iPI, that combines the best of both: it matches TarjanSafe's best-case runtime while guaranteeing a polynomial worst-case. Experiments confirm our theory and show that in problems amenable to TarjanSafe iPI has similar performance, whereas in ill-suited problems iPI scales exponentially better.

It is well known that computing a minimum deterministic finite automaton consistent with a given set of positive and negative examples is NP-hard. Previous work has identified conditions on the input sample under which the problem becomes tractable or remains hard. In this paper, we study the computational complexity of the case where the input sample is prefix-closed. This formulation is equivalent to computing a minimum Moore machine consistent with observations along its runs. We show that the problem is NP-hard to approximate when the sample set consists of all prefixes of binary strings. Furthermore, we show that the problem remains NP-hard as a decision problem even when the sample set consists of the prefixes of a single binary string. Our argument also extends to the corresponding problem for Mealy machines.

Why do some physical systems possess consciousness, while others do not? A scientific theory of consciousness must explain differences in system behavior in terms of well-defined internal mechanisms. However, many existing approaches introduce higher-level structural or informational descriptions without specifying how these structures contribute to the generation of behavior, raising the concern that they may become theoretically ineffective.A further difficulty arises from the status of causation. Attempts to introduce causally effective mental states appear to conflict with physical theory, while strictly physicalist accounts risk excluding higher-level causation altogether. We argue that this dilemma stems from a conflation of physical determination with causation. To address this issue, we distinguish between two complementary descriptive frameworks: the physical stance and the causal stance. While the physical stance represents systems in terms of state evolution, the causal stance introduces asymmetric relations that enable the explicit representation of internal mechanisms. We show that causal descriptions provide a more constrained and informative representation of internal structure and cannot, in general, be reconstructed from physical descriptions alone. Within this framework, we define mental causation in terms of intrinsic causes and propose the Dual-Laws Model (DLM), which explicitly implements whole-to-parts causal mechanisms. This approach provides a principled way to model the causal role of consciousness without violating physical determinism.