arXiv:2607.05410v1 Announce Type: new Abstract: We present CANONIC: governed intelligence that compiles digital artifacts into an evidence ledger at scale. Large language models generate prose faster than anyone can check it, the failure Oxford Languages named 'slop', its 2025 Word of the Year. CANONIC governs whether content may enter a corpus the way a compiler decides whether a program is well-formed: mechanically, by a grammar, at the boundary of admission. Governance reduces to three axioms (Triad, Inheritance, Introspection) that map one-to-one onto compiler theory's syntax, scope-resolution, and type-system layers, and admission is a decidable, linear-time check. We then ask, with a pre-registered cross-provider benchmark across four regimes, whether structural admission keeps slop out. It does not: no prose-reading gate reliably separates reliable from unreliable content. Slop is not a property an algorithm computes. It is a verdict of domain expertise. So a governance layer does not decide slop; it keeps the record auditable -- every claim anchored to a definition, a commit, and an evidence window, reproducible and checkable end to end.
Science Journals
arXiv:2606.25258v4 Announce Type: replace-cross Abstract: We prove endpoint continuation criteria for stress-diffusion-free incompressible viscoelastic flows by working modulo pressure. In two space dimensions, the pressure-free part of any smooth spectral isotropic stress reduces to a single active deviatoric channel (q_1(a,|Y|^2)Y), where (C=aI+Y) and (\operatorname{tr}Y=0). This scalar quotient structure allows a weighted active-deviatoric energy to cancel the top-order coupling between polymer stretching and the divergence of the active stress. On compact conformation windows the resulting high-order estimate depends only on an endpoint velocity clock and a logarithmic conformation norm. For Oldroyd--B this gives continuation of strong two-dimensional solutions under (\nabla u\in L^1_tB^0_{\infty,1}), while for FENE-P it gives continuation under (\nabla u\in L^2_tB^0_{\infty,1}). In both models the compact conformation window and logarithmic bound are derived from the velocity clock and the model barriers, rather than imposed as independent hypotheses. The criteria are formulated in integer Sobolev strong-solution classes and do not assert Leray-type weak-solution or critical-space local well-posedness results. We also identify a static operator obstruction showing the functional necessity of the logarithmic threshold for the pressure-free stress map. In three dimensions the quotient contains an additional residual channel (q_2(Y^2)^\circ), so the exact scalar closure is intrinsically two-dimensional. On prescribed compact windows this residual can be absorbed by viscosity; for Oldroyd--B and FENE-P it vanishes because (q_2\equiv0).
arXiv:2607.05832v1 Announce Type: new Abstract: Counting queries are ubiquitous in database systems, particularly for driving internal system optimization. Learned models for cardinality estimation rely heavily on large-scale training data, yet generating such data by executing massive batches of counting queries is expensive. We propose BaCon, an efficient algorithm for batch evaluation of counting queries on top of a database system, without modifying its internals. BaCon integrates the idea of factorized databases with a workload-aware domain quantization strategy, allowing it to evaluate batches of counting queries using compact data structures rather than materializing massive join results. BaCon's design is compatible with most database management system, and we have implemented it as a client-side application on PostgreSQL with a lightweight C-language UDF (user-defined function). This implementation delivers speedups between 2$\times$ and 178$\times$ over baselines and good performance across various workloads, making training and maintenance of learned cardinality estimation models significantly more practical.
arXiv:2507.01577v3 Announce Type: replace Abstract: We consider interpolation from the viewpoint of fully automated theorem proving in first-order logic as a general core technique for mechanized knowledge processing. For Craig interpolation, our focus is on the two-stage approach, where first an essentially propositional ground interpolant is calculated that is then lifted to a quantified first-order formula. We discuss two possibilities to obtain a ground interpolant from a proof: with clausal tableaux, and with resolution. Established preprocessing techniques for first-order proving can also be applied for Craig interpolation if they are restricted in specific ways. Equality encodings from automated reasoning justify strengthened variations of Craig interpolation. Contributions to Craig interpolation that emerged from automated reasoning include variations for logics used in databases and logic programming. As an approach to uniform interpolation we introduce second-order quantifier elimination with examples and describe the basic algorithms DLS and SCAN.
arXiv:2607.05596v1 Announce Type: new Abstract: AI/ML workloads increasingly run as containers, where a container image must be downloaded to the host before the workload can start. This cold image pull lands on the critical path whenever a training or inference job scales up or a host is updated, and for GPU workloads it has become the dominant component of startup time as AI/ML images reach 31--48~GiB compressed. We present Disk-Backed Parallel Pull (DBPP), an alternative to the in-memory ordered reassembly used by containerd~2.2, the upstream container runtime. containerd splits layers into chunks fetched concurrently over HTTP range requests, but chunks that arrive out of order accumulate in the runtime heap until a sequential consumer drains them in order. This backlog grows with image size, and on GPU nodes where host memory is shared with frameworks and model weights, it leads to out of memory (OOM) termination of the runtime itself. DBPP writes each chunk directly to its target byte offset on disk, eliminating the ordering dependency and bounding memory regardless of image size. Because each layer lands on disk as a complete, seekable file, DBPP runs SHA-256 digest verification and decompression simultaneously, two passes containerd must run one after the other. In controlled experiments across five production-scale images (up to 48.5~GiB), DBPP reduces peak daemon memory by 8.7--25.3$\times$ while maintaining comparable pull throughput. On a memory-constrained node, containerd~2.2 is OOM-killed pulling a 31.4~GiB image while DBPP completes the same pull. The underlying idea reaches past container images: any pipeline that buffers data in memory only to enforce ordering can move that buffer to disk once the backing store is fast enough, trading a scarce, contended resource for an abundant one.
arXiv:2607.05758v1 Announce Type: cross Abstract: Automated experimentation is moving from closed-loop optimization toward open decision-making, where human or AI planners must forecast the consequences of candidate actions before executing them. Such forecasts require a model of both sides of the experiment: how the sample is likely to respond and what the instrument is likely to detect. We therefore introduce a coupled digital-twin framework that separates these roles and then links them. In this framework, the sample twin encodes material state inferred from prior knowledge and measurements till the moment. The instrument twin captures signal formation, feedback dynamics, and operating constraints based on prior knowledge. When coupled, the two twins estimate expected outcomes, uncertainty, and risk for candidate microscope operations. For amplitude-modulation scanning probe microscopy, we realize this framework with a physics-informed encoder of force-distance curves, a deterministic scanner model of cantilever and feedback dynamics, and sparse learned residual corrections. The encoder first recovers scanner-driving descriptors with sub-nanometer accuracy. The calibrated scanner then reproduces typical traces within a few nanometers and identifies operating-point noise amplification as the main source of mismatch. Supplementary phase analysis localizes residual error to the phase channel, which clarifies where added physics is needed. Together, these results establish coupled sample and instrument twins as a practical foundation for predictive microscope operation and autonomous experimental planning.
arXiv:2607.05778v1 Announce Type: cross Abstract: Using unprecedentedly long 2D particle-in-cell simulations, we study electron and ion acceleration in weakly magnetized quasi-parallel shocks, propagating at velocities ranging from transrelativistic to subrelativistic. At a fixed upstream magnetic field strength, low-velocity quasi-parallel shocks are dominated by the Bell instability, whereas high-velocity shocks are dominated by the Weibel instability. Both regimes accelerate ions with similar efficiency, with the Bell-dominated regime exhibiting faster growth in the maximum particle energy. The electron acceleration efficiency is strongly dependent on shock velocity. Weibel-dominated shocks have $\sim15\,\%$ of shock energy in nonthermal electrons, whereas in the Bell-dominated regime we attribute less than $\sim2\,\%$ of shock energy to nonthermal electrons. We discuss applications of our results to the bright X-ray emission from the late-stage afterglows of gamma-ray bursts, the radio emission from fast blue optical transients, and the X-ray variability in microquasars.
arXiv:2607.06082v1 Announce Type: cross Abstract: We study a generalization of the star coloring problem on hypergraphs. For a family of connected subhypergraphs $\mathcal{F}$, we define an $\mathcal{F}$-coloring of a hypergraph as a coloring avoiding monochromatic hyperedges and any 2-colored member of $\mathcal{F}$. We let $\chi^r_{\mathcal{F}}(d)$ be the maximum of the minimum number of colors needed for an $\mathcal{F}$-coloring of an $r$-uniform hypergraph with maximum degree $d.$ We show bounds for $\chi^r_{\mathcal{F}}(d)$, that also yield results on star and acyclic coloring problem on hypergraphs.
arXiv:2607.06040v1 Announce Type: cross Abstract: There are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around $90\%$ reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.
arXiv:2607.06177v1 Announce Type: cross Abstract: We characterize the Tanner graph spectrum of hypergraph-product (HGP) / lifted-product (LP) codes and bivariate-bicycle (BB) codes, informing qubit routing for three-dimensional reconfigurable qubit architectures. Syndrome-extraction routing depth on HGP/LP Tanner graphs reduces to a single SVD on the base parity-check matrix, using a spectral ratio $\beta_\text{HGP} = (1 + \beta_\text{base})/2$ where $\beta_\text{base} = \sigma_2(H)/\sigma_1(H)$ for the base parity-check matrix, and a diameter identity $D_T = 2 D_\text{base}$ where $D_\text{base}$ is the base Tanner graph diameter. Fourier spectral reduction reveals that the BB Tanner graph spectrum equals the union, over the $l \times m$ grid of characters of $\mathbb{Z}_l \times \mathbb{Z}_m$, of the singular values of a single $2 \times 2$ symbol matrix built from the two defining polynomials. This reduces spectral analysis from an $O((lm)^3)$ diagonalization of the $4lm$-node Tanner graph to $lm$ independent $2 \times 2$ SVDs. These results compose into a multi-layer three-dimensional AOL routing protocol with one-time setup cost $T_\text{Valiant} = O(\log N)$ atom rearrangements amortizable over a memory experiment of $R$ rounds. For a Tanner graph chromatic index $\chi'$ and $L_\text{layers}$ stacked AOL planes, the per-syndrome-cycle depth is $\lceil \chi'/L_\text{layers} \rceil$ AOL pattern activations with no atom motion, an $8\times$ step-count reduction at $L_\text{layers} \geq \chi' = 8$. Contingent on multi-layer AOL hardware, this yields an estimated $\sim50-300\times$ per-cycle wall-clock advantage over a single-layer AOD baseline (degrading to $\sim5-100\times$ under AOD-crosstalk overhead), reducing to equality in the single-layer limit. This paper therefore presents a route toward practical routing improvement for future quantum hardware incorporating multi-layer reconfigurable qubit architectures.
arXiv:2607.06179v1 Announce Type: cross Abstract: There are some datasets of varying scales for audio classification (AC) applied to different tasks. However, annotated data is limited for most scenarios, such as domestic environments. To address this challenge, we propose an $\textbf{A}$utomatic $\textbf{A}$udio $\textbf{A}$nnotation Pipeline--TriA Pipeline, which can efficiently convert audio from various scenarios into high-quality training data with audio event annotations. A TriA dataset was constructed with the TriA Pipeline, over 2130 hours of audio covering 431 audio classes. Furthermore, we partitioned a prior-knowledge-guided subset (TriA$_{\mathrm{GK}}$) from TriA and conduct comparative experiments on three domestic AC tasks. Comparing the result on manually annotated data only and that on manually annotated data combines TriA$_{\mathrm{GK}}$, TriA$_{\mathrm{GK}}$ could achieve average relative gains of 3.97% in accuracy and 3.35% in Macro-F1, validating the effectiveness of TriA$_{\mathrm{GK}}$ and the TriA Pipeline.
arXiv:2308.16041v2 Announce Type: replace Abstract: Talking head generation has progressed rapidly from landmark- and GAN-based facial animation to diffusion models, neural rendering, 3D-aware avatars, and foundation-model-assisted systems. This progress has enabled increasingly realistic audio-, image-, and video-driven talking heads, but it has also made the field difficult to navigate because methods differ substantially in their inputs, assumptions, controllability, temporal stability, computational cost, and risks of misuse. This survey provides a critical review of talking head generation techniques, organizing the literature into four broad families: image-driven, audio-driven, video-driven, and 3D/neural-rendering-based approaches. For each family, we discuss the underlying technical ideas, representative methods, strengths, limitations, datasets, and evaluation practices. Beyond cataloguing prior work, we analyse the persistent gap between commonly reported quantitative metrics and perceptual quality, and compare publicly available models in terms of inference time, memory requirements, and human-rated visual quality. We also examine emerging trends, including diffusion-based generation, 3D-aware representation learning, controllable emotional expression, real-time deployment, and the growing importance of provenance, watermarking, and deepfake detection. Finally, we identify open challenges around robust evaluation, identity preservation, lip synchronisation, temporal consistency, demographic fairness, computational efficiency, and responsible use. This review aims to provide researchers and practitioners with a structured and up-to-date map of the talking head generation landscape, while highlighting the technical and societal questions that should shape future work.
arXiv:2607.05888v1 Announce Type: new Abstract: i-EXAM is a planning-powered tool that helps system administrators to create security profiles of complex networks and perform what-if analyses to identify network hardening strategies. It leverages planning compilation that provides soundness and completeness guarantees to identify attack paths, evaluate security metrics, generate diverse hardening strategies, and explain these strategies in natural language using Large Language Models.
arXiv:2607.05773v1 Announce Type: new Abstract: As Large Language Models (LLMs) evolve into autonomous agents, traditional static evaluation fails to capture multi-step decision-making. We introduce AgenticAI-Supervisor, an API and UI-driven RL Gym environment that decouples environment creation from scalable execution. By moving to verifiable execution outcomes, the platform generates high-fidelity traces and applies multi-dimensional reward shaping. Critically, our framework mitigates reward hacking through rigorous internal state validation and testing. This work provides a first look at our platform's core capabilities through a Customer Support Agent case study demonstrating a consistent closed-loop feedback for model optimization. Future work will focus on advanced features such as Computer Use, Tool Use, automated "stumping", and edge-case generation.
arXiv:2607.05845v1 Announce Type: new Abstract: Soccer is widely popular for its simple rules and complex yet coordinated play that unfolds on the pitch. Nevertheless, the fundamental mechanisms governing such play are not well understood: what shapes player interactions on the pitch? What short-term goals guide players' decisions about their movements over the next few seconds? We address these questions by focusing on one-on-one settings in open play, in which the attacker, in possession of the ball and typically dribbling, faces a defender aiming to stop or delay the attacker's actions over a short period. Here we develop a mathematical model of attacker-defender interactions and analyze 306 professional soccer games. Synthesizing the large-scale dataset with an analysis of the model reveals a simple behavioral principle that may underlie these interactions: the defender seeks to minimize their future relative speed to the attacker, whereas the attacker initiates their movements to preempt the defender's objective. This principle, relative-speed minimization, provides a consistent and unified account of the empirical data. Since our framework depends little on soccer-specific details, this principle may govern diverse pursuit-evasion scenarios as well as other invasion team sports.
arXiv:2606.00476v2 Announce Type: replace Abstract: Do LLM agents act on the reasoning they state? This question of process fidelity is central to LLM-based social simulation, yet hard to measure where no reference for correct behavior exists. We study it in a controlled setting: a Texas Poker simulator with a verifiable reference action for every decision by splitting the faithfulness gap into two steps: reasoning-to-conclusion (does the stated decision follow from the agent's own reasoning?) and conclusion-to-action (does the agent execute what it states?). The two steps behave very differently. Conclusion-to-action is reliable: inconsistency is 0.7% for Claude Haiku 4.5 and 1.4% for DeepSeek-Reasoner once the conclusion is read from an explicit tag, whereas free-text conclusion extraction reports 22-26%. Reasoning-to-conclusion is where fidelity frays, but not through a single dominant failure. In a step-level diagnostic the agent's errors split roughly evenly between bad inputs, borderline cases, and rule misapplication deriving a conclusion that contradicts the agent's own restated rule from inputs it estimated correctly. This composition is model-dependent: rule misapplication accounts for a third of Haiku's interpretable errors but only 8% of DeepSeek's. The one robust signal is directional: when an agent does misapply its own stated rule, it almost always (99.5% for Haiku) errs in the risk-averse direction. The override is partly hedging behavior, not a capability limit: instructing the agent to apply the rule mechanically halves the misapplication rate (13.9% to 6.8% of decisions) and raises adherence by eight points. Process-fidelity evaluation should therefore elicit machine-checkable conclusions and probe for directional biases rather than assume a single upstream failure mode, lest it conflate measurement noise with model behavior.
arXiv:2607.05891v1 Announce Type: new Abstract: Coreset selection aims to identify a small and highly representative subset of a massive dataset for efficient model training. The problem remains challenging even in the few-shot knowledge distillation (KD) setup, where a full-scale pre-trained teacher informs the student network. Typical sample selection strategies often struggle to surpass the random selection baseline. In this paper, we showcase few-medoids, an embarrassingly simple coreset selection strategy that chooses the samples closest to the centroid (average image) of each class. We present extensive KD experiments on four datasets, covering a wide range of image classification problems, and three teacher-student model pairs, comprising both convolutional and transformer networks. Although the proposed method is embarrassingly simple, our empirical results indicate that few-medoids is able to consistently surpass the random selection baseline, as well as the other coreset selection strategies. We therefore consider that few-medoids can be used as a drop-in replacement for commonly-used baselines (e.g. herding or k-center Greedy), in future research on coreset selection. To reproduce the reported results, we publicly release our code at https://github.com/CemilAndreiDilmac/Few-Shot-KD-Coreset.
arXiv:2607.06393v1 Announce Type: new Abstract: We give faster exponential-time randomised approximation algorithms for counting problems where polynomial-time approximation is unavailable and exact exponential-time counting remains expensive. For general \(n\)-vertex graphs, our independent-set counter runs in \(O^{\ast}(1.1869^{n})\) time, improving the previous \(O^{\ast}(1.2041^{n})\) general-graph bound. For \(n\)-variable \#\textsc{2-SAT}, we obtain an \(O^{\ast}(1.2373^{n})\)-time approximation algorithm, narrowly below Wahlstr{\"o}m's currently cited \(O^{\ast}(1.2377^{n})\) variable-parameter exact bound. The new algorithmic point is to take the square root after decomposition. For a single bounded unweighted self-reduction with \(f(x)\) positive leaves and recursion-compatible upper bound \(b(x)\), an enumerate-or-sample estimator gives an \((\varepsilon,\delta)\)-approximation in \[ O^{\ast}\!\left(\sqrt{b(x)}\,\varepsilon^{-2}\log \tfrac1\delta\right) \] time. After preprocessing decomposes an input into many bounded cores, the combined estimator pays \[ O^{\ast}\!\left(\sqrt{\sum_i b_i(x_i)}\,\varepsilon^{-2}\log \tfrac1\delta\right), \] rather than estimating the cores separately at cost \(\sum_i \sqrt{b_i(x_i)}\). The same conversion improves the bases for counting maximal cliques, minimal separators, and perfect matchings in subcubic graphs. Bounded unweighted self-reductions provide the formal language; at the level of counting classes, the resulting unweighted formulation has the same Karp closure as TotP. With explicit recursion-tree access, the framework yields black-box quantum speed-ups.
arXiv:2604.03148v2 Announce Type: replace Abstract: The absorption of light is one of the most fundamental processes in condensed-matter physics and optics. Here we investigate under which conditions laser light is absorbed by a crystalline material as an electromagnetic wave with delocalized properties or rather as photons that cause discrete, localized, nanometer-sized consequences. We excite the first-order phase transition of vanadium dioxide with laser pulses of sufficient frequency to overcome the band gap but with insufficient pulse energy to overcome the latent heat. According to Maxwell's equations and Bloch theory, no transition should occur, because nowhere in the material is enough energy. Nevertheless, we observe with ultrafast electron diffraction a disordered crystal geometry with nanometer-sized spots of switched material that grow and diminish with time. The amount of localized spots matches approximately to the number of photons in the absorbed laser wave. Two optical experiments substantiate this phenomenon, and simulations reproduce all measurements results. We discuss whether crystals defects, temperature, or a genuine wavefunction collapse can explain the discovered phenomenon. Practically, the reported absorption mechanism enables local consequences at substantially higher energy than average and provides insight into symmetry breaks and non-thermal fluctuations within complex materials.
arXiv:2604.19311v2 Announce Type: replace Abstract: We demonstrate a spatially resolved method for imaging millimeter-wave (mmWave) electric fields using Rydberg-state fluorescence in a warm atomic vapor. By utilizing a multi-photon ladder excitation scheme, we leverage a specific decay channel that remains dark in the absence of the mmWave field, resulting in high-contrast imaging with effectively zero background. Absolute calibration of the local electric field is achieved by reconstructing the Autler-Townes splitting of the Rydberg resonance across the imaging volume. To ensure robust field extraction across a wide dynamic range--including regimes where spectral features are not fully resolved--we employ a steady-state analysis based on the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. We apply this technique to visualize standing-wave interference patterns within a vapor cell and demonstrate the ability to engineer local field distributions using structured dielectric reflectors. This approach provides a versatile and self-calibrating platform for the diagnostic imaging of high-frequency electromagnetic fields and the characterization of mmWave-optical interfaces.
arXiv:2605.11692v2 Announce Type: replace Abstract: We study a triplet majority-rule opinion-dynamics model with collective reversal on quenched networks. Interactions occur on local triplets composed of one agent and two of its neighbors, while collective reversal acts only on unanimous triplets. This rule separates local conformity from external perturbations that disrupt local agreement. We show that quenched network topology shifts the order--disorder critical point away from the well-mixed value. For Barab\'asi--Albert, Erd\H{o}s--R\'enyi, random regular, and Watts--Strogatz networks, the estimated critical exponents remain close to the mean-field values, suggesting mean-field-like universal behavior within the system sizes studied. The strongest shift of the critical point occurs for Watts--Strogatz networks, where clustering and local correlations make the ordered phase less stable. A rewiring analysis of Watts--Strogatz networks further shows that the ordered phase becomes more stable as the network becomes more random. These results indicate that quenched topology primarily controls the location of the transition, while the collective-reversal mechanism largely preserves mean-field-like critical behavior.
arXiv:2607.06054v1 Announce Type: new Abstract: Off-the-shelf TTS systems are poorly adapted to Taiwanese Mandarin. Their accent defaults to other Mandarin variants, their tokenizers over-segment common Taiwanese text, and their pronunciation degrades at code-switching boundaries where Chinese and English alternate within one utterance. These problems share one root: the text side lacks adaptation to the Taiwanese context. We address the text side from the bottom up. PangolinTokenizer, a byte-level BPE tokenizer trained on Taiwan-context data, reaches the lowest token rate (0.485 tokens/character) with the smallest vocabulary among nine tokenizers. Barbet, a billion-parameter Traditional-Chinese language model trained on PangolinTokenizer, serves as the text-semantic frontend and ranks first among comparable public models on a 14-task evaluation. BlueMagpie-TTS attaches Barbet to the pretrained acoustic stack of VoxCPM2 through a learned bridge, keeping the acoustic stack fixed. On a 1000-sentence Taiwan-localized test set, it lowers CER from 11.45% to 4.81% and WER from 14.83% to 5.36%, relative reductions of 58.0% and 63.9%. In a blind listening study on 500 of these sentences with ten listeners, 65.6% of majority votes prefer BlueMagpie-TTS.
arXiv:2607.06056v1 Announce Type: new Abstract: Social pressure -- the awareness of being observed by others -- is a fundamental driver of prosocial behavior in human societies. Yet it is typically assumed that only direct neighbors exert vigilance pressure on an individual, despite empirical evidence that social influence persists to at least three degrees of separation. Here we show that extending the reach of social vigilance beyond direct neighbors substantially promotes cooperation. We couple a Prisoner's Dilemma on one layer of a multiplex network to a vigilance cascade on the other, with influence decaying geometrically with network distance. Extending vigilance to just the second circle of influence shifts the critical temptation for defection by nearly 30\% in sparse networks. Extending to four circles raises this threshold by over 50\%. The $L=1\to2$ transition already accounts for most of the gain, consistent with the decay coefficients of social influence reported in controlled experiments. The effect is strongest in sparse topologies, requires that the vigilance and game layers be aligned, and reproduces directly on a real social network of physicians; in dense, hub-dominated networks the gain instead depends sharply on how fast influence decays with distance, switching between weak and strong cooperation as the decay rate crosses a threshold. Our results strongly suggest that even modest expansions of social awareness -- such as those enabled by online social platforms -- can substantially reshape the landscape of cooperative behavior in human populations.
arXiv:2602.22600v2 Announce Type: replace Abstract: Training selects for behavior, not circuitry: many weight configurations can implement the same function. Studying any single trained neural network thus risks describing accidents of one training run rather than the computation itself. This work shifts focus from what transformers happen to do to what they must do by extracting algorithmic cores, compact subspaces that are necessary and sufficient for a task and that recur across independently trained models. Here, Algorithmic Core Extraction (ACE) is introduced to isolate these subspaces, causally validate them, and recover the algorithms they implement across settings ranging from synthetic tasks to large-scale pretrained models. Markov-chain transformers embed three-dimensional cores in nearly orthogonal subspaces yet recover identical transition spectra. Modular-addition transformers form compact cyclic cores at grokking that later inflate under continued regularization, redundantly distributing the same computation across many functionally equivalent modes. This functional redundancy is found to accelerate the transition from memorization to generalization, yielding an inverse scaling law for grokking time. In six language models spanning more than two orders of magnitude in scale (GPT-2 Small/Medium/Large, LLaMA-3.1, Gemma-2, and Qwen2.5), subject-verb agreement is governed by a single, steerable axis that aligns across architectures. Flipping this axis inverts grammatical number throughout open-ended generation. Together these results suggest that beneath the apparent complexity of trained transformers lies a simpler, shared computational structure, and that targeting invariants rather than parameterizations may offer a more tractable path to mechanistic understanding and control. Code: https://github.com/joshseth/cores
arXiv:2607.05536v1 Announce Type: cross Abstract: Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers. However, its application to regression remains under-explored and faces unique challenges. Existing regression certificates rely on probabilistic acceptance regions and fail to exploit the local geometry of the function. In this work, we present a novel framework for certified robust regression that addresses these limitations. We derive a prediction-centered certificate that guarantees the stability of the smoothed model's prediction and ensures practical computability at test time. We investigate several alternatives for constructing these certificates by explicitly incorporating means, variances, and gradients. In particular, we demonstrate on the MNIST rotation task that utilizing gradient information yields significantly tighter robustness certificates compared to the current state-of-the-art, alpha-smoothing.