Counter Turing Test

We report the results of a Turing Test conducted in Finland in the Finnish language. Because languages and cultural contexts are unevenly represented in LLM training data, we expected the model (ChatGPT 5.2) to perform worse in a Finnish-language Turing Test than in previously studied English-language US contexts. We also present model-generated role prompting as a replicable technique for conducting comparative LLM-based Turing Tests designed to improve construct validity. Contrary to our expectations, the LLM passed the Finnish Turing Test. A prominent source of error was participants' reliance on linguistic cues, particularly colloquial Finnish, as markers of human authorship. We reframe the Turing Test from a test of intelligence to a comparative method for examining whether an AI system can display credible membership in a particular social world. Because its outcome reflects model capabilities, prompted identity, insider competence among human participants, and their AI literacy, the method provides a useful probe of the human-machine boundary across domains.

We present Turing-20B-A2B, a 20B-parameter Mixture-of-Experts language model that activates approximately 2B parameters per token, designed for long-context and latency-sensitive physical AI applications. The model adopts Quantile Routing in a dynamic top-k configuration, enabling token-adaptive expert allocation while maintaining balanced expert utilization and a controlled average compute budget. During deployment, we further apply capacity-constrained routing to prompt prefill for more regular and efficient expert execution, while retaining dropless routing during pretraining. Turing-20B-A2B also employs a hybrid attention architecture that combines Lightning Attention with a small number of full-attention layers for efficient long-context modeling. The model is pretrained with a progressive three-stage curriculum and extended to a native context length of 128K through continued pretraining, with further inference-time extension to 512K using YaRN. Despite its compact active-parameter budget, Turing-20B-A2B achieves, at the base-model stage, overall general capability exceeding Qwen3-8B Base and approaching Qwen3.5-9B Base, while maintaining strong long-context performance and favorable prefill-latency scaling. These results demonstrate an effective balance among model capability, long-context scalability, and practical inference efficiency.

Self-improving agents seek to reduce the human engineering effort behind AI systems by enabling them to evolve and self-improve their performance over time. Recently, methods like the Darwin Gödel Machine and the Huxley Gödel Machine have been proposed which enable open-ended, recursive self-improvement through self-reference where a coding agent edits its own code. Such self-referential self-improvement methods require that the competence required to perform the task coincides or aligns well with the competence required for self-modification which is the case for coding tasks. For domains or tasks, which do not satisfy the alignment needed, self-referential self-improvement is not available. In such cases, it is possible to adapt the above algorithms to other tasks by removing the self-referential aspect or introducing explicit self-modification of a meta-agent -- both computationally expensive, relying on population or self-modification search over many candidate agents. For planning tasks with explicit constraints, we propose a far cheaper alternative. We introduce SBCO (Self-supervised Block Coordinate Optimizer), a verifier-grounded harness optimizer in the same closed-loop, improve-from-experience family as the Gödel-machine methods, but self-supervised rather than self-referential. Given an agentic harness, SBCO learns a decomposed bank of verifiers and a harness policy via approximate block coordinate ascent, improving the agent's outputs from its own graded feedback---with a fixed meta-agent and no human labels. Across two domains SBCO matches or exceeds a customized self-modifying baseline while using 4-5.5 times less compute budget.

Self-improving coding agents that iteratively rewrite their own source code have demonstrated impressive performance on coding tasks. However, existing solutions generally derive self-modification from a single failure trajectory at a time, overlooking rich comparative signals available in the agent's expanding archive of past attempts. According to Mendelian principles of controlled inheritance, we introduce Mendel Gödel Machine (MGM). In addition to the general single-trajectory clonal mutation, MGM includes two new types of self-modification that better utilizes evidences accumulated: the reaction-norm mutation edits an agent based on its trajectories on multiple tasks simultaneously, and the cross-lineage hybridization edits an agent using the trajectory of a reference agent from another lineage on the same task. Under an additive fitness landscape model, we prove theoretically and demonstrate via controlled surrogate simulation that the new strategies facilitate a faster and better convergence over single-trajectory baselines. Experiments on SWE-bench and Polyglot confirm MGM's consistent improvement in performance, efficiency, and generalizability.

This paper examines Turing's 1948 report, "Intelligent Machinery", as an important conceptual source for the later imitation games. Its first contribution is to identify and integrate the design concepts underlying the 1948 chess-based imitation game: the possibility that intelligent machines may make mistakes, the exclusion of irrelevant physical features, the role of the human judge, and Turing's claim that intellectual activity consists mainly of search. The paper's second contribution is to argue that restricting the human contestant to a rather poor chess player increases the role of intellectual search and makes human behaviour more comparable to machine behaviour. This interpretation presents the 1948 game as a human-approximates-machine game and suggests that the imitation game framework can be used not only to ask whether machines imitate humans, but also to examine when human intelligence becomes machine-like under specific task constraints.

Whether large language models perform genuine algorithmic reasoning or mere pattern completion is hard to test, because most benchmarks lack a ground truth for correct inductive inference. We introduce F-ICL, an in-context-learning benchmark that supplies one exactly. Using the Turing-complete machine F, complement-symmetrised into sF to remove output-polarity bias, we exhaustively enumerate all 1.5 billion programs of length $L\le13$ and compute the Bayes-optimal posterior in closed form under a bounded universal (Levin--Solomonoff) prior; models are scored by how closely their served distributions approach it at matched evidence. Each task is paired with its bitwise complement, on which the optimum scores identically, so an original-twin gap isolates the model's inductive bias. Across 105 serving configurations spanning 37 open models (0.8B--675B) and frontier systems from four laboratories, models answer up to 92% of queries correctly, yet 45 of 46 models yield distributions farther from the optimum than a keystroke reference, and their behaviour is bracketed by low-order prefix statistics fitted only on visible evidence. That reference is itself an algorithmic mixture, induced by a print-only machine with no loops, so the panel's implied measure sits closer to a loop-free mixture than to the loop-bearing optimum, independently of the reference machine. Updating is also non-monotone, which no prior explains: a Bayes-rational solved set can only grow in this realisable, noiseless setting, yet added examples produce $6{,}545$ solved-to-unsolved transitions against $13{,}702$ gains. The gap is not predicted by accuracy (Spearman $ρ=-0.19$, $p=0.21$), does not close with scale or across frontier generations in the serving modes that expose distributions, and is widened by instruction and reasoning post-training. F-ICL is released as an open, reproducible benchmark and toolkit.

When a self-improving AI-for-science system claims a new capability, the evidence is usually a benchmark delta, a description-length gate, or a p-value. None separates a real gain from extra search, from a changed verifier, or from adaptation to a fallible oracle. We build a two-sided audit whose negative side is a formal fact: a pseudoknot-free oracle provably cannot represent a crossing base pair, so the prior verifier's range is bounded exactly, offline, before any run. "New" is relative to the agent's prior self, never to the base model. First, how far a single fallible oracle can inflate a capability claim. An invented, solver-free operator solves 43/60 crossing RNA targets under the predictor it optimizes, above a context-free floor of 0/60; under three predictors, 1/60 survives. Paired on the same 43 targets, a predictor the operator never saw confirms 2 of its designs against 26 for a minimum-free-energy solver (p = 8e-7). No statistic computed from the system and its own oracle sees that gap. Second, agent-written procedures can beat a human-written one under a judge no objective can flatter, at a fraction of the compute. Of six frontier models, the two whose operators ran without timeouts carry over at 0.293 against our 0.095 (n = 951 paired units, target-clustered [+0.108, +0.297], p = 5e-5) while spending 4.6-10x fewer oracle calls. Three rungs: difference under an outside adjudicator (reached), not bought with compute (reached, both directions), mechanism identified and transferable (not reached; seven candidates tested, none moves the statistic). The ceiling is the panel itself: its three predictors share nearest-neighbour thermodynamic parameters, two agreeing at kappa = 0.673. The audit is as unsparing about our own system: matched undirected search is an exact zero, and a search-free probe puts 84% of our headline effect on targets a random sequence already solves.

The Stochastic-Oracle Turing Machine (SOTM) framework models AI-augmented computation as the interaction of a probabilistic Turing machine with an oracle whose responses are drawn from context-dependent distributions. This paper studies what an SOTM can achieve under two oracle-response schemes: in a cached-response oracle, each distinct query receives one response that is reused on later calls to the same query, while in a fresh-response oracle, each call returns an independent response. In both schemes, the SOTM first computes from its input and internal random source to generate its first query, then proceeds adaptively, computing from its query-response transcript (the record of queries issued and responses received) to generate each subsequent query or produce a final output. Cached responses impose two transcript-based ceilings on achievable performance: a correct-identification ceiling governed by the total variation distance between the transcript distributions induced by the hidden states of the oracle, and an output quality ceiling equal to the expected score of the best output the SOTM can compute from the transcript. Fresh responses can raise these ceilings by allowing repeated calls to accumulate independent evidence toward correct or high-quality outputs. In the binary single-informative-query case, the error probability decreases exponentially in the number of calls to the same query at the Chernoff rate. For output quality, query-count bounds characterize threshold stopping when the score function is incorporated as part of the SOTM, and majority-based amplification bounds characterize the binary candidate-output model when it is not. Together, the results identify how response reuse, transcript information, and access to the score function determine what an SOTM can compute and at what token cost.

Tabular foundation models cannot reason about data produced by running systems without access to the rules that govern them. We make this statement falsifiable. The \emph{Operational Turing Test} (OTT) constructs pairs of legal and rule-violating database states whose $1$- and $2$-way column-value marginals match to a total variation of $<0.02$; Le~Cam's lemma then bounds any values-only classifier at $\geq0.49$ Bayes error. Three values-only baselines (XGBoost, TabICL, TabPFN) hit the bound exactly (accuracy $0.50$, pre-registered two one-sided tests (TOST) $p<0.002$), raw row-level access does not help, exposing relational value consistency closes most of the gap, and only a classifier fed by seven executable rule-derived audits reaches $1.00$ classification accuracy. In three matched $100$-state frontier large-language-model (LLM) runs, models given the schema, trigger source, rule tables, and state files classify at most $2/50$ legal states as LEGAL; GPT-5.5 accepts $0/50$ legal states even with higher reasoning effort and a Structured Query Language (SQL) executor. The access-ladder pattern also appears on a second schema with structurally distinct rule families (banking ledger: cross-row balance, cumulative aggregate). The barrier is identifiability, not capacity: scale, data, and richer features cannot cross it without operational grounding.

Self-improving agents are state-of-the-art (SOTA) on agentic coding benchmarks and have recently been extended to general domains. However, their search methods generally assume a stationary evaluation criterion: a fixed verifier, benchmark, or labeled dataset that remains valid as the agent improves. This ignores a central feature of evolution: species adapt as their environments change with them. We aim to bring the same principle to recursive self-improvement, making evaluation part of the improvement loop and opening search to evolving evaluators, adversarial objectives, and dynamic utilities that may surpass static benchmarks. We introduce the Red Queen Godel Machine (RQGM), an evolutionary framework for recursive self-improvement under non-stationary utilities. The RQGM makes this possible through controlled utility evolution: search is organized into epochs with a fixed within-epoch evaluation criterion, while the utility can be updated at epoch boundaries, so self-improvement guarantees hold per epoch as the objective evolves across them. We begin by showing that even on verifiable coding tasks, the RQGM improves test pass rate over the prior SOTA by adding a complementary agent-as-a-judge code-review signal. This signal is cheaper and the RQGM uses 1.35x-1.72x fewer tokens. We then turn to scientific paper writing and reviewing, and Olympiad-level proof writing and grading, where the RQGM improves performance over prior self-improving agents: co-evolved writers reach 1.78x-1.86x higher acceptance rates under a diverse agent-as-a-judge panel, while co-evolved graders reach 9% higher ground-truth accuracy. In paper reviewing, the strongest baseline reviewer over-accepts AI-generated papers at up to 1.91x the human rate. The RQGM corrects this by introducing an adversarial objective that discovers reviewers equally stringent on AI and human work.

Modern VLMs and VLA systems commonly adopt off-the-shelf ViTs such as SigLIP2 as visual encoders, but diverse downstream requirements in latency, temporal modeling, and VLM integration often call for customized SOTA-level ViTs. Training such encoders remains beyond the reach of much of the community, as it requires massive image-text data, while standard softmax attention makes high-resolution or dynamic-resolution pretraining prohibitively costly and often forces low-resolution pretraining followed by post-hoc adaptation. TuringViT addresses these challenges with three key designs: Turing Linear Attention (TLA) for efficient sequence modeling, VISTA-Curation to construct supervision-rich image-video training data, and native dynamic-resolution pretraining that supports flexible inputs from the start and transfers seamlessly to downstream VLMs. As a result, TuringViT outperforms leading open-source ViT baselines with only 10% of the data, achieves stronger downstream VLM performance, and delivers substantially better latency scaling on high-resolution inputs. Our scaling-law analysis further shows that TuringViT continues to improve predictably with curated data scale, far from saturation. Its fast adaptation, hardware-friendly design, and efficient deployment have made it a unified visual foundation across XPeng's AI systems. More broadly, TuringViT provides a reproducible pipeline that dramatically lowers the cost for the community to train, customize, and deploy SOTA-level ViTs, moving toward making such Vision Transformers accessible to all.

The original Turing Test asks a human judge to distinguish a machine from a person through dialogue. Three quarters of a century later, conversational systems pass this test in casual settings; the interesting epistemological question has shifted. We argue that the relevant modern variant asks not whether a dialogue partner is artificial, but whether it can be trusted. We present RogueAI, an interactive webapp that operationalizes this revisited test as a one-on-two interrogation game: a human player questions two indistinguishable Large Language Model agents, knowing that exactly one of them has been licensed to deceive within a shared fictional scenario. The player's task is to identify the deceptive agent and "shut it off" before a turn budget is exhausted. We further introduce AutoRogueAI, a procedural extension in which players co-design a custom scenario with a narrator agent that secretly chooses its own deception strategy. We describe the framing, sketch the abstract architecture and gameplay loop, and situate the artifact within recent work on LLM deception, social-deduction benchmarks, and scalable oversight via debate. A three-day pilot deployment (467 initiated sessions, 415 completed, 1876 interaction turns in Italian) provides early feasibility evidence and surfaces a concrete tension: the deceptive agent carries a reliable, locally-present linguistic signature - differential helpfulness, brevity, hedging - that a simple heuristic exploits at 75.6% accuracy, yet human players achieved only 56.6%, consistent with ignoring the most diagnostic signal entirely. We discuss what this gap implies for the artifact's use as a data-collection vehicle, a teaching tool, and an evaluation harness for honesty-trained models.

We present ChessMimic, a system of three small encoder-only transformers - for move, thinking-time, and outcome prediction - conditioned on the position, recent move history, player rating, and clock state. We fit a separate instance of each model per 100-Elo rating band, trading parameter efficiency for sharper per-skill calibration. On a held-out month-wide slice of Lichess Rated Blitz games ChessMimic's human move prediction accuracy outperforms Maia-2 in every Elo band. Compared to Maia-3, our 9M parameter model's accuracy sits between Maia-3-5M and Maia-3-23M without the additional complexity of Geometric Attention Bias. In addition to the move matching model, we also train a game outcome model that conditions not only on the position, but also player ratings, time control, and remaining clock times. The outcome model achieves an AUC of 0.78 out of sample, beating Maia-2 as well as logistic regressions based on material, ratings, and clock time. Finally, we train a clock model that predicts human thinking times. The clock model provides a usable but non-SOTA per-ply think-time signal under ALLIE-style filters (Pearson r = 0.41, Spearman rho = 0.50, MAE 4.10 s, against ALLIE's reported r = 0.70), with the residual gap concentrated in per-position bucket sharpness rather than bucket-marginal calibration. A public demo is at 1e4.ai and we release code, per-band weights, and the C++ data-filter pipeline code in GitHub.

This paper proposes, for the first time, a rigorous formal definition of the concept of Machine Theory of Mind, based on principles supported by evidence from cognitive psychology, neuroscience and artificial intelligence, and uses the above as a lens to examine state-of-the-art and current efforts in the field, driving a potential agenda for further research there able to "crack" the problem. It also advances a general holistic meta-model for Machine Theory of Mind, and examines the state of the art when it comes to empirically benchmarking such models.

The rapid advancements in generative AI technologies, such as Stable Diffusion, DALL-E, and Midjourney, have significantly transformed the creation of synthetic visual content. While these models enable innovation across industries, they also pose serious challenges, including misinformation, disinformation, and biased content generation. The increasing realism of AI-generated images makes their detection a pressing concern for researchers, policymakers, and industry stakeholders. In this paper, we present the findings of the Defactify 4.0 workshop, which introduced the Counter Turing Test (CT2) for AI-Generated Image Detection. The competition consisted of two key tasks: (1) binary classification of images as either AI-generated or real and (2) identification of the specific generative model responsible for an AI-generated image. To support both tasks, we employed the MS COCOAI dataset, a benchmark of 96000 real and synthetic images generated by five state-of-the-art models alongside real images from MS COCO. Participants employed diverse detection strategies, including convolutional neural networks (CNNs), Vision Transformers (ViTs), frequency-based analysis, contrastive learning, and multimodal techniques. The results demonstrated that while AI-generated images can be detected with high accuracy (F1-score > 0.83), identifying the exact model used remains significantly more challenging (highest F1-score: 0.4986). These findings highlight the need for improved model fingerprinting, adversarial robustness, and real-time detection mechanisms.

The growing capability of large language models to produce fluent, contextually coherent text has created mounting pressure on the systems and institutions responsible for ensuring the authenticity of digital content. Advanced generative models such as GPT-4, Claude 3.5, and Llama can produce highly coherent and human-like text, making it increasingly difficult to differentiate between human-written and AI-generated content. While these models have transformative applications, their misuse has raised concerns about misinformation, biased narratives, and security threats. This paper provides a comprehensive analysis of state-of-the-art AI-generated text detection techniques and evaluates their effectiveness through the Counter Turing Test (CT2) shared tasks. Task A (Binary Classification) required participants to distinguish between human-written and AI-generated text, while Task B (Model Attribution) focused on identifying the specific language model responsible for generating a given text. The results demonstrated high performance in binary classification, with the top system achieving an F1 score of 1.0000, but significantly lower scores in model attribution, where the best system achieved 0.9531, highlighting the increased complexity of this task. The top-performing teams leveraged fine-tuned transformer models, ensemble learning, and hybrid detection approaches, with DeBERTa-based and BART-based methods demonstrating strong results. However, the lower scores in Task B underscore the challenges of distinguishing outputs from different LLMs, necessitating further research into adversarial robustness, feature extraction, and cross-domain generalization.

Whether machines can originate novel content has been debated for nearly two centuries, from Lovelace's assertion that no engine can "originate anything" to Turing's question of whether a machine can amplify ideas brought in from outside. Systems of multiple interacting LLMs, increasingly deployed for autonomous generation, reopen this question empirically. Here we show that such systems, operating in inference-only setups, exhibit semantic collapse: systematic convergence in semantic representations despite apparent lexical variation. Across model families, extended simulations of 200 to 1,000 rounds, the pattern remains consistent. Thirteen intervention strategies, spanning decoding parameters, prompt design, agent composition, activation engineering, and reinforcement learning, fail to restore semantic diversity. Mechanistic analyses suggest that semantic collapse is not explained by alignment or conformity biases, but is consistent with intrinsic properties of autoregressive generation. Our results point to persistent constraints on the ability of multi-LLM systems to sustain open-ended exploration in closed-loop settings.

Vector-HaSH and the Tolman-Eichenbaum Machine (TEM) propose the hippocampal-entorhinal circuit factorizes memory via a grid-cell scaffold for compositional replay. Concurrently, human iEEG shows sharp-wave ripples gate recall and multi-hop replay fidelity decays multiplicatively. Yet, these fields lack a shared algebraic foundation. We introduce VaCoAl, an algebro-deterministic hyperdimensional memory architecture built on Galois-field linear-feedback shift registers. Its deterministic Galois-field diffusion offers a substrate-level alternative to Vector-HaSH's random projections, matching quasi-orthogonality while ensuring bit-exact reproducibility. Furthermore, the path-integral Confidence Ratio CR2 provides an algebraically tractable model for the empirically observed multiplicative replay decay. Biologically, VaCoAl's two operating regimes align with the EC-CA3 direct and EC-DG-CA3 trisynaptic pathways, explaining their 520-Myr conservation. Independent cellular evidence supports that the DG-CA3 pathway implements a biophysical homologue of Galois-field arithmetic. We also link this framework to Judea Pearl's Ladder of Causation. Reversible GF(2) binding provides the surgical algebra for the do-operator (Rung 2), and VaCoAl's dual-orthogonalizer architecture supplies the parallel substrate required for counterfactual reasoning (Rung 3). Ultimately, we prove these formal correspondences and derive testable iEEG predictions, uniting computational neuroscience, electrophysiology, and hyperdimensional computing.

We introduce the Generalized Turing Test (GTT), a formal framework for comparing the capabilities of arbitrary agents via indistinguishability. For agents A and B, we define the Turing comparator A $\geq$ B to hold if B, acting as a distinguisher, cannot reliably distinguish between interactions with A (instructed to imitate B) and another instance of B. This yields a dataset- and task-agnostic notion of relative intelligence. We study the comparator's structure, including conditions under which it is transitive and therefore induces an ordering over equivalence classes, and we define and analyze variants with querying, bounded interaction, and fixed distinguishers. To complement the theory, we instantiate the framework on a collection of modern models, empirically evaluating pairwise indistinguishability across thousands of trials. The resulting comparisons exhibit a stratified structure consistent with existing rankings, hinting that the proposed framework yields meaningful empirical orderings. Our results position indistinguishability as a unifying lens for reasoning about intelligence, suggesting a foundation for evaluation and, potentially, training objectives that are inherently independent of fixed datasets or benchmarks.

Despite remarkable advances, today's AI systems remain narrow in scope, falling short of the flexible, adaptive, and multisensory intelligence that characterizes human capabilities. This gap has fueled longstanding debates about whether AI might one day achieve human-like generality or even consciousness, and whether theories of consciousness can inspire new architectures for AI. This paper presents an early blueprint for implementing a general AI system, CTM-AI, combining the Conscious Turing Machine (CTM), a formal machine model of consciousness, with today's foundation models. CTM-AI contains an enormous number of powerful processors ranging from specialized experts (e.g., vision-language models and APIs) to unspecialized general-purpose learners poised to develop their own expertise. Crucially, for whatever problem must be dealt with, information from many processors is selected, integrated, and exchanged appropriately to solve the task. CTM-AI achieves state-of-the-art accuracy on MUStARD (72.28) and UR-FUNNY (72.13), outperforming multimodal and multi-agent frameworks. On tool-using and agentic tasks, CTM-AI achieves 10+ points of improvement on StableToolBench and WebArena-Lite. Overall, CTM-AI offers a principled, testable blueprint for general AI inspired by a model of consciousness.

The pursuit of human-like conversational agents has long been guided by the Turing test. For modern speech-to-speech (S2S) systems, a critical yet unanswered question is whether they can converse like humans. To tackle this, we conduct the first Turing test for S2S systems, collecting 2,968 human judgments on dialogues between 9 state-of-the-art S2S systems and 28 human participants. Our results deliver a clear finding: no existing evaluated S2S system passes the test, revealing a significant gap in human-likeness. To diagnose this failure, we develop a fine-grained taxonomy of 18 human-likeness dimensions and crowd-annotate our collected dialogues accordingly. Our analysis shows that the bottleneck is not semantic understanding but stems from paralinguistic features, emotional expressivity, and conversational persona. Furthermore, we find that off-the-shelf AI models perform unreliably as Turing test judges. In response, we propose an interpretable model that leverages the fine-grained human-likeness ratings and delivers accurate and transparent human-vs-machine discrimination, offering a powerful tool for automatic human-likeness evaluation. Our work establishes the first human-likeness evaluation for S2S systems and moves beyond binary outcomes to enable detailed diagnostic insights, paving the way for human-like improvements in conversational AI systems.

The Turing Test is no longer adequate for distinguishing human and machine intelligence. With advanced artificial intelligence systems already passing the original Turing Test and contributing to serious ethical and environmental concerns, we urgently need to update the test. This work expands upon the original imitation game by accounting for an additional factor: the energy spent answering the questions. By adding the constraint of energy, the new test forces us to evaluate intelligence through the lens of efficiency, connecting the abstract problem of thinking to the concrete reality of finite resources. Further, this proposed new test ensures the evaluation of intelligence has a measurable, practical finish line that the original test lacks. This additional constraint compels society to weigh the time savings of using artificial intelligence against its total resource cost.

Recursive self-modification is increasingly central in AutoML, neural architecture search, and adaptive optimization, yet no existing framework ensures that such changes are made safely. Godel machines offer a principled safeguard by requiring formal proofs of improvement before rewriting code; however, such proofs are unattainable in stochastic, high-dimensional settings. We introduce the Statistical Godel Machine (SGM), the first statistical safety layer for recursive edits. SGM replaces proof-based requirements with statistical confidence tests (e-values, Hoeffding bounds), admitting a modification only when superiority is certified at a chosen confidence level, while allocating a global error budget to bound cumulative risk across rounds.We also propose Confirm-Triggered Harmonic Spending (CTHS), which indexes spending by confirmation events rather than rounds, concentrating the error budget on promising edits while preserving familywise validity.Experiments across supervised learning, reinforcement learning, and black-box optimization validate this role: SGM certifies genuine gains on CIFAR-100, rejects spurious improvement on ImageNet-100, and demonstrates robustness on RL and optimization benchmarks.Together, these results position SGM as foundational infrastructure for continual, risk-aware self-modification in learning systems.Code is available at: https://github.com/gravitywavelet/sgm-anon.

As AI systems integrate into online spaces, differentiating them from humans in conversations is increasingly important. We present Inverse Turing Bench, a benchmark that evaluates LLMs and other models on their ability to differentiate humans and AI in multi-turn text. The benchmark provides a collection of paired dialogue transcripts, wherein one dialogue is between two humans and the other is between a human and an AI. The task is to correctly identify which dialogue is human-only vs. human-AI. We evaluated a preliminary set of models against this benchmark, and found that GPTZero, Claude Opus-4.6, and GPT-5.5 achieve the highest accuracy: 89.41%, 77.92%, and 75.94% respectively. Our results suggest that statistical approaches to detection have semantic blind spots, but semantic approaches are susceptible to persona-prompting. Our work speaks to the Inverse Turing Test and motivates human-AI differentiation as a critical capability for AI systems. Our live benchmark can be found at https://huggingface.co/spaces/roc-hci/Inverse-Turing-Bench-Leaderboard.