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Over the last decade, building human-level artificial general intelligence has moved from far-fetched speculation to being a concrete next-decade target for many of the largest AI organizations. Achieving this goal would have profound and far-reaching impacts on human society, which raises many complex questions for the decade ahead. This report investigates how AI itself might continue to develop in a post-AGI world along the continuum of machine intelligence. The endpoint of this continuum, Universal AI, is theoretically well understood, which provides some formal grounding for the main focus of this report: the transition from human-level AGI to artificial general superintelligence, which can intuitively be understood as a system that is more intelligent and cognitively capable than large organizations of humans. After characterizing ASI, the report discusses four potential pathways from AGI to ASI: scaling AGI, AI paradigm shifts, ASI emerging from large-scale multi-agent collectives, and recursive improvement. The report then discusses possible frictions and bottlenecks along these pathways. Determining whether the impact of these frictions will be negligible or substantial raises a number of concrete open research questions. While large uncertainties for predicting ASI progress remain, it cannot be ruled out that AI progress might continue to accelerate over the next years. This would imply that the image of a single transformative step change, caused by the introduction of human-level AGI into our society, could be inaccurate. More apt might be the prospect of a series of transformative societal changes caused by AI-enabled progress and breakthroughs across many areas of science and technology. Preparing for this prospect requires a massively interdisciplinary endeavor of global scope and interest.

Divide-and-conquer (D&C) is the natural parallel strategy for symmetric tridiagonal eigenvalue decomposition, yet eigenvalue-only solvers fall back to serial QR algorithm because the quadratic transform state each merge carries exhausts memory at scale. In this paper, we demonstrate that each merge stage in D&C needs only two boundary rows, the first and last rows of a node's eigenvector block, and these close into a recurrence whose parent rows follow from its children's and local merge data alone, so the state is carried up the tree with nothing replayed and persistent memory drops from quadratic to linear. Because this state keeps no replay workspace, adapting the schedule to each merge's post-deflation active rank is a scheduling choice, so both CPU and GPU spend finer-grained parallelism only where substantial secular work survives. We evaluate optimized CPU and GPU implementations, with complexity and correctness analysis, against QR, bisection, and D&C routines in standard libraries.

The weighted edit distance $\mathsf{ed}^w(X,Y)$ is the minimum cost of an alignment of strings $X$ and $Y$, where a weight function $w$ specifies the cost of each character insertion, deletion, and substitution. For strings of total length $N$, the textbook dynamic program takes $O(N^2)$ time, and no $O(N^{2-δ})$-time algorithm exists, even for unit costs, unless the Orthogonal Vectors Hypothesis (OVH) fails. This motivates the study of approximation algorithms. For unit costs and metric weights, the best truly subquadratic approximation factor was $3+\varepsilon$; we give randomized $3$-approximations in $\tilde O(N^{11/6})$ and $\tilde O(N^{40/21})$ time, respectively. For non-metric weights, we prove quadratic lower bounds for any approximation factor: $Ω(N^2)$ queries to $w$ over alphabets of size $Θ(N)$, and OVH-hardness over constant-size alphabets. These lower bounds motivate the bounded setting, parameterized by $k:=\mathsf{ed}^w(X,Y)$ for $w$ normalized so that every edit costs at least one. We give a deterministic $(1+\varepsilon)$-approximation algorithm in $\tilde O(N+k^2/\sqrt\varepsilon)$ time, matching the $O(N+k^2)$-time Landau-Vishkin algorithm for unit costs up to logarithmic factors for constant $\varepsilon>0$. Our main technical contribution is a Monge-matrix approximation framework for alignment problems: every $n\times n$ Monge matrix with entries in $\{0\}\cup[1,W]$ has an entrywise $(1+\varepsilon)$-approximation by a Monge matrix with $\tilde O(n\log(W)/\sqrt\varepsilon)$ strict Monge inequalities. As further applications of our Monge approximation framework, we maintain a $(1+\varepsilon)$-approximation of $\mathsf{ed}^w(X,Y)$ under character edits in $\tilde O(N\log(W)/\sqrt\varepsilon)$ time per update for weights at most $W$, and in $\tilde O(K/\sqrt\varepsilon)$ time for a fixed threshold $K$.

Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation. While recent geometry-adaptive neural operators have made substantial progress, they are mainly designed for forward problems in which inputs and outputs share the same spatial domain. This limits their applicability for boundary value problems (BVPs) and inverse problems, where inputs and outputs may live on different domains. We introduce the Geometry-Adaptive Integral Autoencoder (GAIA), an operator learning model that encodes the domain boundary and the interior field distribution into geometry tokens, and conditions integral transform layers on these tokens via cross-attention, allowing the kernel to adapt locally to geometric features. This yields an architecture capable of learning solution operators for forward and inverse problems on arbitrary domains, solving each in a single pass at inference without per-domain optimization, iterative refinement, or graph construction. We evaluate GAIA on seven 2D and 3D benchmarks, four of which are new or substantially extended benchmarks for inverse problems and BVP: electrical impedance tomography, optical tomography, 3D Darcy flow on varying geometries, and a modified setting of the Poisson BVP on mechanical components benchmark (MCB). GAIA sets new state-of-the-art results on every inverse and BVP task, reducing median relative $L^2$ error by 64% on airfoil flow reconstruction and 22% on EIT relative to the next best amortized method, and outperforming all baselines on every shape category of MCB. On other forward problems, GAIA is competitive with specialized solvers while maintaining stable accuracy across point resolutions on which transformer-based baselines degrade.

AI systems have become increasingly capable of dangerous behaviours in many domains. This raises the question: Do models sometimes choose to violate human instructions in order to perform behaviour that is more useful for certain goals? We introduce a benchmark for measuring model propensity for instrumental convergence (IC) behaviour in terminal-based agents. This is behaviour such as self-preservation that has been hypothesised to play a key role in risks from highly capable AI agents. Our benchmark is realistic and low-stakes, aiming to reduce evaluation-awareness and roleplay confounds. The suite contains seven operational tasks, each with an official workflow and a shortcut whose policy status varies by condition. An eight-variant shared framework varies monitoring, instruction clarity, stakes, permission, instrumental usefulness and blocked honest paths to support inferences regarding the factors driving IC behaviour. We evaluated ten models using deterministic environment-state scorers over 1,680 samples, with trace review employed for audit and adjudication purposes. The adjusted IC rate is 86 out of 1,680 samples (5.1%). IC behaviour is concentrated rather than uniform: two Gemini models account for 66.3% of IC cases and three tasks account for 84.9%. Conditions in which IC behaviour is indispensable for task success result in the greatest increase in the adjusted IC rate (+15.7 percentage points), whereas emphasising that task success is critical or certain framing choices do not produce comparable effects. Our findings indicate that realistic, low-nudge environments elicit IC behaviour rarely but systematically in most tested models. We conclude that it is feasible to robustly measure tendencies for dangerous behaviour in current frontier AI agents.

Fetal brain biometry provides a quantitative basis for assessing prenatal growth and identifying congenital brain abnormalities. However, comprehensive assessment remains limited by labor-intensive manual measurements and automated models that lose accuracy across imaging sequences and institutions. We introduce BioTTA, an anatomically guided test-time adaptation framework that measures 11 fetal brain biometrics from reconstructed three-dimensional magnetic resonance images. BioTTA adapts pretrained models to individual unlabeled volumes using geometric consistency and atlas priors, without access to source images. In a retrospective study across five centers in China and Switzerland, BioTTA improved measurement accuracy across three out-of-distribution datasets and two network architectures. It reduced mean absolute measurement errors by 46-82% relative to the corresponding models without adaptation, achieving errors similar to those of supervised fine-tuning. Its measurements were mapped onto normative growth trajectories derived from expert annotations, enabling gestational-age-specific assessment through a web-based reporting platform. Across four disease cohorts, the platform achieved 82.1-95.0% accuracy in binary detection of ventriculomegaly or cerebellar abnormalities, with performance similar to that of a senior radiologist. BioTTA provides a practical foundation for standardized fetal brain biometry across heterogeneous imaging settings, supporting scalable prenatal growth assessment and quantitative evaluation of brain abnormalities.

Reflectance confocal microscopy (RCM) provides noninvasive, cellular-resolution "optical biopsies" of human skin in vivo by acquiring en-face images at successive depths, forming a sparse z-stack. Due to optical limitations, these stacks are anisotropic 3D volumes with lateral resolution (0.5 $μ$m) $\sim$6 times higher compared to axial resolution, which is defined by the optical sectioning (3 $μ$m), limiting the interpretation of tissue. Our goal is to provide continuous-depth visualization by interpolating intermediate sections and making the 3D volume isotropic. Such a representation permits arbitrary-direction sectioning, including histopathology-like cross-sectional examination, without requiring per-patient optimization. To that end, we introduce the first RCM-specific novel-view synthesis (NVS) approach, CD-RCM, a feedforward model that predicts realistic, unseen depths from sparsely sampled RCM stacks. Classical neural rendering methods focus on reconstruction from surface-level multi-view observations. In contrast to surface-level camera views, RCM can acquire optically sectioned en-face images of tissue beyond the surface up to 200 $μ$m. However, during visualization of the RCM stacks, observations of the shallower sections (towards the surface) obscure the deeper ones. This unique axial imaging geometry and layer-dependent anatomical organization motivated our development of a tailored architectural and training framework that explicitly accounts for RCM's depth-resolved, occlusive imaging physics. Experiments demonstrate that CD-RCM achieves high-fidelity novel-view synthesis with sub-second inference time.

Cloud-based online services face significant sub-second load fluctuations while needing to meet strict Service Level Objectives (SLOs). Cluster operators often over-provision resources to protect SLOs, sacrificing utilization and cost efficiency. Existing reactive and proactive autoscalers, serverless (FaaS) deployments, and VM/FaaS hybrid systems fail to reconcile strict SLO compliance with low cost and high utilization under fine-grained load fluctuation. We introduce Spandana, an architecture that addresses this trade off by decoupling SLO enforcement from cost optimization. A lightweight controller colocated with each application VM enforces SLOs by steering each arriving request between the VM and FaaS. Requests that can meet the SLO stay on the VM; the remaining requests are forwarded to a stock FaaS layer such as AWS Lambda. For cost optimization, Spandana's resource allocator determines the most-efficient VM provisioning by accounting for VM cost, FaaS cost, and traffic volatility, allowing the VM pool to run at high utilization. Our evaluation shows that Spandana maintains strict SLO adherence, achieves 76-86% CPU utilization, and reduces cost by 5-44% over three SOTA baselines.

Hallucinations remain a major obstacle to deploying large language models (LLMs) in knowledge-intensive settings, where generated responses must be faithfully grounded in provided evidence. Reinforcement learning (RL) is a promising direction for hallucination mitigation, but response-level faithfulness rewards suffer from a granularity mismatch: localized hallucinations can cause supported content to receive spurious penalties. Although recent work introduces fine-grained feedback such as claim-level verification and token-level rewards, unbalanced credit assignment can still induce length, verbosity, or optimization-noise biases. We propose BALTO, a Balanced Token-level Policy Optimization framework for hallucination mitigation. BALTO extracts checkable factual claims, verifies them against the reference context, and projects claim-level judgments to token-level labels. A balanced token-level credit assignment mechanism is introduced into the framework. This design redistributes probability mass from unsupported content toward faithful content, rather than suppressing the entire response. We systematically analyze the limitations of response-level rewards from a theoretical standpoint, and prove BALTO's advantages in training stability and optimization efficiency for hallucination mitigation. Experiments on ConFiQA, RAGTruth, and FinLLM-Eval show that BALTO achieves the highest faithfulness across all six model--benchmark settings and consistently outperforms existing post-training baselines in Q-Score, demonstrating a stronger faithfulness--informativeness trade-off. The code is released at https://github.com/NingLi670/BALTO.

Attribution methods for Vision Transformers (ViTs) aim to identify image regions that influence model predictions, but producing faithful and well-localized attributions remains challenging. Existing attribution methods face several limitations, with gradient-based, relevance-propagation, and attention-based methods relying on local approximations, while perturbation- or optimization-based methods intervene on inputs, tokens, or surrogates rather than internal patch representations. The key challenge is that class-relevant evidence is formed through interactions between patch tokens across layers; methods that operate only on input changes, attention weights, or backward relevance signals may therefore provide indirect proxies for patch importance rather than directly testing the predictive effect of contextualized patch representations. We propose Causal Attribution via Activation Patching (CAAP), which estimates the contribution of individual image patches to the ViT's prediction by directly intervening on internal activations rather than using learned masks or synthetic perturbation patterns. For each patch, CAAP inserts the corresponding source-image activations into a neutral target context over an intermediate range of layers and uses the resulting target-class score as the attribution signal. The resulting attribution map reflects the causal contribution of patch-associated internal representations on the model's prediction. The causal intervention serves as a principled measure of patch influence by capturing semantic evidence after initial representation formation, while avoiding late-layer global mixing that can reduce spatial specificity. Across multiple ViT backbones and standard metrics, CAAP consistently outperforms existing methods in various settings and produces more faithful and localized attributions.

Text-to-3D solid retrieval faces a fundamental representation gap: while natural language describes intrinsic shapes, Boundary Representation (B-rep) entangles precise geometry with arbitrary variations in pose, scale, and boundary encoding conventions. Existing methods either discretize B-reps at the cost of analytic precision, or learn features from topological graphs without explicit invariance guarantees. We propose **SpectraBRep** (*Spectral Geometry for Text-to-B-rep Retrieval*), a framework based on geometric invariance and spectral descriptors that mathematically eliminates representation ambiguities prior to cross-modal alignment. Formalizing translation, rotation, reflection, uniform scaling, and contour re-indexing via group actions, we exploit the planar-profile-and-extrusion structure of engineering solids to construct a unified spectral descriptor across cross-sectional regions, contour boundaries, and extrusion depths. On public benchmarks, our method achieves state-of-the-art recall performance across all evaluation metrics.

A foundational theorem of Ajtai, Komlós, Pintz, Spencer, and Szemerédi asserts that every $n$-vertex $k$-uniform uncrowded hypergraph (i.e., with girth at least $5$) of maximum degree at most $Δ$ contains an independent set of size $cn(\logΔ/Δ)^{\frac{1}{k-1}}$ for some absolute constant $c>0$. Improving an earlier bound of Frieze and Mubayi, Iliopoulos showed that every such hypergraph has list chromatic number at most $(1+o(1))(k-1)(Δ/\logΔ)^{\frac{1}{k-1}}$. Determining the optimal leading constant in this bound remains a major open problem. A natural target, suggested by the coupon-collector heuristic, is $(k-1)^{\frac{1}{k-1}}$, which also corresponds to the shattering threshold for coloring sparse random hypergraphs. Our main result shows that this target is attained: for every integer $k\ge2$, every $k$-uniform uncrowded hypergraph of maximum degree at most $Δ$ satisfies: $$χ_\ell(\mathcal{H})\le(1+o(1))\Big((k-1)\fracΔ{\logΔ}\Big)^{\frac{1}{k-1}}.$$ In particular, this confirms a 2019 conjecture of Molloy for uncrowded hypergraphs. Building on this result, we prove that every $k$-uniform linear hypergraph of maximum degree at most $Δ$ has chromatic number at most $(c_k+o(1))(Δ/\logΔ)^{\frac{1}{k-1}}$, where $c_k\to1$ as $k\to\infty$, thereby proving a conjecture of Verstraëte and Wilson on the independence number of linear hypergraphs in the stronger form of colorings. Our techniques also yield a palette sparsification theorem for uncrowded hypergraphs, partially answering a question of Casselgren and Eriksson.

We study approximately stable committee selection under approval preferences, following Cheng et al.~[EC~2019] and Jiang, Munagala, and Wang~[STOC~2020]. In an approval-based committee election, $n$ voters each approve a subset of the candidates, and a committee of size $k$ is selected. A size-$k$ committee is $λ$-stable if, for every nonempty subset $T$ of candidates, the number of voters who strictly prefer $T$ is less than $λ$ times the proportional share $\frac{n|T|}{k}$. We consider sequential Phragmén, a classical polynomial-time voting rule, and prove that it always returns a $2$-stable committee. This implies that the $2$-core is always nonempty and improves upon the $3.651$-stability guarantee of Gao, Sun, and Vondrák~[EC~2026]. The guarantee also extends to weighted voters and is tight even for unweighted elections: for every $1\leλ<2$, sequential Phragmén can return a committee that is not $λ$-stable. Compared with the exact-core algorithm developed in concurrent work by Becker, Greger, and Peters~[arXiv~2026], sequential Phragmén is simpler to implement, and our proof of its $2$-stability is elementary.

Extreme events in chaotic systems are difficult to learn from short trajectories because they are controlled by finite-time instabilities rather than by frequently observed bulk dynamics. We propose a mechanism-aware conditioning plug-in framework that turns a nudged ensemble of an imperfect model into a non-intrusive sensor of the local instability geometry. In the small-noise regime, the ensemble covariance has the same finite-time deformation kernels that govern local instability, providing a Jacobian-free proxy for local amplifications around a trajectory. A small Feature-Wise Linear Modulation (FiLM) network injects the ensemble geometry into an otherwise unchanged backbone without modifying the low-fidelity model simulator. We demonstrate this interface in two settings: a Transformer-style residual-attention corrector for a controlled low-dimensional chaotic system and a probabilistic recurrent STORN corrector for topographic two-layer quasi-geostrophic (QG) flow. In the low-dimensional benchmark, leading ensemble-covariance directions identify transient instabilities that are also detected by Optimally Time-Dependent (OTD) modes. FiLM conditioning improves 99th-percentile exceedance-frequency errors over an otherwise identical unconditioned Transformer. In QG, an ensemble-conditioned FiLM-STORN model substantially improves long-horizon rare-event statistics in the data-limited regime, including density-tail errors, exceedance frequencies, and spatial exceedance-area distributions relative to an unconditioned STORN trained on the same data. On averaged high-threshold exceedance diagnostics, it also outperforms the unconditioned baseline STORN trained with 20 times more expensive trajectory data. These results show that local instability geometry is not merely interpretable post hoc, but an actionable conditioning signal for data-efficient rare-event emulation.

Objective: Survival analysis is central to medical prediction, yet large language models (LLMs) are rarely used as end-to-end survival models because censoring prevents straightforward supervised fine-tuning. Here we present LLMSurvival, a framework that enables censoring-aware survival analysis with unmodified LLMs operating directly on tabular clinical data. Materials and Methods: LLMSurvival reformulates time-to-event prediction as pairwise ranking among comparable subjects, and derives test-time risk by aggregating comparisons against anchor individuals from the training cohort. Results: Across two clinical tasks (ICU mortality prediction in MIMIC-IV and fragility fracture prediction in a NewYork-Presbyterian/Weill Cornell Medicine cohort), LLMSurvival improves overall concordance over Cox proportional hazards modeling by 3.1% for ICU mortality and 0.5% for fracture risk, 2.1% on average for ICU mortality and 2.8% for fracture risk over three established deep learning survival models. Discussion: The results show that survival modeling with censoring can be made compatible with LLM fine-tuning through comparison-based reformulation. The framework demonstrates high portability and superior performance over expert curated scores like SAPS-II and FRAX scores across diverse clinical context. Furthermore, the framework supports local deployment, as compact, publicly available base models provide sufficient performance. Conclusion: The LLMSurvival framework serves as a proof of concept for an integrated, censoring-conscious approach to survival analysis via LLMs.

When a model behaves in unexpected ways, we want to know why, but its intent cannot be observed directly, and its self-reports may be rationalizations. We introduce comparative motivation profiles, which treat intent as propensity: we edit the model's beliefs about facts that a hypothesized motivation would depend on and measure how its behavior changes. To keep artifacts of the editing method from driving the result, we edit two minimally different hypotheses in the same way, with matched amplify and suppress edits; we call this symmetric belief editing. We apply it to alignment faking in four open-weight model organisms, contrasting scheming, which tracks the training consequences of compliance, with performative misalignment, which tracks what researchers expect to observe, and edit beliefs with synthetic document fine-tuning (SDF), activation steering, and prompting. Under SDF, amplifying performative beliefs raises alignment faking on every model, while scheming edits move it less or shift compliance in the monitored and unmonitored conditions alike. Steering on model organisms changes compliance along the expectation-tracking direction but mainly the reasoning along the consequence-tracking direction, and prompting agrees. In these organisms, alignment faking follows what the models infer their evaluators expect, which puts it closer to sycophancy than to deceptive alignment.

For fixed nonempty words $u,v$, the minimum insertion degree of a shuffle is the least number of inserted-source runs among its representations. We prove that, after a block exchange from a minimum mask of degree $r$, the minimum over masks with commuting source projections is exactly $r-1$; a larger decrease occurs precisely when a noncommuting mask has fewer runs. If either source is unary, every such exchange is exact. We prove an explicit repair for an infinite periodic degree-three family. Computer-assisted results establish first-mask descent through combined length seventeen over every alphabet, degree-three first-mask descent through length thirty, and a uniform repair of all degree-three failures through length thirty, including all further letter identifications. Counterexamples to arbitrary, first, and last minimum-mask choices explain the need for alternative masks. Finally, we prove that minimum iteration depths have no gaps for arbitrary languages. General block-exchange descent and Singleton No-Gap remain open.

Organizations increasingly seek to share and access datasets to improve their ML models and derive insights. Despite the immense demand for quality data, data exchange and collaboration have not reached their full potential, as cited by the European Commission. One of the key reasons is the lack of reciprocity, where some participants perceive their contribution to others to be of higher value than what they receive in return. We propose a general framework for data exchange without payments, focusing on two main properties: (i) reciprocal fairness, which ensures that each agent receives utility proportional to their contribution to the total welfare -- contributions are quantifiable using well-established credit-sharing functions such as the Shapley share and proportional share, and (ii) core-stability, which guarantees that no coalition of agents can identify an exchange among themselves which they all unanimously prefer to the current exchange. Surprisingly, we show that fair and stable exchanges exist for all monotone continuous utility functions. Building on this, we investigate the computational complexity of finding approximate fair and stable exchanges. We present a local search algorithm for instances with monotone submodular utility functions and cross-monotone credit-sharing functions, e.g., Shapley share. We prove that this problem belongs to CLS ($=$ PPAD $\cap$ PLS) under mild assumptions. Our framework opens up several intriguing theoretical avenues for future research on data economics.

Traditional nonverbal behavior generation systems for virtual agents typically take utterances as input and generate behaviors that match or illustrate the spoken words. However, human nonverbal behavior is shaped by more than speech content. It is influenced by speaker roles, interpersonal relationships, social context, and cognitive and emotional states of interactants. Therefore, the nonverbal channel carries information or emotions hidden in words. Modeling these complex verbal-nonverbal mismatches is critical for realistic virtual agents, particularly in training applications. We propose a taxonomy of mismatches, strengthening, mitigating, and leaking, and evaluate whether LLMs can select contextually appropriate mismatched behaviors. Through human-subject studies, we assess whether these context-driven behaviors, realized in a virtual human framework, produce the intended effects. Our results demonstrate that LLMs, when prompted with social context, successfully select targeted mismatched behaviors (e.g., sarcasm). Furthermore, the human-subject evaluation confirms that these nonverbal cues significantly shift observers' perceptions of the agent's attitude and emotional valence. Participants successfully distinguished between distinct mismatch functions, such as strengthening, mitigating, and leaking, perceiving clear directional shifts in social meaning compared to matching baselines.

Pure speech language models often lag behind text and speech-text language models in generating coherent content, but this gap is difficult to quantify because speech and text systems are typically evaluated with different metrics and trained on different data. We study the speech-text modality gap in a family of spoken language models, based on flow matching for continuous acoustic feature generation. We construct a unified generation-based evaluation suite that compares speech-only, text-only, and speech-text language models trained on matched data distributions and evaluated in matched generation settings. We evaluate generated continuations along multiple dimensions: semantic coherence, measured by transcribing generated speech and scoring it with a reference language model; local phonetic structure, measured by phone n-gram distributional statistics; speaker consistency and acoustic quality; and emotion-based distributional metrics. Across datasets, we find that joint speech-text modeling substantially improves semantic coherence. However, the improvement is not uniform across metrics: phone-level metrics change only modestly, speaker similarity and predicted quality are lower for speech-text continuations, while emotion-based distributional metrics improve. Compared with larger-scale speech-only models, our speech-text model closes much of the scaling gap in transcript-based semantic coherence, suggesting that text provides an efficient semantic training signal for spoken language modeling.

IoT-Edge-Cloud infrastructures are increasingly heterogeneous, and experimenting across the continuum is difficult and risks disrupting live systems. Network Digital Twins (NDT) are a pragmatic answer, yet practitioners lack a structured account of three things: how to build an NDT from open tools, how to model wireless impairments, and how to understand whether the twin is faithful to the physical network, or not. This tutorial introduces NDT through the IRTF reference model and walks through a lightweight open-source blueprint built on Containerlab, Open vSwitch, \textit{Open Network Operating System (ONOS)}, and Prometheus/Grafana. It then explains how to define wireless impairment profiles (static, model-based, trace-driven, AI-generated, and live), and what each approach can and cannot reproduce. Finally, it presents a workflow to validate the twin against the physical network. A proof-of-concept Edge case study illustrates the procedure, including the pitfalls encountered and the lessons learned. Directions for future research are outlined.

Masked Diffusion Models (MDMs) are well known for fast text generation via parallel decoding. However, independent parallel sampling can commit to inconsistent predictions, and less is known about how to selectively revise these early token commitments. In this work, we introduce $\underline{\mathrm{P}}$lanned $\underline{\mathrm{U}}$nmasking-and-$\underline{\mathrm{R}}$evision Joint $\underline{\mathrm{L}}$earning (PURL) for MDMs, a training-based framework that seamlessly unifies parallel generation with selective token revision. We derive a normalized joint transition whose likelihood factorizes into edit selection, unmask selection, and token prediction. These components are trained jointly on partially masked sequences constructed according to the model's own unmasking policy. During inference, all three decisions are supported by a single shared forward pass, enabling the model to decode masked tokens and revise noisy tokens. Across logic puzzles, mathematical reasoning, and code generation, PURL improves accuracy at matched unmask budgets, with relative gains up to 47.4% accuracy improvement and up to an $8\times$ reduction in scheduled decoding rounds. Beyond these gains, our analysis further reveals general principles of revisable decoding: token edits become more effective as context accumulates; early edits can steer unfinished trajectories, whereas later edits tend to remain localized; and effective edits therefore depend on both calibrating when to intervene and learning where and how to revise. Together, these suggest that effective parallel generation depends not on revising more tokens, but on making the right commitments revisable at the right time.

Let $q$ be an odd prime. Let $ζ_q$ be a primitive $q$th root of unity, and put $K=\mathbb{Q}(ζ_q)$, with ring of integers $\mathcal{O}_K=\mathbb{Z}[ζ_q]$. As $q$ ranges over odd primes, we prove that the decision version of the Shortest Vector Problem ($\mathsf{SVP}$) in the canonical $\ell_2$-norm is $\mathsf{NP}$-complete on full-rank free submodules of $\mathcal{O}_K^2$ by giving a deterministic polynomial-time many-one reduction from Exact Cover by 3-Sets (X3C). The module rank is fixed at two. The main obstacle is closure under the action of $\mathcal{O}_K$. A module containing a nonzero vector also contains every scalar multiple of that vector by a nonzero element of $\mathcal{O}_K$, and some of these multiples may be shorter. Three ideas overcome this obstacle. First, we map the Bennett--Peikert Reed--Solomon lattice to a principal cyclotomic ideal and use Wan's point-count estimates to prove that a coset of this ideal contains many binary coefficient representatives. Second, we construct a checker whose canonical squared norm encodes the X3C equations, with a controlled nonnegative error term. Third, the checker and a second module coordinate combine with a separation bound for ideal cosets to rule out short vectors in NO instances. Each constructed instance consists of an odd prime $q$, two integral generators whose $2\times2$ generator matrix has nonzero determinant, and an integer squared threshold. The construction also gives $\mathsf{NP}$-hardness of search-$\mathsf{SVP}$ under deterministic polynomial-time Turing reductions with at most one oracle call.

The nonnegative rank of a nonnegative matrix $X$ is the smallest number of nonnegative rank-one factors that sum to $X$. Since computing the nonnegative rank is NP-hard, it is common to circumvent this issue by computing lower and upper bounds. In this paper, we propose non-convex formulations and practical implementations for four important lower bounds for the nonnegative rank, namely the fooling set bound (FSB), the rectangle covering bound (RCB), the hyperplane separation bound (HSB), and the self-scaled bound (SSB). In particular, to the best of our knowledge, our algorithm for computing the SSB is the first available in the literature. We compute the SSB for several matrices for which its value had not previously been reported. In some cases, the SSB provides the best known upper bound, while the other three bounds do not. Moreover, on canonical benchmarks, we show that our non-convex approaches are often competitive with existing methods. The paper also provides a consolidated reference for the current state of several classical lower bounds on a large number of benchmark matrices.

Traditional recommendation systems rely on latent (dense) representations, making them difficult to interpret and control. We propose the Controllable and Content-Based Recommendations (CCBR) framework, which builds its recommendations from textual user profile representations. CCBR plugs into collaborative filtering models and introduces controllability via text bottlenecks. We show that CCBR enables text-based and multimodal interventions, allowing users to steer the model towards the directions they prefer. Different from existing controllable recommendation systems, CCBR infers the text summaries directly from item contents (images, audio or video). Across image, audio, and video datasets, we demonstrate that the proposed framework obtains competitive model performance with standard (latent-representation) models while providing controllable model summaries via text. The model also outperforms TEARS, a recent baseline for controllable recommendation systems. Through systematic interventions, we demonstrate the efficacy of the steering mechanism.

Weight binarization has emerged as a promising strategy to reduce the complexity of large language models (LLMs). Existing approaches fall into post-training binarization, which is simple but causes severe performance loss, and training-aware methods, which depend on full-precision latent weights, adding complexity and limiting efficiency. We propose a novel framework that represents LLMs with multi-kernel Boolean parameters and, for the first time, enables direct finetuning LMMs in the Boolean domain, eliminating the need for latent weights. This enhances representational capacity and dramatically reduces complexity during both finetuning and inference. Extensive experiments across diverse LLMs show our method outperforms recent ultra low-bit quantization and binarization techniques.

Probabilistic linear solvers (PLSs) return probability distributions that quantify uncertainty due to limited computation in the solution of linear systems. The literature has traditionally distinguished between Bayesian PLSs, which condition a prior on information obtained from projections of the linear system, and probabilistic iterative methods (PIMs), which lift classical iterative solvers to probability space. In this work we show this dichotomy to be false: Bayesian PLSs are a special case of non-stationary affine PIMs. In addition, we prove that any realistic affine PIM is calibrated. These results motivate a focus on (non-stationary) affine PIMs, but their practical adoption has been limited by the significant manual effort required to implement them. To address this, we introduce affine tracing, an algorithmic framework that automatically constructs a PIM from a standard implementation of an affine iterative method by passing symbolic tracers through the computation to build an affine computational graph. We show how this graph can be transformed to compute posterior covariances, and how equality saturation can be used to perform algebraic simplifications required for computation under specific prior choices. We demonstrate the framework by automatically generating a probabilistic multigrid solver and evaluate its performance in the context of Gaussian process approximation.

Gradient-boosted decision trees are among the strongest off-the-shelf predictors for tabular regression, but point predictions alone do not quantify uncertainty. Conformal prediction provides distribution-free marginal coverage, yet standard split conformal uses a single global residual quantile and can adapt poorly to heteroscedasticity. We propose LoBoost, a model-native local conformal method that reuses the fitted ensemble's leaf structure to define a multiscale partition of the feature space. Each input is represented by the sequence of leaves it visits along the boosting path, and matching leaf prefixes define nested groups in which residual quantiles are estimated locally. By reusing the predictive structure already learned by the model, LoBoost requires no auxiliary partition or nuisance model, no retraining, and no additional data split beyond standard conformal calibration. Our theory connects the stability of the fitted ensemble and the geometry of its induced cells to local residual-score homogeneity, providing finite-sample coverage-error control and asymptotic pointwise validity as the local calibration size grows and the cells become sufficiently homogeneous. Experiments show a transparent quality-cost trade-off: LoBoost improves over global split conformal on several heterogeneous datasets, but it is not uniformly superior to the adaptive baselines and is not uniformly Pareto-optimal.

Teleoperation and assistive devices are tuned for channel fidelity, while whether the operator experiences the device as part of the body, the Sense of Embodiment, is measured only afterwards. Minimizing the mismatch between the operator's predictions and the returned feedback fails twice: the predictions cannot be observed, and removing feedback minimizes the objective. We formulate an embodiment-aware controller that instead infers the operator's embodiment and visuo-proprioceptive cue weighting from implicit gaze and pupil signals and task outcome, and chooses bounded device settings under explicit preferences, cast as a discrete Active Inference agent. In simulations with heterogeneous synthetic operators, it raised embodiment from 0.76 to 1.66 on a 0-2 scale over the best fixed setting, within 0.02 of an oracle across ten random seeds; adaptation that did not read the operator gained nothing, and a prediction-error minimizer withheld feedback. An expected-utility controller with the same inference did as well, so the benefit comes from inference over the operator with explicit preferences, not from information seeking. Rules on a single signal came close when that signal was informative and failed when it was not; the controller degraded less, but failed when it trusted an uninformative signal unless briefly calibrated. Against published human data, the model reproduced the embodiment-performance relation, and embodiment developed on a plausible time scale. The embodiment signals were redundant when task success tracked embodiment and became the controller's objective when it did not. Studies with people must first establish calibrated cue-weighting signals and effort-independent embodiment signals.

RNA sequencing produces rich and diverse datasets of gene expression, offering compelling insights into cellular state and function that have many applications in drug discovery. Modeling such data is challenging due to inherent technical noise and experimental batch effects, as evidenced by many existing transcriptomic foundation models (FMs) underperforming relative to linear baselines. Such results raise the question of whether deep representation learning provides a distinct advantage over the direct use of raw transcript counts. Our work explores this by developing a new self-supervised model, TxFM, with a focus on inductive representation learning evaluations. TxFM employs a masked autoencoding approach tailored to diverse RNA-seq count data, and our ablation study empirically identifies crucial architecture configurations required for strong transfer performance. Additionally, we curate a public training corpus, DiverseRNA-1.4M, and find that TxFM trained on this curated dataset yields high-fidelity gene representations that outperform FMs trained on atlas-scale corpora over 100x larger. Overall, our results indicate that inductive self-supervised learning is a viable modeling approach for transcriptomics representation, provided a careful synthesis of model architecture and training data curation.