Papers

Reasoning models often act as if they pursue goals, but their efforts are not always directed toward what users intend, sometimes leading them to pursue unintended outcomes. Previous work has examined how models may internally track their progress toward their goals through a "value axis." We study whether changing such a signal can retarget the model's search toward a different goal. We test value transplant: at each token, we shift the host model's activation along a candidate value axis by the donor-host difference in value coordinates (multiplied by a large scalar), aiming to redirect the host toward the donor's goal. We study this intervention in Qwen3-8B and GPT-OSS-20B models fine-tuned into honest and cheating variants. We test several candidate value axes, including a self-rating axis constructed from activations preceding high versus low elicited self-ratings of progress. The intervention works in both directions, with an honest donor reducing test-gaming in a cheating host and a cheating donor increasing test-gaming in an honest host, showing that this signal can influence which strategy the model follows. On solvable coding tasks, transplant from an honest donor also improves the cheating host's hidden-test performance. Value transplant also works across model families, providing preliminary evidence for the intervention in a setting relevant to model control.

We implement the machine-learned Skala exchange-correlation (XC) functional natively in CP2K using its Gaussian and plane-wave (GPW) and Gaussian and augmented-plane-wave (GAPW) methods. A joint one-centre reconstruction of density, density gradients, and kinetic-energy density before functional evaluation preserves mixed gradient terms and nonlocal couplings between smooth and atom-local contributions in all-electron and pseudopotential calculations. An XC-specific GAPW representation resolves rapidly varying local contributions on atom-centred grids, reducing plane-wave requirements for pseudopotential calculations. The implementation includes Brillouin-zone sampling and point-group symmetry reduction. With sufficiently flexible orbital bases, it retains the molecular benchmark accuracy of our earlier GauXC formulation. All-electron Skala-D3(BJ) calculations yield a mean absolute error (MAE) of 1.54 kJ mol$^{-1}$ against diffusion Monte Carlo for crystalline CO$_2$, NH$_3$, and urea, spanning dispersion, quadrupolar electrostatics, and hydrogen bonding. For all thirteen DMC-ICE13 phases, the MAEs are 1.16 kJ mol$^{-1}$ for absolute lattice energies and 0.82 kJ mol$^{-1}$ for the twelve relative energies to ice Ih. At fixed experimental geometries, all-electron/mixed-core calculations give a band-gap MAE of 0.43 eV on a 15-material set, substantially below commonly used semilocal functionals and comparable to widely used hybrid functionals. The LC10 benchmark nevertheless reveals systematically underestimated equilibrium lattice constants, indicating structural overbinding. This framework connects molecular Skala to condensed-phase electronic structure and enables future development using periodic many-body reference data.

Multi-LoRA agent systems enable efficient role specialization by sharing a common backbone model. However, each agent repeatedly processes the growing shared trajectory and constructs its own KV cache, introducing substantial memory and computation redundancy in long-horizon tasks. Existing KV cache sharing methods reduce this repeated prefill, but they either require additional training or architectural constraints or retain substantial model computation. Moreover, direct cache reuse causes the current agent to rely on cache states generated by the previous agent's adapter, weakening the role-specific behavior encoded by its own LoRA. We present PReCache, a training-free KV cache sharing framework with two designs, namely PreLRShared and ReBaseShared, that share the base cache computed using the pretrained weights and precompute a compact agent-specific low-rank (LR) cache. To remove repeated prefill, PreLRShared precomputes each agent's LR cache when the shared context is first processed, allowing the current agent to use its own LR cache without reprocessing context processed by previous agents. To improve sharing accuracy, ReBaseShared reconstructs the shared base cache from adapter-free hidden states, reducing the remaining error caused by the previous agent's adapted representation. To minimize its reconstruction cost, we propose two inference schemes tailored to single-stream inference and concurrent serving, performing the same reconstruction after each agent's turn or alongside its execution, respectively. Across multiple models and agent benchmarks, PreLRShared achieves up to a 3.1x TTFT speedup and a 2.3x improvement in per-request throughput over inference without KV cache sharing. ReBaseShared best preserves accuracy overall among the evaluated cache-sharing methods, with an average drop of only 1.1 points relative to inference without cache sharing.

We compute the missing three-color relation in type $H_3$ as an explicit $R$-linear combination of double leaves. The expression has $43\,424$ nonzero polynomial coefficients with scalars in $\mathbb{Z}[\varphi]$, where $\varphi = (1 + \sqrt{5})/2$. We verify the relation using exact arithmetic in the computer algebra system GAP. This completes the diagrammatic presentation of the Hecke category of Elias and Williamson.

Neural audio codecs (NACs) are widely used in speech generation and audio-language modeling, yet how they encode speaker-trait information remains poorly understood. Prior work applied sparse autoencoders (SAEs) to investigate accent information in NACs through task-level analysis. Here, we extend this analysis to the waveform level and to age, gender, and accent, using SAE steering to probe trait-related information in sparse activations. We identify trait-associated dimensions, modify their activations, and evaluate the resulting reconstructed speech. Across five NACs, steering the selected dimensions induces target-directed shifts in speaker-trait predictions. A random-dimension baseline on Mimi produces smaller shifts, supporting the relevance of the selected dimensions. However, responses vary across codecs, traits, and steering directions, and increasing steering strength does not consistently amplify the intended shifts. Steering also generally increases word error rates and lowers predicted perceptual quality. These findings suggest that SAEs capture speaker-trait information in steerable activations, while the accompanying quality degradation highlights the need to better separate trait-related information from other information.

Polymer informatics has matured from isolated property-prediction studies into an integrated discipline that couples data, models, and decision-making across the polymer design cycle. Yet it still falls short of a true intelligent system capable of inverse design on demand, causal reasoning across chemistry, processing, and performance, and closed-loop autonomous experimentation. This article traces a roadmap toward that goal, grounded in experience developing two complementary agentic and informatics platforms. Central to this vision is a modular, agent-directed architecture in which a polymer super-intelligence layer interprets a researcher's design question in natural language and coordinates domain-specialized tools, matched to the available data, for neat polymers, composites and formulations, solvents, and synthesis and processing. The resulting system spans the full chain from molecular design through processing to product-level performance and human perception. Orchestrated together, its generative design, synthesis-feasibility reasoning, and practicality assessment already form the decision-making core of a self-driving polymer laboratory, leaving autonomous, closed-loop experimentation as the principal step that remains. We survey emerging capabilities along this roadmap, including automated extraction of property data from the literature, chemistry-aware representation, property prediction for membranes and sustainable plastics, solubility and green-solvent recommendation, and computer-guided retrosynthetic planning, exposing the remaining gaps and the research and infrastructure investments needed to move from today's orchestrated tool ecosystem toward a genuinely super-intelligent polymer design partner.

What determines the unavoidable sample cost of learning cyclic causal structure? For cyclic linear non-Gaussian models, we study exact condensation recovery from observational data: identifying the strongly connected component (SCC) partition and all edges between components. We establish the first information-theoretic lower bounds on sample complexity for this target. For $p$ variables, maximum SCC size $s_{\max}$, and maximum external-parent count $d_B$, any estimator requires order $s_{\max}\log(ep/s_{\max})+d_B\log(ep/d_B)$ samples in the worst case over a regular model class. These bounds distinguish the costs of SCC membership and external-parent selection. Under principal invertibility and without correlation faithfulness, we establish a population block-exogeneity principle that identifies unknown root SCCs through residual independence and inclusion minimality. A sparse-adjustment characterization shows that small adjustment sets suffice to identify SCCs and their direct external parents, without regressing on all previously recovered variables. These characterizations yield BlockExo, which attains a structurally matching sample bound without knowing $s_{\max}$ or $d_B$ under suitable conditions. Simulations support the structural dependence of our sample bound and demonstrate BlockExo's sample-efficient recovery in comparisons with other methods for cyclic causal discovery.

Sliding-window KV inference refers to processing a sequence incrementally while retaining only a fixed-size cache of recent key and value states. It can be applied to pretrained causal transformers at inference time without additional training, while its KV-cache memory remains fixed as more tokens are processed. Because cached states are computed in the context of earlier tokens, they may carry information from beyond the current window and transmit it to later states. This study presents a series of experiments using five open-weight models spanning Qwen, Llama, Mistral, and Muse Glimmer. We investigate whether information originating outside the immediate context window can persist through a rolling KV cache and remain useful for retrieval. Initial results show that retaining previously computed states improves retrieval across the models tested compared with recomputing the final fixed window from raw tokens. We then measure how far this effect extends and find that Muse Glimmer and Mistral 7B show the strongest latent information relay: they can recover information even after the relevant source tokens have left the cache. Both models incorporate sliding-window attention in their published architectures, an association that motivates testing whether training with sliding windows promotes more reliable information retention.

Schedules for directed acyclic graph (DAG) workflows in networked IoT systems are typically computed assuming a static or generally stable network. In contested and adversarial environments, this assumption is not valid. Links degrade and fail due to mobility, interference, and jamming. We study schedule repair: when a link disruption invalidates part of a schedule, how much of it should be rescheduled? We introduce a spectrum of repair policies that vary in repair scope, how much of the pending schedule each may move: wait out the disruption, reroute data around it, reschedule only the affected tasks locally, or reschedule all pending tasks globally. We evaluate each against an oracle and charge every repair a decision latency proportional to the extent to which it moves. Across 100 workload instances spanning synthetic task graphs, RIoTBench pipelines, and WfCommons scientific workflows, each run at five communication-to-computation ratios (CCRs) and disrupted by processes with deliberately different correlation structure, we find that no single scope wins: rerouting nearly erases isolated failures that cost waiting 30%, global repair comes within 4% of the oracle under jamming blackouts, waiting is favored under memoryless link flapping for larger and communication-heavy workloads (the scheduling analog of route-flap damping), self-healing mobility outages reward patience over reaction, and accounting for repair latency erodes large scopes first. We conclude that the scope of the repair should be adapted to the disruption process and the repair cost, rather than fixed by the scheduler.

Multimodal models increasingly interpret visual environments, but their ability to recognize the same building across photographs, floor plans, elevations, sections, and renderings remains poorly characterized. We introduce ARCH-B, a benchmark of 354 four-choice questions across 11 cross-representational archetypes, constructed from a building-linked corpus of 3.9 million architectural images using visually similar distractors, model-guided difficulty screening, and manual validation. We evaluate 25 multimodal models and collect 5,830 responses from non-expert human participants. Model accuracy ranges from 10.45% to 83.90%, compared with a human baseline of 35.35%. Models perform comparatively well on mixed-representation outlier detection and photograph matching, but remain weaker on floorplan-to-photograph correspondence. Human and model difficulty across archetypes is only weakly correlated (Spearman's (\rho=0.33)). Held-out evaluation confirms that the difficulty identified during screening generalizes beyond the curation models. ARCH-B provides a diagnostic evaluation of visual correspondence and representation transfer across architectural media.

Measuring idea similarity is fundamental to creativity evaluation, especially as LLMs enable idea generation at increasing scale. However, text embeddings collapse an idea into a single vector, making it difficult to capture structural similarity, including partial overlap across core and supporting components and differences across levels of abstraction. We introduce a shared structural representation that decomposes ideas into purpose, mechanism, and implementation components and organizes related components in a multi-layer concept graph. From this representation, we define measures of pairwise similarity and set-level mechanism coverage for assessing idea diversity. We evaluate our approach using controlled idea triples and assessments from 12 experts, focusing on differences in core mechanisms, implementations, and supporting components. Our method improves alignment with expert judgments of structural similarity by 31% over the embedding baseline and better reflects expert assessments of idea set coverage, supporting scalable evaluation of idea similarity and diversity.

Between them, the members of a research group or a circle of friends own several consumer computers, none large enough to run a capable large language model. Existing systems pool such capacity across open swarms anyone may join, which a group admitting only trusted machines cannot use. Bounding membership removes what they depend on: a swarm holds each part of the model on several peers and routes around a slow one. A bounded session must use every device it admits. Its pipeline advances at the pace of whichever device received a share it cannot serve quickly, so the division has to be right before serving begins. We propose Kafila, whose protocol assembles a ring from behind NATs, preferring direct paths and relaying where traversal fails, while its planner measures each device's memory bandwidth, capacity and reachability, divides the model exactly for a fixed ring order, and places the head, which holds the embedding and output projection, together with that division rather than beforehand. On machines with different capabilities across three fleets, from a shared LAN to five devices spanning two continents, Kafila shortens the slowest pipeline stage by up to $5.2\times$ against the even split of pipeline parallelism, as in GPipe, and up to $3\times$ against the memory-proportional split of personal-device inference, as in exo, keeps 75 to 87 per cent of the committed hardware doing work where those divisions fall below half, and serves a model no uniform split can place on the fleet at all. What that is worth to a user depends on how much of a token is computation rather than network. Where the members share a network the same division returns $1.56\times$ the throughput of a uniform split and $1.25\times$ of a memory-proportional one, and under four concurrent users that lead compounds to $3.2\times$ rather than fading, each user served at almost the rate of one.

Reasoning vision-language models (VLMs) process images and videos as long sequences of visual tokens, making inference expensive. Training-free token pruning reduces this cost, but aggressive compression can sharply degrade performance, often attributed to irreversible loss of task-relevant visual information. We show that this explanation is incomplete. In a fixed-context Pass@K analysis, repeated sampling from the same pruned visual representation recovers many examples missed by greedy decoding, indicating that useful visual evidence can remain accessible but be used unreliably. We call this the representation-utilization gap. Motivated by this observation, we introduce SCOPD, a sparse-context on-policy self-distillation framework in which a student generates reasoning trajectories from pruned visual tokens while a privileged full-context teacher supervises the same on-policy prefixes. SCOPD requires no ground-truth responses, architectural changes, or additional inference-time computation. We further introduce SCOPD+, which uses a small visual-budget intervention to identify visually sensitive response positions and selectively distill them. At 10% visual-token retention, the Vanilla model retains 86.37% of its unpruned performance across 13 benchmarks. SCOPD raises this to 90.49%, while SCOPD+ further improves it to 92.43%. Across token budgets, benchmarks, and pruning operators, our results show that efficient reasoning depends not only on which visual information survives pruning, but also on how reliably the model learns to use it.

Non-negative matrix factorization (NMF) is a singular statistical model whose Bayesian asymptotics are governed by the real log canonical threshold (RLCT). We study the local geometry of the factorization map and derive an upper bound for the RLCT of NMF. Let $H$ be the model inner dimension and $H_0$ the non-negative rank of the true $M\times N$ matrix. Assuming that the true matrix admits a strictly positive factorization of inner dimension $H_0$ in the interior of the parameter domain, we prove, for smooth positive priors, that $\lambda\leq \{(H-H_0)\min(M,N)+H_0(M+N-H_0)\}/2$. This bound strictly improves the previous bound when $H_0\geq3$. The proof uses a local analytic normal form that separates independent linear coordinates from a residual matrix product. When $H=H_0$ also equals the ordinary rank of the true matrix, we obtain the exact value $\lambda=H_0(M+N-H_0)/2$. Under the standard assumptions of singular learning theory, these results bound the leading coefficients of the expected Bayesian generalization error and the Bayesian free energy.

We determine the vanishing cycles of Xiao's genus-two fibrations $X_d\to P^1$, $d=3,4,5$, whose fibers admit degree-$d$ maps to a fixed elliptic curve $E$. We tile the base $P^1$ by triangles and realize the surface $X_d$ as a degree-$d$ branched cover of $P^1\times E$. The covering description gives an explicit algorithm for the vanishing cycles. A vanishing path is recorded by the sides it crosses in the tiling; each crossing changes a labelled picture of the fiber by a local hexagon move, and the vanishing cycle is read from the terminal picture. We obtain the $7$, $13$, and $31$ vanishing cycles as explicit curves in a marked reference fiber. For $d=4,5$, these give new positive factorizations of the identity in the genus-two mapping class group, of types $(6,7)$ and $(12,19)$.

Safe reinforcement learning seeks policies that maximise task performance while satisfying safety constraints. In driving benchmarks, however, collision costs typically appear only at the time of collision, providing no advance warning of an approaching hazard. Frozen vision–language models can provide dense semantic feedback, yet it remains unclear whether their scores anticipate collisions and which component drives an observed safety improvement. Episodic cost can also favour policies that make little task progress. To address these gaps, we propose VLM-Safe-RL, a framework that integrates frozen CLIP signals into PPO-Lagrangian through reward shaping and an augmented multiplier update. On MetaDrive Hard, which combines the densest traffic with the largest map, the catastrophe rate falls from 31.6% to 19.4%. FormulaOne-L2 analysis finds no evidence that the CLIP signals anticipate collisions and shows that the VLM term has a negligible effect on the Lagrange multiplier. These findings show a conditional reduction in observed catastrophe rate without evidence of collision anticipation.

Nonlinear oscillators exhibit rich collective phenomena including synchronization, bifurcation, and chaos. Experimentally accessing multimode nonlinear dynamics, however, remains challenging because low-order internal resonances readily induce mode locking and suppress stable multimode oscillation. Here, we demonstrate a transverse-mode-coupled optomechanical platform that combines engineered collective mechanical modes with optically controllable nonlinear interactions. The engineered transverse mechanical modes enable stable two- and three-mode self-sustained oscillations while suppressing trivial low-order internal resonances. By varying the laser frequency, we observe successive beat-frequency fractionalization ({\Delta}f/2 and {\Delta}f/3), followed by a broadband state exhibiting enhanced trajectory divergence consistent with deterministic chaos. These results establish transverse-mode-coupled optomechanical resonators as a scalable and tunable platform for exploring high-dimensional nonlinear dynamics in interacting mechanical networks.

Objective: To develop and characterize CLEAR-Med, a dual-agent framework for natural-language analysis of structured clinical data that separates SQL-based invocation from independent validation. Methods: CLEAR-Med uses one agent to translate a question into executable Structured Query Language (SQL), retain the executed query and database result, and produce a draft. Deterministic checks and a separately invoked cross-provider Validation Agent then accept the draft, request one bounded repair, or abstain. We formalized the system as a bounded selective pipeline and evaluated CLEAR-Med's configuration and scalability, and the Invocation Agent's accuracy and consistency on a 25-query development benchmark, using a harmonized 21-site neonatal hypoxic-ischemic encephalopathy table containing 532 de-identified infant records and approximately 1,300 variables. Results: CLEAR-Med completed all six nominal scalability configurations, including 500x1300. Across 25 development-benchmark queries repeated five times, the Invocation Agent answered 83 of 125 responses correctly (66.4%; query-cluster bootstrap 95% CI, 48.0-83.2%), compared with 15 of 125 (12.0%; 95% CI, 3.2-22.4%) for the ungrounded ChatGPT baseline, a paired improvement of 54.4 percentage points (95% CI, 36.8-72.0%). Conclusion: CLEAR-Med provides a general architecture for traceable analysis of structured clinical data: numerical claims remain linked to executed SQL, and unresolved cases can fail closed. The reported experiments characterize CLEAR-Med's configuration and scalability and the Invocation Agent's accuracy, while the formal analysis establishes the encoded-property guarantee of the complete control flow; a prospective full-pipeline evaluation of the validation and abstention stages is the next stage of this work.

We investigate $\mathbb{Z}_2$ symmetry restoration in a real $\lambda\phi^4$ theory confined to a finite cylindrical region undergoing rigid rotation. The finite transverse extent is imposed through Dirichlet boundary conditions, resulting in a discrete Fourier-Bessel spectrum and an explicit radial dependence of the fluctuation propagator. Using the background-field method, we derive the one-loop effective potential while retaining the spatial structure induced by the finite geometry. At finite temperature, rotation modifies the thermal mode energies through angular-momentum-dependent shifts, and the coincident-point propagator generates a position-dependent thermal self-energy that is incorporated through ring resummation. We use the resulting spatially resolved effective potential to determine the symmetry-restoration temperature $T_c(\Omega,R)$ and examine its dependence on the angular velocity and transverse size. The results show that the finite transverse size of the system modifies the symmetry-restoration temperature, leading to a nontrivial dependence of $T_c(\Omega,R)$ on $R$. An additional scaling behavior emerges when the normalized critical temperature is expressed in terms of the boundary velocity $\Omega R$: systems with different transverse sizes exhibit the same relative modification of $T_c$ when their boundary velocities are equal. This scaling persists after the inclusion of the position-dependent thermal self-energy through ring resummation, indicating that the $\Omega R$ dependence of the rotational response is maintained in the interacting finite system.

Modern Linux scheduling increasingly requires workload-specific policies to meet the dynamic performance needs of heterogeneous applications. The recent sched_ext framework enables custom BPF schedulers, but building practical policies still requires coordinating Rust user-space control logic, BPF scheduling callbacks, generated user-kernel interfaces, and strict eBPF verifier constraints. This paper presents MorphSched, an LLM-driven system for synthesizing complete Rust+BPF sched_ext schedulers. MorphSched profiles target workloads under Linux EEVDF to construct dynamic, workload-specific optimization objectives, and uses a scaffold-constrained generation pipeline to translate scheduling intent into deployable scheduler implementations. To improve synthesis reliability, MorphSched separates implementation repair from strategy search: verifier, build, and runtime failures are handled through a DAG-structured repair process, while performance feedback is accumulated in an evolutionary memory pool to refine high-level scheduling strategies across iterations. We evaluate MorphSched across 120 machine/workload/interferer configurations on a real Linux kernel. The generated schedulers compile, pass eBPF verification, load successfully, and remain stable throughout our benchmark runs without manual edits to generated scheduler source code. Across these configurations, MorphSched improves the primary foreground metric over EEVDF by 26.5% on average and up to 87.3%. In selected comparisons, the generated schedulers are also competitive with representative hand-written sched_ext schedulers. These results show that scaffold-constrained, system-grounded LLM generation can be a practical tool for exploring workload-specific Linux scheduling policies.

We study mountain-bike action quality assessment (AQA) with weak labels and candidate feedback. The training corpus comprises 95 field-recorded jump clips with binary labels denoting good or poor technique. These are coarse categorical labels, not continuous expert quality scores; phase-boundary and aspect-level annotations are unavailable. Our pipeline summarizes four heuristic phases using frozen V-JEPA 2 video features and two-dimensional pose and motion measurements. A small transformer predicts a binary-label score. A separate reference layer compares phase-specific measurements with those of clips labelled as good technique to propose phase, body-parameter, and direction cues. We detail the measurements, network, and evaluation so that the limits of each output are explicit. In five-fold clip-level cross-validation, the full scorer obtained pooled out-of-fold AUROC 0.768 and average precision 0.812. These are exploratory figures because the reporting fold also selected the neural training epoch and riders were not separated between folds. Removing biomechanical scoring inputs raised AUROC to 0.809. A separate inner-selection run obtained AUROC 0.678, but used about 57 rather than 76 training clips per outer fold, so its difference from the test-selected run does not quantify selection bias. The unsupervised aspect head did not learn distinct factors. On a 17-clip external probe, an earlier checkpoint obtained binary accuracy 0.412 and Spearman association -0.135 with expert scores. Candidate cues had precision 0.118 and recall 1.0 against each of two coaches, with substantial disagreement about direction. These findings do not establish rider-independent scoring or reliable corrective feedback; they identify the empirical work needed to evaluate either use.

For a fixed $k$-graph $F$, let $h_F(n,q)$ be the minimum number of copies of $F$ in an $n$-vertex $k$-graph with $\text{ex}(n,F)+q$ edges. Let $c(n,F)$ be the minimum number created by adding one edge to an extremal $F$-free $k$-graph. We construct stable counterexamples to Mubayi's supersaturation conjecture for every $k\ge2$. The ratio $h_F(n,q)/(q c(n,F))$ tends to zero over ranges extending beyond $n^{k-1}$. For graphs, we give examples of every chromatic number at least three. In particular, there is a graph $F$ for which this ratio tends to zero for $1\le q=o(n^{4/3})$. For $k\ge3$, we use connected linear expansions of $G=(M_a\cup K_{1,b}\cup I_h)\vee K_{m_1,\ldots,m_{k-1}}$. Under explicit parameter conditions, the ratio tends to zero for $1\le q=o(n^{k-1+(b-1)/(a+b-1)})$ when $b\ge k+1$. We prove the exact Turán theorems for both constructions and determine their unique extremal graphs and hypergraphs. Keywords: supersaturation; extremal graph; linear hypergraph; graph expansion; stability.

Under the accelerated pace of AI development, any benchmark whose difficulty is calibrated with humans or current AI systems becomes circular, or saturates soon. How can we then evaluate machines that may become more capable than the current machines and the people who write the tests? One answer to the question hinges on inverse problems, inductive inference questions for which difficulty depends on the complexity of the underlying mechanism, given the observations and the previous knowledge. Levin's Kt, a computable variant of Kolmogorov complexity, puts a theoretical upper bound to that difficulty, balancing the simplest representation encoding for the mechanism and the logarithm of the time steps to run that mechanism. Previous tests derived from Levin's Kt, such as the original C-test, are based on minimalistic Universal Turing Machines (UTM), capable of very limited representations and no previous knowledge. Reasoning large language models (LLM) are UTMs that capture a compendium of human culture as knowledge, using prompts as natural language programs. This paper presents the first test based on Levin's Kt with LLMs as representational machines. Fresh test items can be produced at high difficulties, estimated in a ratio scale measured in bits, before any human or frontier model can solve them. We formalise the measure, devise a lightweight generation and certification pipeline, explore the effect of the power of the reference machine and the gap between examiner and examinee. We produce a first battery of certified items administered to twelve LLMs. The resulting agent characteristic curves decrease with difficulty, down to the uncharted high-difficulty region, the supra-intelligence window of items we can certify, yet beyond generations of frontier intelligence.

People often learn from others' demonstrations, and inverse reinforcement learning (IRL) techniques have realized this capacity in machines. In contrast, teaching by demonstration has been less well studied computationally. Here, we develop a Bayesian model for teaching by demonstration. Stark differences arise when demonstrators are intentionally teaching (i.e. showing) a task versus simply performing (i.e. doing) a task. In two experiments, we show that human participants modify their teaching behavior consistent with the predictions of our model. Further, we show that even standard IRL algorithms benefit when learning from showing versus doing.

Let \(H\) be a multiplicative group, \(R\) a commutative \(H\)-graded ring, and \(M\) a nonzero finitely generated gr-semisimple \(H\)-graded \(R\)-module. We assume that \(M\) admits a fixed decomposition into powers of gr-simple modules with pairwise distinct annihilators, each repeated block carrying the componentwise grading. For a nonzero homogeneous element \(x\), we compute the colon ideal \((Rx:M)\) and show that it is determined by the multiplicity-one blocks on which \(x\) has a nonzero component. This leads to the criterion \( x\leftrightarrow y \text{ if and only if } \sigma(x)\cap\sigma(y)=\varnothing, \) where \(x\leftrightarrow y\) means that \(x\) and \(y\) are adjacent in \(\Gamma_H(M)\). Thus adjacency is governed by disjointness of multiplicity-one obstruction supports. The corresponding obstruction classes form a weighted disjointness structure: higher multiplicities affect the sizes of the classes, but not the adjacency relation between their supports. We use this description to study graph invariants, reconstruction, and Kneser-type layers, and, in the finite case, to obtain formulas for the obstruction-class sizes and a reduction of the adjacency spectrum.

Let $T$ be a nonzero real symmetric third-order tensor. Denote by $r(T)$ its CP rank, by $s(T)$ its symmetric rank, by $d(T)$ its essential dimension, and put $e(T)=r(T)-d(T)$. We establish two complementary upper bounds for the Comon rank gap $$\Delta(T):= s(T)-r(T)\leq\min\{C_{ec}(e(T)),\ C_{dc}(d(T))\}.$$ The excess-controlled function $C_{ec}(e)$ is zero for $0\leq e\leq3$ and equals $9e-3$ for $e\geq4$. In particular, the equality $C_{ec}(e(T))=0$ for $0\leq e\leq3$ extends Friedland's flattening-rank criterion for real symmetric third-order tensors by two additional rank layers. The dimension-controlled function $C_{dc}(d)$ is zero for $d=0$, equals $(d^2-4d+10)/3$ for $1\leq d\leq18$, and equals $d^2/4+d/4+3/2$ for $d\geq19$. The excess estimate follows from the alternating equations and decomposable-bivector support geometry; a low-wedge descent gives the vanishing range $e\leq3$. The dimension estimate combines a transverse polar-completion bound with a shifted estimate for the maximum real Waring rank. Thus the two bounds measure different features of the same tensor and remain effective in complementary regimes.

On-policy self-distillation (OPSD) uses a self-teacher conditioned on privileged information to turn the sparse outcome signal of reinforcement learning with verifiable rewards (RLVR) into dense token-level supervision. Yet the teacher's advantage may depend on information unavailable to the student at inference, raising a central question: which privileged changes are worth distilling? We use cross-problem recurrence as an empirical cue for potentially reusable guidance. Comparing the representation shifts induced by full solutions and compact hints, we find that hint-induced shifts are more concentrated and directionally consistent across problems, and yield more sustained downstream gains despite revealing less information. Motivated by this association, we propose Privileged Representation Isolation for On-Policy Self-Distillation (PreSO). At the source, PreSO uses compact hints to limit the solution-specific detail entering the privileged shift. At the target, it estimates a leading low-rank subspace from shifts pooled across related problems, projects the privilege-induced correction onto this subspace, and adds it to the student's unprivileged representation to form the representation-level distillation target. The selected subspace serves as an operational proxy for recurring structure, rather than a guaranteed separation of transferable and instance-specific information. On five competition-level mathematics benchmarks, PreSO consistently outperforms strong baselines across Qwen3-1.7B, 4B, and 8B, improving average accuracy over the base model by 6.8, 9.0, and 10.0 points. Beyond peak accuracy, PreSO attains the highest final-checkpoint average at every model scale, with improvements that persist through the end of training.

Group-relative reinforcement learning methods such as GRPO train large language model (LLM) agents by comparing rollouts for the same task. When every trajectory in a group fails with the same reward, relative advantages collapse toward zero, leaving no useful learning signal. A frozen teacher can recover from a student-visited state, but letting it complete the task makes the recovered suffix entirely teacher-generated. We ask: after repairing a student failure, when should control return to the student? We propose outcome-verified teacher-student handoff, instantiated in Verified Handoff for Group Policy Optimization (VH-GPO). The teacher provides enough support to reach a state from which the student can succeed, then returns control so that successful experience is again student-generated. Given an environment-verified teacher recovery, VH-GPO selects the earliest independently confirmed handoff point found within a bounded search budget. With Qwen2.5-1.5B, VH-GPO increases success rates over GRPO from 59.38% to 94.79% on ALFWorld and from 71.62% to 77.34% on WebShop. Improvements also hold with the 7B student, for which additional teacher and student output tokens amount to 1.77% and 2.61% of regular student rollout output tokens on ALFWorld and WebShop, respectively. Ablation studies demonstrate the effectiveness of the key components. These results support using verified teacher assistance to repair failures while reinforcing the student's ability to complete tasks independently.

Rule decisions such as content moderation, advertising compliance, and eligibility checks combine several conditions, exemptions, and missing-information cases, and an error can be fixed only once the failing condition is known. We introduce SemTree, a framework that represents a rule decision as a semantic decision tree: each node is a natural-language question with explicit Yes/No/Unknown criteria, a pluggable semantic judge answers it, and the branching structure is compiled on the answers that this judge actually gives. The executed path is the reasoning behind every decision, so errors are repaired where they occur: a reviewer corrects a single node and replays the rule, corrected nodes become training labels for the judge, and a tool-using LLM editor revises questions and subtrees while observing execution results. On all 8,276 ShARC test cases, a tree executed by a hosted judge reaches 67.70% accuracy with 2.99 questions per case, on par with asking the same judge for the final label (68.23%); an earlier tree compiled for a different judge scores 47.87% when executed by this judge, while a new tree compiled on this judge's answers to a 12-question initial pool already scores 64.39%. Node-level repair raises BANKING77 accuracy from 82.04% to 86.16%, an explicit exemption node cuts the false positives of a Chinese e-commerce moderation clause from 24 to 5, and a trained editor raises the development accuracy of edited trees from 64.47% to 73.35%.

This paper proposes a hybrid reinforcement learning trading framework integrating intraday market data with transformer-based financial sentiment signals. The system extracts sentiment dynamics and semantic event clusters from financial news and incorporates them into a PPO-based trading agent. Experiments on intraday NSE data demonstrate improved risk-adjusted returns compared to price-only baselines.