Papers

We argue that pattern recognition and step-by-step reasoning are two ends of a spectrum. A large language model (LLM) learns to reason step-by-step when data is structured such that the next token depends on a small amount of preceding context. Inference in LLMs resembles pattern recognition when the next token depends on a large amount of preceding context. If the next token depends on only the $c$ most recent tokens, reasoning traces are paths on a De Bruijn graph whose nodes are $c$-length contexts and edges are next-token transitions between contexts. The set of reasoning traces of a task forms a directed acyclic subgraph of the De Bruijn graph. An LLM that has learned all edges of this subgraph can compose them to solve longer, unseen tasks, i.e., it reasons step-by-step. We prove that the number of edges is vanishingly small compared to the number of reasoning traces. Empirically, the number of training samples a transformer needs is a power law in the number of edges, so learning to reason step-by-step is sample efficient. We can induce De Bruijn structure in any task by maintaining a “state” that makes future reasoning independent of the past. The frequency of states in the reasoning trace determines $c$. We show, by fine-tuning Qwen2.5-1.5B-Instruct to solve equations and answer questions about stories, that frequent states (small $c$) result in higher accuracy but greater fragility to perturbations at test time. LLMs trained with a large $c$ are only as good as models that perform pattern recognition without reasoning. A moderate density of states balances accuracy and robustness. We show that real-world data has De Bruijn structure: Qwen3-14B and Qwen3-32B retain over 75% of their accuracy on GSM8K, MATH-500 and GPQA-Diamond when attention is restricted to a sliding window less than 15% as long as the full reasoning trace.

Quantization-aware training (QAT) leverages lower-precision arithmetic to reduce the cost of LLM deployment, but aggressive quantization degrades final model performance. A common remedy is mixed-precision training, in which high precision is assigned to some of the layers to maintain performance while keeping the cost constrained. This approach then requires precision assignments for model layers during training. We provide a new approach, called Q-PACE, consisting of a second-order sensitivity model that predicts the loss increase as a sum of quantization noise MSE weighted by per-layer curvature coefficients. During training, we periodically re-compute these coefficients using perturbations across layers, and re-assign precision. Pretraining and supervised fine-tuning experiments on LLMs of up to 4B parameters show that Q-PACE consistently improves over existing mixed-precision training recipes, and achieves comparable loss at substantially lower total memory budgets. We further find that quantization sensitivity is highly predictable by depth and layer type, and its stability during training allows for infrequent, cheap recalibration.

As data propagates through a Transformer, the norm of its hidden states grows by orders of magnitude with depth, a phenomenon framed as 'curse of depth' and nearly universally treated as a pathology to be suppressed. We take the opposite view. Across 16 pre-trained LLMs from 9 families, spanning dense, mixture-of-experts and hybrid architectures and Pre-, Peri- and Post-Norm designs, we find that this growth reflects an emergent depth-positional encoding, carried by the only learned per-layer gain on the residual stream, the normalization weight $\gamma$: with depth, $\gamma$ grows in magnitude and rotates in direction, jointly encoding the layer index. We make this depth-conditioned encoding explicit with LayerRoPE, an implicit analog of RoPE along the depth axis, which replaces all layerwise $\gamma$ vectors with a single shared vector and depth-conditioned scalars, at a net reduction in parameters and $<0.02\%$ change in FLOPs. Across a model ladder scaled up to $100$B+ tokens, LayerRoPE consistently outperforms Pre-, Post- and Peri-Norm and Layer-Norm Scaling, reaching Pre-Norm's 1.3B loss with $3.4\times$ less compute; LayerRoPE is the only approach that shows strong convergence and improves near monotonically as depth scales to 512 layers. It improves learning-rate sensitivity by $3$-$10\times$, and transfers naively to and consistently improves looped latent models and Vision Transformers. Inspecting its learned schedule inverts the prevailing premise: LayerRoPE does not shrink the residual stream but widens it, damping what each block reads while amplifying what it writes. Depth stability, our results suggest, calls not for suppressing the residual stream, but for depth-conditioned regulation of the computational blocks it feeds.

Reliable and interpretable trajectory prediction is critical for cooperative and autonomous driving in complex and uncertain environments. This paper introduces a Context-Aware Attention-based Gaussian Mixture Model (CAA-GMM) for multimodal, uncertainty-aware motion forecasting. The proposed approach models future motion as a probabilistic mixture conditioned on both scene context and agent dynamics, capturing diverse behavioral modes with interpretable Gaussian components. A lightweight attention mechanism adaptively encodes inter-agent interactions and contextual salience, enabling efficient fusion of rasterized environment cues and motion history in dense traffic scenes. Comprehensive evaluations on the nuScenes and Argoverse 2 datasets demonstrate that CAA-GMM achieves competitive or superior accuracy compared with state-of-the-art raster-based baselines, while maintaining low computational complexity. Ablation analyses confirm the importance of the attention module for robust contextual reasoning and predictive precision. Furthermore, evaluations under imperfect communication and perception conditions highlight the framework's resilience to uncertainty, establishing CAA-GMM as an efficient and scalable solution for cooperative trajectory prediction in intelligent transportation systems.

Standard diffusion samplers generate samples through repeated evaluations of a learned score function. Parallel sampling methods seek to accelerate generation by trading additional evaluations for fewer sequential rounds. This raises the question of how much sequential dependence is unavoidable, even when many score queries can be made simultaneously. We establish the first polynomial parallel-round lower bounds for diffusion sampling with approximate scores. Specifically, we prove (1) a $\widetilde{\Omega}(d^{1/3})$-round lower bound for sampling smooth, near-isotropic Gaussian mixtures in $R^d$, and (2) an $\Omega(d)$-round lower bound for uniform sampling from anisotropic axis-aligned boxes contained in the unit ball. Both bounds hold for arbitrary randomized algorithms making polynomially many queries per round at arbitrary locations and noise levels, with inverse-polynomial score error and constant total variation accuracy. The linear bound is tight for our box family. Our constructions use fixed approximate score oracles that enforce sequential access to hidden information while satisfying the accuracy guarantee at every noise level.

In the Wilson formulation of lattice gauge theory, the fundamental degrees of freedom are group-valued link variables, while the action is a sum over the trace of the plaquettes, the smallest Wilson loops. For generative sampling methods such as normalizing flows, this poses a challenge: the distribution of an individual plaquette is easy to model, but mapping sampled plaquettes to the links is the obstruction. We explore a statistical way around this in two dimensions for the $\mathrm{SU}(N)$ gauge theory with the Wilson plaquette action. The action can be written in terms of holonomy variables, which determine the links once a consistency condition at the four corners of an extended lattice is satisfied. Using a boundary condition that only affects the holonomies, we trade this consistency condition for a conditional sampling problem, which reduces to sampling $X,Y\in\mathrm{SU}(N)$ given the group commutator $Z=XYX^\dagger Y^\dagger$, where $Z\in\mathrm{SU}(N)$ depends on the four corners. Plaquettes are sampled independently, and the resulting configurations carry weights due to the additional conditional sampling. We obtain the density of $Z$, which determines these weights, in closed form for $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$. A normalizing flow models the single-plaquette distribution for $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$; for the group-commutator problem we use a closed-form sampler for $\mathrm{SU}(2)$ and a trained normalizing flow for $\mathrm{SU}(3)$. In our tests on $2\times2$ and $32\times32$ lattices at two couplings each, per-plaquette acceptance rates exceed $99\%$ and the effective sample size of the final weights is moderate, typically above one half.

We revisit a standard accepted practice in the continuous diffusion language model literature of fixing conditioning prompt tokens clean during training. We make a very simple modification: also noise the conditioning prompt tokens during training. We demonstrate that under this modified training objective, we achieve better generalization in combinatorial reasoning tasks such as Sudoku and N-Queens, with the largest gains on harder variants ($3.73\% \to 24.65\%$ solve rate on Sudoku Hard), and increased diversity of generated solutions ($50.60\% \to 73.79\%$ coverage on 10x10 N-Queens). We also show measurable improvements to natural language generation quality in modest dataset regimes with Gigaword summarization, but notably demonstrate that gains do not transfer to all natural language tasks (e.g open ended dialogue generation). Our method is a single line change to the training objective, requires no additional inference costs by default, and provides the flexibility of classifier-free guidance inspired guided sampling. Our \href{https://github.com/LateralIntelligence/noise-your-prompt}{code} is publicly available.

We present a hybrid quantum-classical framework that detects affinity and romance-investment fraud by modelling the cognitive biases in a manipulative conversation. In our proposed framework, cognitive biases central to this fraud class are carried by dedicated qubits in a structured parameterized quantum circuit, together with a frame qubit makes the encoding sensitive to the temporal order of manipulative reframing, and a narrative qubit that aggregates co-occurrence through a trainable entanglement layer. The circuit parameters are trained jointly with a classical reinforcement-learning agent that decides, turn by turn, whether to flag the conversation, modeled as an optimal stopping problem. We evaluate the model's performance on synthetic conversations that include hard negatives, legitimate but urgent, and legitimate but pushy sales conversations.

Learning a directed acyclic graph (DAG) from observational data is a challenging combinatorial problem due to the exponential growth in the number of candidate parent-set configurations. Existing exact score-based methods often require computationally intensive combinatorial search, whereas constraint-based methods can become unreliable or computationally demanding as graph size and conditioning-set complexity increase. We develop a non-parametric hybrid framework, referred to as DECO (Directional Evidence-guided Configuration Optimization), that extracts dependency and directional evidence from observation data to construct admissible parent sets prior to exact optimization. It reduces the optimization search space by eliminating empirically unsupported parent configurations while preserving flexibility for all plausible edge orientations. Theoretical analysis establishes an exponential reduction in the admissible parent-set configuration space and quantifies how bounded edge-level omission affects the probability of retaining the true parent structure. Experiments on benchmark Bayesian networks and synthetic discrete and continuous DAGs demonstrate substantial search-space reduction while achieving competitive structure-recovery performance, with favorable structural Hamming distance across many evaluated settings. These results show that directional evidence can provide an effective preprocessing mechanism for reducing the computational burden of exact DAG learning without requiring a fixed parametric structural~model.

In wide Bayesian neural networks, Gaussian mean-field variational inference is prone to "prior dominance": the Kullback-Leibler (KL) regularization term of the ELBO outweighs the expected log-likelihood, and the variational predictive distribution collapses to the prior predictive as the width $M$ grows. Tempering the likelihood, by raising it to the power $1/T$ for a temperature $T < 1$, is equivalent to scaling the KL term by $T$. We ask in this paper how fast $T$ must decrease with $M$ to counteract this degeneracy and strike a good balance between the two terms. For single-hidden-layer linear networks with isotropic Gaussian priors, we derive the limiting predictive distribution under schedules of the form $T = \tau/M^{c}$, with constants $\tau, c > 0$, as $M \to \infty$ and compare it with the untempered neural network Gaussian process (NNGP) posterior, the infinite-width limit of the exact posterior. Our main result is that the predictive expectation and variance undergo phase transitions at different scales: the limiting expectation leaves its prior value at $c = 1/2$, once $\tau$ falls below an explicit threshold, and equals the least-squares prediction for $c > 1/2$, whereas the limiting variance keeps its prior value for $c < 1$, matches the NNGP's for $c=1$, and vanishes for $c > 1$. With suitable choices of $\tau,c$, one can recover either the NNGP posterior expectation or its variance.

Reconstructing an editable CAD model from a 3D shape remains a challenging engineering task. Existing methods can propose CAD operations, but no single source of proposals works equally well across different part geometries and stages of reconstruction. We introduce CADFather, an autonomous agentic system that coordinates complementary tools to recover parametric CAD programs from 3D meshes. A vision-language assistant inspects renders of the target and intermediate reconstructions, then decides which candidate CAD programs to extend, which tools to invoke, how many proposals to generate, and when to finish. Learned and algorithmic tools propose CAD operations, while numerical optimization refines the parameters of existing programs. Proposed or refined programs are executed and evaluated to provide feedback for subsequent decisions. The agent maintains alternative candidate programs for each target part and preserves the best valid result throughout reconstruction. CADFather uses pretrained generation and assistant models without additional training. We evaluate reconstruction quality and execution validity on the full DeepCAD, Fusion360, and MCB test sets, as well as on CADENA-Bench, CADBench, and BenchCAD. We additionally analyze computational cost and the trade-off between cost and reconstruction quality.

Accurate thermal modeling is essential in metal additive manufacturing (AM) for understanding the process-structure-property chain. Physics-informed neural networks (PINNs) offer effective surrogate thermal modeling by minimizing physics-based residual losses at collocation points. However, prior works typically rely on manually-crafted, static collocation sampling strategies, which are neither principled nor scalable across process conditions, hindering their generalization capability. In this work, we provide theoretical analysis through empirical risk minimization, showing that process condition-aware adaptive sampling is strictly more favorable than conventional static sampling for generalization. Building on this insight, we propose an adaptive sampling strategy within a two-stage framework: (1) a conditional Flow Matching model that learns approximate high-residual distributions across different process conditions, and (2) a mixed sampling strategy combining this distribution with a domain-informed base distribution to generate adaptive collocation points for refining the PINN predictor. Experiments on metal AM numerical benchmarks demonstrate that our method consistently outperforms state-of-the-art PINN baselines, achieving an average 62.1% reduction in relative $L_2$ error under an identical collocation budget, by capturing process-dependent heat dissipation regions often overlooked in the literature. To the authors' knowledge, this is the first adaptive sampling strategy for PINNs in metal AM, contributing to the enhanced generalization and broader applicability.

Induction heads provide a mechanistic account of in-context learning in sequential data, but existing theory largely assumes that the context relevant to a prediction forms a contiguous block. In multidimensional data, serialization breaks this assumption by scattering spatial neighbors across distant positions in the token sequence. We study how transformers overcome this routing problem in multidimensional stochastic and deterministic cellular automata, where each trajectory is generated by an unknown local rule and presented as a flattened sequence without an explicit coordinate-based spatial inductive bias. We introduce spatial induction heads, two-layer gather-and-match circuits in which the first layer reconstructs the relevant spatial neighborhood and the second matches the resulting configuration against earlier occurrences. We give two explicit realizations of the gather and show that the positional dimension required for spatial routing depends only on the local neighborhood and spatial dimension, not on grid volume or trajectory horizon. We further construct a matching layer which implements Bayesian counting. The end-to-end circuit can approximate the Bayesian posterior arbitrarily closely for stochastic rules and can predict exactly for deterministic rules. Empirically, trained two-layer transformers generalize to unseen rules in one and two dimensional settings, achieving near-perfect deterministic rollouts and less than 0.005 nats KL from the Bayes-optimal predictor on stochastic rules. Attention patterns and layerwise probes align with the predicted gather-and-match computation, providing mechanistic evidence for spatial induction in trained transformers.

Parameter-efficient fine-tuning (PEFT) offers many parameterizations, yet their methodological and functional differences remain unclear. We compare six methods in language and diffusion models to examine how their parameterizations relate to task performance, forgetting, and changes in pretrained weight geometry. Motivated by the spectrum-preserving design of orthogonal fine-tuning (OFT), we first ask whether spectral preservation is itself important for adaptation and retention. We find that the selected LoRA-family methods also approximately preserve pretrained geometry, and that restoring their slightly drifted singular-value spectra largely preserves task performance, questioning the necessity of explicit geometric preservation. Beyond this, we observe that some methods exhibit distinct adaptation–retention trade-offs that vary across settings: LoRA most consistently limits forgetting at competitive performance, DoRA achieves higher mean task scores than LoRA in most comparisons, while PiSSA often incurs greater retention costs. Further intervention experiments suggest that while performance gains from different PEFT methods can be attributed to modifications in different groups of spectral components, we consistently find that restoring dominant rather than intermediate or trailing components produces the largest mean reduction in general-text NLL or base-image drift. Together, these results motivate evaluating geometric constraints through their functional consequences rather than preservation alone. Code is available at https://github.com/Kuaaannn/PEFT_methods.

Randomized exploration is central to bandit learning, multi-agent reinforcement learning, and zeroth-order policy search, yet its independence and privacy are usually only treated as technical assumptions. We show that these properties are critical for security purposes and demonstrate how an adversarial agent can exploit privileged information on another agent's exploration. We analyze a deceiver-victim pair in the minimal two-player strongly monotone setting, where a deceptive player obtains leaked signals that are merely correlated with the victim's exploration. We show that, by coupling their own exploratory action with this information, the deceptive player injects an externality that steers the learning dynamics to a new steady state, called the deceptive Nash equilibrium (DNE). We prove that the deceptive bandit learning (DBL) dynamics converge to an arbitrarily small neighborhood of the DNE while retaining optimal convergence rates. Interestingly, our analysis attains these optimal rates while relaxing second-order smoothness conditions from standard bandit optimization literature. We characterize conditions under which deception strictly shifts the steady state and its effect on the deceiver's cost, illustrating the results in a resource-allocation game.

Humanoid robots still struggle to plan contact-rich whole-body manipulation from egocentric RGB and proprioception. Workhorse learns such manipulation from robot-free human demonstrations. A visual planner predicts five-link targets: the poses of the torso, both wrists, and both feet. A reinforcement-learning whole-body tracker follows them on the robot. Both policies train separately on the same recorded human poses, without retargeting. We augment the training data of each policy to imitate the errors that the other makes at deployment. On a real Unitree G1, Workhorse transport boxes with its hands and a kick, catches a thrown box, and topples and climbs a suitcase. During box transport, we show recoveries after a person pushes the robot or takes the box away. In a simulated copy of the demonstration room, the system completes box transport in 77% of episodes, and in 64% under 40 N.s pushes. With both policies retrained from the same demonstrations, a simulated second humanoid completes box transport in 83% of episodes without pushes.

Steering an LLM agent means deciding whether to correct it, at which step, and with which mechanism. Uncertainty is often used to decide when to correct an agent, but whether it can guide these decisions remains unclear. We steer agent trajectories separately at every non-terminal step with each of four mechanisms and run each continuation to completion. The resulting stepwise outcome table (SOT) holds about 82,000 counterfactual continuations of 1,864 trajectories from three benchmarks and two agents. It shows that uncertainty can identify failing trajectories, but that no single signal reliably locates the step at which steering helps. We therefore propose VoS (Value of Steering), a trajectory-level monitor, offline or online, that learns from SOT the value of steering at each step and decides where to steer by it. A harm-budgeted trigger decides whether to steer, limiting the fraction of successful trajectories that VoS disturbs. VoS improves on unmodified execution in all 12 settings of benchmark, agent, and offline or online use, by 7.8 points on average, and outperforms the strongest of five existing uncertainty-triggered methods in 11, by 2.9 points on average. Ablations show that training on measured outcomes and a tight harm budget are both essential.

Deterministic inference is essential for reliable and trustworthy machine learning. Prior studies of text generation have shown that changing factors such as batch size, batch composition, hardware, or inference engine can alter the generated text, even when the prompt, model parameters, and sampling randomness are fixed. These differences have been attributed in part to floating-point non-associativity, shape-dependent kernel selection, and other implementation-level differences in numerical execution. However, it remains unclear whether, when, and to what extent the same factors affect text classification. We present a systematic study of serving-context non-invariance in text classifiers, which prior work has measured only through generated text. We train 180 models spanning discriminative, pseudo-generative, and fully generative classifier formulations and evaluate each across four categories of serving contexts, holding the checkpoint and the text fixed. Label stability does not imply score stability. Changing only the batch shape changes no labels across fp32 comparisons, yet under bf16 it moves up to 56.7 percentage points of predicted probability mass, with label changes concentrated at small margins. Fully generative classifiers change more labels than their discriminative counterparts under the same serving changes. We derive sufficient conditions for label stability under each serving change and give a separate mitigation for each mechanism. Our results identify and quantify the serving conditions that must be fixed for reproducible text classification.

Many organizations fine-tune publicly available pretrained Automatic Speech Recognition (ASR) models and deploy them in black-box settings, assuming limited access provides protection. We show this assumption is fragile: adversarial perturbations crafted on the public base model transfer effectively to fine-tuned target models, severely degrading performance and posing concerns for safety-critical applications. We propose TransferBreaker, a unified fine-tuning framework that suppresses adversarial transfer by integrating Base Adversarial Fine-Tuning, which restricts adversarial training to base-effective perturbations; Latent Jacobian Regularization, which enforces latent-space invariance by suppressing adversarially sensitive directions; and HybridGrad-AFT, which improves robustness against adaptive attacks by interpolating transferable perturbations from base and target gradients. We theoretically justify all components and evaluate TransferBreaker across three languages and four large ASR models, reducing adversarial WER from 92.6 to 27.8. Our code is publicly available at https://github.com/rohban-lab/TransferBreaker.

Policy learning drives many of the most consequential and heavily-invested applications of reinforcement learning today. Yet the core optimization problem it rests on (maximizing expected return) is notoriously non-convex, even under a direct policy parameterization, and the field has largely responded by avoiding it: optimizing convex surrogate approximations of the return under trust-region constraints (NPG, TRPO, PPO, AWR). We show that this seemingly unstructured problem is not actually structureless. In log-density-ratio coordinates $y := \log[\pi/\pi_n]$, the exact per-iteration objective, computable via per-decision importance sampling (PDIS), is a difference-of-convex-constrained difference-of-convex (DC-constrained DC) program. This structure lets us move beyond surrogate approximations: it recovers CPI, NPG, TRPO, and AWR as special cases along interpretable axes, and it opens a multi-step axis $k$ that couples consecutive decisions. We solve the per-iteration program with sequential convex programming (SCP), the standard solver for difference-of-convex problems, and give convergence guarantees under mild conditions, bridging the difference-of-convex optimization and RL literatures. Empirically, multi-step Convex-Concave RL (CCRL) wins on diagnostic MDPs where credit must propagate across a horizon (its advantage growing with the dependency length), is competitive with a tuned PPO on classic control, and on a realistic, stochastic, mid-horizon healthcare domain converges markedly faster than tuned PPO to the same near-optimal survival, with an 11.3% higher area under the training curve.

Identification is the task of recovering the parameters of an unknown ground-truth model from sampled data. When parameters other than the ground truth induce the same output distribution, data alone does not provide enough information to recover the ground truth, and the model is thus called unidentifiable. We study the identifiability problem for hidden Markov models (HMMs): given an HMM, is it identifiable? Existing work on HMM identification establishes conditions under which the ground-truth HMM can be identified. However, most of these conditions are sufficient but not necessary, meaning that, when a model does not satisfy them, its identifiability remains inconclusive. We instead take a computational perspective: is there a sound and complete algorithm that decides whether a given HMM is identifiable, and if so, what is the complexity of this decision problem? We consider the decision problems arising from the various notions of identifiability in the literature, including deterministic, generic, global, local, state-permutation- invariant, and finite-alphabet identifiability. We show that all of these problems are decidable in PSPACE, via reductions to the theory of the reals at various levels of its quantifier-alternation hierarchy. We further show that the deterministic variants are already coETR-hard (and hence coNP-hard) for simply parameterized families.

While established literature underscores the pivotal role of preprocessing in forecasting accuracy, this stage remains largely overlooked in current research. Modern benchmarks typically resort to simple scaling, failing to account for critical transformations required to address nonstationarity, such as differencing. This omission creates a significant structural preprocessing bias that favors models with built-in data treatments while obscuring the true potential of simpler architectures. We study this effect through a preprocessing-aware benchmark that evaluates 11 forecasting models across 16 reversible preprocessing pipelines on 29,000 M4 time series. Our results identify preprocessing as a key driver of forecasting performance. Optimizing preprocessing per series yields gains of approximately 27% to 87% across all evaluated models, with architectures lacking internalized preprocessing experiencing the most substantial improvements. This allows simpler architectures to become highly competitive with complex, state-of-the-art models in modern forecasting benchmarks. All resources and experimental results from this benchmark are stored in a comprehensive metadataset to support future metalearning tasks.

State Space Models (SSMs) offer an efficient alternative to Transformers for sequence modeling, yet conditioning pre-trained SSMs for iterative generation typically operates outside the recurrent operator, through input injection or activation modulation. While such mechanisms expose the model to conditioning information, they leave the underlying temporal dynamics fixed. We introduce MaRK (Markov-adapted Recurrent Kernels), a dynamic operator-conditioning framework that maps context vectors directly into bounded modulations of a frozen SSM's recurrence ($A$), read-in ($B$), read-out ($C$), skip ($D$), and discretization ($\Delta$) parameters. Viewed through the lens of LPV-SSM systems, MaRK induces a context-indexed family of Markov parameter sequences, allowing each diffusion timestep to reshape the model's input-output memory kernel. We instantiate MaRK on a frozen 111M-parameter Hydra SSM backbone and study three adapter geometries: Hypernet, Chebyshev polynomial, and Discrete Cosine Transform kernels. Since these adapters modify the Markov parameter sequence through low-rank auxiliary maps on the frozen backbone, parameter-efficient fine-tuning arises as a structural consequence of the adaptation mechanism itself, requiring only 6.3–11M trainable auxiliary parameters to transition from a bidirectional objective to an iterative diffusion regime. The bounded recurrence parameterization further yields an analytic Affine Quadratic Stability certificate for the modulated recurrence. Through synthetic LPV recovery experiments and Markov-operator diagnostics, we show that MaRK recovers coordinate-invariant temporal operators under matched assumptions and produces distinct, stable timestep-conditioned memory profiles. Empirically, the Chebyshev variant yields the strongest performance, achieving an average validation loss of 2.55, followed by the DCT (2.59) and Hypernet (3.77) geometries.

Decision-focused learning (DFL) trains predictive models for downstream optimization, but existing methods largely assume centralized data. In cross-silo settings, federated learning offers a natural alternative, yet standard federated methods optimize prediction over decision quality and do not address heterogeneity in downstream objectives or feasible sets. This heterogeneity is especially challenging for DFL because small perturbations in polyhedral problems can cause discontinuous changes in optimal decisions, destabilizing client updates and aggregation. We propose FedRSPO+, a heterogeneity-aware framework for decision-focused federated learning, built on RSPO+, a regularized predict-then-optimize surrogate that smooths the decision map through projection. We show that RSPO+ upper bounds decision error and regret for the regularized decision and, under exact regularization and consistent LP solution selection, for the original LP decision. We further derive cross-client heterogeneity bounds that depend on both objective and feasible-set heterogeneity, vanish at homogeneity, and require no strong convexity. FedRSPO+ uses an annealed, modular training procedure compatible with standard federated personalization and aggregation methods. Experiments on synthetic knapsack, shortest-path, and real-world energy pricing tasks compare against prediction-only federated learning and DFL baselines under varying heterogeneity and communication budgets. Results suggest that smoothing is a useful ingredient for stable collaborative decision learning and provide a heterogeneity-aware foundation for federated DFL.

The quadratic cost of self-attention limits scalability to long sequences from multidimensional data. We introduce Tucker bottleneck attention (TuBA), which exploits low-rank tensor structure for efficient global token mixing. TuBA projects hidden tensors into compact Tucker cores, performs multi-head self-attention and linear projections on the cores, and writes updates back to the ambient space, enabling subquadratic computation. Its autoregressive extension combines bidirectional interactions within cores with causal attention across cores. On video prediction and global weather forecasting, TuBA achieves favorable accuracy-efficiency trade-offs over standard and efficient attention and task-specific models. Compared to standard self-attention, TuBA reduces error and computation by up to 24.7% and 66.6% for video prediction and 37.1% and 85.1% for autoregressive weather forecasting, with speedups up to 4.27 times. Low-rank Tucker cores and multi-frame generation also outperform full-rank attention and frame-by-frame generation, respectively.

Large language models are informing decisions with ever-higher stakes. As the consequences of their errors grow, a central question becomes harder to ignore: how much can we trust an individual answer? Yet recognizing when to defer remains difficult because language models can present incorrect conclusions with fluent explanations and an authoritative tone. Uncertainty quantification seeks to address this disconnect by estimating the reliability of individual predictions. However, many existing methods require repeated generations or separately trained components, and their scalar estimates do not reveal where uncertainty arises or how it evolves during reasoning. Recent work has also shown that generation length can be strongly associated with uncertainty estimates and correctness, raising the question of how much of an estimator's predictive power comes from uncertainty-specific information rather than output length alone. Mechanistic interpretability offers a way to address these limitations by connecting human-interpretable concepts to intermediate model states. Building on this capability, we introduce the U-Space, a low-dimensional subspace that makes a model's evolving uncertainty measurable and interpretable. We identify semantic anchors for doubt and certainty, map their unembedding directions back into the residual space, and combine their contrasts into an orthogonal basis. The U-Lens projects each token state onto these basis vectors, yielding an interpretable token-level uncertainty map that can be inspected directly or aggregated into a scalar uncertainty score. Our approach requires no correctness labels, repeated generations, or training. Across reasoning benchmarks, its confidence score outperforms established baselines under both standard and length-controlled evaluation and transfers more reliably than supervised estimators. Code: https://github.com/s2labres/U-Space.

The rapid expansion of text-to-music generative models challenges traditional paradigms of music creation and intellectual property. Plagiarism in this context is rarely an absolute mathematical binary, but an ambiguous threshold negotiated over harmonic structure, melodic contours, or overall perceived stylistic character. In this work, we test the transferability of state-of-the-art music version identification architectures from the human-to-human cover domain to the human-to-AI plagiarism setting. To evaluate this task, we introduce COPYCAT, a benchmark derived from real-world plagiarism cases and extended through generative re-synthesis and digital signal processing obfuscations, yielding 350,654 evaluation pairs. We show that scalar distance thresholding collapses under generative re-synthesis, while a supervised framework leveraging coordinate-wise embedding shifts recovers the dispersed plagiarism signal, raising overall $F_{0.5}$ from $0.612$ to $0.803$.

Emerging long-horizon agentic tasks require repeated model calls, worsening the inference cost of already-costly language models. While narrow agentic tasks suggest potential for aggressive model pruning without performance drop, empirical results show existing methods proposed for question answering tasks severely degrade task performance when applied to agentic models. We trace this failure to two decisions: what to prune and how to recover. For pruning, one-shot importance estimates fail to track how the pruned model adapts. For recovery, offline distillation covers only teacher prefixes, while full-trajectory on-policy distillation causes student errors to compound across turns. In this work, we propose Trajectory-Anchored Pruning (TAP), the first structural pruning framework for reinforcement learning (RL)-trained agents. TAP couples structural pruning with efficient on-policy recovery, anchoring interactions to teacher trajectories while allowing the student to generate each reasoning-action response. A frozen dense teacher supervises the student's response prefixes, addressing within-response training-inference mismatch while preventing student-induced deviations from propagating across training turns. Instead of one-shot pruning, TAP re-scores channels using gradients of the recovery objective on the recovered student, connecting iterative channel selection to the evolving policy. With 60% of FFN channels removed, TAP retains 99.2% and 88.0% of the dense 7B agents' task success rates on ALFWorld and WebShop, respectively, while reducing GPU time per successful task by approximately 22% and 17%. These results demonstrate effective structural compression of long-horizon agents under a limited recovery budget.

Multivariate ordinal data along with covariates are commonly collected in problems ranging from alignment of language models with human preferences, as well as in recommender systems. For example, data sets such as MovieLens contain several movies rated on a scale 1–5 by human users, along with their demographic information such as age or gender. Similarly, data sets such as HelpSteer collect human feedback on several attributes such as "helpfulness" or "verbosity" of LLM response on an ordinal scale, with covariates depending on the LLM prompt–response pairs. Unfortunately, the standard approaches for modeling these data (a) look at the attributes individually rather than jointly, and (b) often convert the data into pairwise or list-wise win–loss comparisons for fitting models such as Bradley–Terry and Plackett–Luce. Both of these lead to a coarsening of what is actually observed, which we address via a joint covariate-dependent consecutive ratio Markov random field model. We also show pairwise or listwise comparison models are obtained under restrictions of our joint model, and that joint modeling improves comparisons. We also develop a maximum likelihood inference procedure even in the presence of an intractable normalizer.

When we interact with large language models (LLMs), are we having a conversation? They are designed to invite us to treat them as intelligent interlocutors who remember, act, and make commitments. But appearances deceive. We introduce the artifactual stance, a framework that reconceives human-AI interaction as artifact-mediated exchanges of candidate texts. LLM outputs are candidate texts optimized for utility, not utterances bearing meaning or force. LLMs are sophisticated text generators, not speakers. Between sessions, nothing runs; between turns, no one remembers. What persists is a configuration and a transcript. The "conversation" is a user's solo performance, interpretive labour disguised by interface and artifact design. This shift dissolves recent philosophical puzzles. Questions about what 'I' and 'you' refer to in AI exchanges, about whether systems can lie or be held to promises, about the identity of our supposed interlocutors all rest on a false presupposition. There is no speaker behind the screen, hence no one to refer to, no one to hold responsible. What feels like dialogue with someone is interaction with an artifact that generates text at unprecedented scale and fit. By abandoning the conversational framing, we see these systems for what they are: immensely sophisticated artifacts that afford varied uses. The philosophical questions that matter are about the normative underpinnings of design, adoption, authorization, and human practices of use.