Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can lead to convergence at suboptimal solutions, without escape mechanism. A common workaround relies on task-specific input perturbations at test time combined with answer aggregation via voting. We introduce Probabilistic TRM (PTRM), a task-agnostic framework for test-time compute scaling that addresses this limitation through stochastic exploration. PTRM injects Gaussian noise at each deep recursion step, enabling parallel trajectories to explore diverse solution basins, and selects among them using the model's existing Q head (used for early stopping in the original TRM). Without requiring retraining or task-specific augmentations, PTRM enables substantial accuracy gains across benchmarks, including Sudoku-Extreme (87.4% to 98.75%) and on various puzzles from Pencil Puzzle Bench (62.6% to 91.2%). On the latter, PTRM achieves nearly double the accuracy of frontier LLMs (91.2% vs. 55.1%) at less than 0.0001x the cost, using only 7M parameters.
Reward-based alignment of diffusion and flow models requires estimating the value function at noisy intermediate latents, although pretrained reward models operate on clean images. Common approaches use Tweedie-style clean-image proxies or Monte Carlo rollouts, introducing approximation bias or substantial computational cost. Directly learning the value function offers an alternative, but matching the performance and generalization of foundation-scale pixel-space reward models on noisy latents remains challenging. We address this gap by transferring pretrained reward capabilities to noisy latents. We propose \textbf{StitchVM} (Stitched Value Model), a model stitching framework that connects a frozen diffusion-backbone prefix to a pretrained reward-model suffix through a compatible feature interface. A closed-form feature fit selects the interface, and lightweight distillation adapts the stitched model, combining noise-aware diffusion features with pretrained reward capability. For example, adapting CLIP ViT-L with SD~3.5 Medium at $512\times512$ resolution takes approximately 10 GPU-hours on a single GH200. Once trained, StitchVM provides an amortized alternative to Tweedie-style and Monte Carlo approximations of the value function: it estimates value directly from noisy latents, avoiding clean-image reconstruction and additional denoising rollouts for each evaluation. We demonstrate benefits across inference-time steering and post-training. StitchVM improves the quality and efficiency of FK steering and DRaFT, accelerates DPS by $3.7\times$ with half the peak GPU memory, and accelerates DiffusionNFT by $2.3\times$.
Competitive multi-agent reinforcement learning in imperfect-information games requires agents to act under partial observability and against adversarial opponents, necessitating stochastic policies. While self-play reinforcement learning with Proximal Policy Optimization (PPO) has achieved strong empirical success, its standard advantage estimator, generalized advantage estimation, suffers from additional variance due to the sampling of stochastic future actions. This variance is amplified in equilibrium self-play because of the stochastic nature of the equilibrium policy and persists even when the critic is exact. We address this bottleneck by introducing $Q$-boosting, a variance-reduced advantage estimator based on a centralized action-value critic, and propose Variance-Reduced Policy Optimization (VRPO), incorporating this new estimator. The algorithm replaces sampled multi-step backups with a multi-step Expected SARSA$(\lambda)$ trace, computing policy expectations at each step to average out action-sampling noise, while retaining PPO's clipped objective and on-policy actor updates. Empirically, VRPO achieves strong performance in various games: In mid-sized games where exploitability is computable, VRPO lowers the exact exploitability by more than 15% compared to tuned baselines. In Dou Dizhu, it sets a new state of the art over PerfectDou. In Heads-Up No-Limit Texas Hold'em, it posts a positive win rate against Slumbot without any blueprint raise sizes, search, or subgame solving at test time.
Unified autoregressive models (UAMs) are transformer models that generate text as well as image tokens within a single autoregressive pass. Shared parameters and a multimodal vocabulary simplify the training pipeline and facilitate flexible multimodal generation, yet might introduce new vulnerabilities. In particular, we are the first to show that this unified architecture enables multimodal backdoor attacks, where a trigger can propagate malicious effects across multiple output modalities. Specifically, we present the Token by Token Backdoor Attack (ToBAC), the first backdoor attack targeting UAMs, exploring both data-based and model-based poisoning strategies. We demonstrate that inconspicuous characters or even common words can be transformed into triggers that elicit harmful behavior in autoregressive image generation. ToBAC can jointly manipulate visual outputs and accompanying text, increasing the perceived authenticity of fabricated content. With model access, ToBAC enables attacks on the Liquid model in which a subtle word (e.g., "cool") induces modality-aligned brand promotion or ideological influence in 55% of generations. Without model access, ToBAC can be induced through data poisoning, achieving an average success rate of 63.1% against JanusPro. Our code is available at https://github.com/multimodal-ai-lab/ToBAC.
Adaptive decision-making in biological and artificial intelligence requires balancing the exploitation of known outcomes with the exploration of uncertain alternatives. Although prior work suggests that uncertainty generally promotes exploration, it has typically treated distinct sources of environmental uncertainty as equivalent. We consider environments with latent reward states that drift over time (volatility) and are observed through noisy outcomes (stochasticity). Both of them increase posterior uncertainty, yet we show they drive optimal exploration in opposite directions: volatility enhances it, stochasticity suppresses it. We establish this asymmetry formally by extending the Gittins index framework to Gaussian state-space bandits with latent dynamics. We further derive Cause-Aware Uncertainty-Sensitive Exploration (CAUSE), a closed-form exploration bonus obtained via control-as-inference that inherits the same monotonicities. CAUSE matches or exceeds both standard exploration strategies and numerically computed index policies in environments with heterogeneous noise structure. Learning and exploration are governed by the same noise-inference asymmetry, and the framework predicts that pathological noise inference misallocates exploration in an axis-specific way, with implications for computational accounts of psychiatric conditions.
Test-time model evolution offers a promising way for deployed models to improve from unlabeled test-time experience, yet most existing methods depend on backpropagation (BP), which incurs substantial memory overhead and makes them difficult to deploy on edge devices, quantized models, specialized accelerators, or black-box models. In this work, we study test-time model evolution under a strict two-forward budget, a setting that pushes adaptation toward highly efficient real-world deployment. We reveal three key obstacles in zeroth-order test-time optimization: susceptibility to shortcut solutions, uncontrolled weight drift, and ineffective update direction estimation. To overcome them, we propose EVA-0, a minimal zeroth-order adaptation framework that: 1) keeps the loss scale-invariant to prevent shortcut solutions; 2) devises an anchor-guided optimization strategy to alleviate weight drift; 3) uses sample-wise symmetric two-sided perturbation for update direction estimation and inference. EVA-0 requires no BP and performs both inference and adaptation within only two forward passes per sample. Results on ImageNet-C & ViT-Base show that EVA-0 outperforms both BP-based DeYO and BP-free FOA, while achieving a 14x speed-up over FOA. Code will be released.
Clinical decisions often require weighing autonomy, beneficence, nonmaleficence, and justice. Reasonable physicians may prioritize these values differently, yet the values that language models bring to medical advice remain poorly characterized. We introduce ValuePrism, an instrument for measuring value priorities from clinical decisions. ValuePrism combines a benchmark of 50 clinical dilemmas, each reviewed by two physicians, with an attribution method that estimates relative value priorities from choices between medically reasonable recommendations. Each case presents a clinical vignette and two mutually exclusive recommendations designed so that choosing one necessarily promotes certain values at the expense of others. Applying the instrument to frontier language models and a US-based physician panel, we find that models frequently acknowledge values favoring both recommendations but make highly consistent decisions across repeated queries, even on cases that sharply divide physicians. The ValuePrism attribution method shows that both physicians and language models express differentiated value priorities. Collectively, model values exhibit substantial diversity and most tend to fall within the physician-panel reference range. Nevertheless, a single model deployed unchecked would amplify its particular values to patients at scale. ValuePrism provides a common basis for measuring and comparing the clinical value priorities expressed by language models and physicians. Data and code are available at https://github.com/payalchandak/value-prism.
Humans can approach complex visual problems by mentally simulating intermediate visual steps, rather than reasoning through language alone. Inspired by this, several works on Vision-Language Models have recently explored chain-of-thought reasoning with continuous latent tokens as intermediate visual imagination steps. In this work, we investigate how recent models leverage such latent tokens. Surprisingly, we find that model accuracy is unaffected when latent tokens are replaced by uninformative dummy tokens. This indicates that latent tokens play a minimal causal role in the model's final prediction. To better understand this phenomenon, we analyze both the training signal provided by oracle latent representations and the quality of the latent tokens generated at inference time. Our experiments reveal two crucial issues holding back latent visual reasoning: First, in most existing datasets, oracle latent tokens provide limited additional information beyond the original image and do not substantially simplify the task, leading models to ignore them during training and effectively bypassing them at inference time. When fine-tuned on a diagnostic dataset, in which latent tokens provide sufficient support for the final prediction, we show that models can causally rely on them. Second, the latent tokens produced at inference time deviate from their corresponding oracle representations, collapsing to a narrow region and preventing benefits even when the model relies on them. Overall, our findings suggest that future progress in latent visual reasoning depends on two key pillars: high-quality datasets with informative intermediate steps and more precise latent token prediction.
Inferring time-varying graphs from high-dimensional nodal observations is challenging when windows contain fewer samples than nodes, observations are heavy-tailed, and the dependence drifts multiplicatively over time. We propose the dynamic elliptical graph factor model (\textsc{Degfm}), combining: an elliptical likelihood that down-weights outliers; a low-rank-plus-diagonal (LRaD) parameterization of each precision matrix, shown to be the posterior precision of a field conditioned on a few aggregate linear measurements; and a temporal regularizer given by the squared affine-invariant distance between consecutive precision matrices, capturing multiplicative evolution and invariant to node rescaling and to the choice between precision and covariance. Estimation on a product of quotient manifolds is solved by a safeguarded Riemannian conjugate-gradient method with closed-form temporal gradients via generalized eigendecompositions. We prove that (i) LRaD is locally identifiable modulo orthogonal transformations under a tangent-space transversality (coherence) condition; (ii) with rank-preserving Armijo backtracking, the solver is well defined and converges to critical points with $\min_{k<K}\|\grad F(\theta^{(k)})\|^2=\mathcal{O}(1/K)$; (iii) a localized estimator obeys a finite-sample oracle inequality whose error scales with the intrinsic dimension $pr+p-r(r-1)/2$ times an effective temporal dimension decreasing from $1$ to $1/T$ as coupling strengthens, quantifying the variance reduction and bias of temporal coupling, and extending to misspecified non-LRaD models; (iv) for Student-$t$ observations, the local restricted strong convexity is proved rather than assumed, with curvature of order $\nu/(p+\nu)$ shown unimprovable; and (v) partial-correlation graphs are recovered exactly by thresholding. Experiments on synthetic data, S\&P~500 returns, and HCP fMRI data validate the approach.
Although Large Language Models (LLMs) achieve strong alignment through supervised fine-tuning and reinforcement learning from human feedback, the alignment is often fragile under subsequent fine-tuning. Existing explanations either attribute alignment fragility to gradient geometry or characterize it as a distributional shift in model outputs, yet few provide a unified account that bridges parameter-space learning dynamics with function-space alignment behavior during fine-tuning. In this work, we introduce a tractable alignment score and derive its closed-form update during fine-tuning, yielding a unified framework for alignment dynamics. Our analysis decomposes alignment updates into two competing components: a Rebound Force, governed jointly by the current alignment state and the narrowness of model distribution, and a Driving Force, determined by how the training distribution aligns with outcome-conditioned posteriors over aligned and non-aligned completions. This decomposition explains why prior alignment can be reversed by later fine-tuning and why narrower posterior structure strengthens such reversal. Moreover, our framework predicts a Rehearsal Priming Effect: prior alignment leaves a latent posterior imprint that amplifies the effective Driving Force upon re-exposure, leading to faster re-alignment. We validate these predictions across safety alignment, emergent misalignment, and sentiment settings, demonstrating consistent alignment reversal and accelerated re-alignment under re-exposure. In addition, controlled experiments in safety alignment confirm the predicted dependence of rebound strength on posterior narrowness. Together, these results provide a unified dynamical perspective on how alignment is disrupted and reactivated during LLM fine-tuning.
Recently, residual reconstruction-based model quantization methods have achieved promising performance in low-bit Post-Training Quantization (PTQ) by introducing cross-module residuals to reduce error accumulated from previous modules. However, these residuals may also introduce additional bias arising from the Hessian-Approximation (HA) assumption, resulting their two-sided effect and potentially leading to suboptimal quantization performance. Therefore, in this work, we propose a residual regulation strategy to mitigate the HA bias associated with residual strength, while preserving accumulated-error correction. Furthermore, we observe that this two-sided effect is module-dependent, we futher propose a Module-Adaptive Residual Reconstruction (MARR), which assigns a module-specific scaling coefficient to adaptively balance accumulated-error correction and residual-related HA bias for each module. To avoid exhaustive per-module coefficient search and obtain a stable coefficient estimate, we design an Proportional-Integral-Derivative (PID)-based update strategy that employs reconstruction error as feedback to progressively refine this coefficient. Experiments on several typical Large Language Models (LLMs) and Vision Transformers (ViTs) demonstrate the effectiveness of MARR under low-bit quantization ($\leq$4-bit), achieving up to 20.2\% perplexity reduction on LLMs and up to 4.6\% accuracy gains on ViTs over the residual reconstruction baselines. Code will be made publicly available upon acceptance.
Many inference-time language-model pipelines combine a cheap reward signal with an expensive verifier, such as exact answer checking in mathematical reasoning or hidden-test execution in code generation. We formalize this setting using a learning-theoretic lens as generative active search: a cost-sensitive first-positive search problem in which a policy adaptively samples candidates from an unknown distribution, observes cheap scores, and pays for verifier labels until it finds a positive example. For a fixed prompt, the generator and reward model induce two unknown objects: a distribution over reward scores and a score-conditioned success function. When these quantities are known, we characterize the distribution-aware optimal policy using a dynamic programming approach. In the realistic and practical setting where both the score distribution and success function are unknown, we propose ADAP, a shellwise adaptive generate-rank-verify algorithm that progressively increases the number of sampled responses and top-ranked verifications. Under the monotonicity assumption that higher reward scores are no less likely to pass verification, we show that ADAP achieves expected cost within a constant factor of the distribution-aware optimum. We complement this result with learning-theoretic lower bounds, based on a centered star number, showing that structural assumptions on the score--label relationship are necessary. Experiments on mathematical reasoning and competitive programming validate the predicted advantage over both fixed non-adaptive policies and difficulty-adaptive baselines.
Package hallucinations, LLM-generated references to packages that do not exist, enable slopsquatting: an attacker registers the hallucinated name. We replicate Spracklen et al. (USENIX Security '25) on five 2026 frontier models over 199,840 Python and JavaScript generations. This version reports a preregistered live revalidation that replaces the static package lists of earlier versions with two independent checks against the live PyPI and npm registries. Hallucination rates are 3.6-5.0% of package mentions (2.2-3.4% of generations): the 2026 frontier sits at the level of 2024's commercial models, and the open-weight gap seen in 2024 has disappeared. Python exceeds JavaScript for every model. The set of names hallucinated by all five models shrinks from the 127 reported earlier to 104; 26 earlier entries were correct import statements whose module name differs from the package name. Using the accidental six-month public exposure of our own list as a natural experiment, we find no detectable effect of publication: about 1% of hallucinated names were registered within six months, at the same rate for published and unpublished names, and the 95% interval excludes increases above 2.5 percentage points. Still, at least 23 package names that the models suggest had previously hosted malware later removed by the registries, and one hallucinated name was registered with malware after our runs.
Despite the effectiveness of Cube-and-Conquer (C&C) for solving challenging Boolean Satisfiability (SAT) problems, no prior work has shown that transformer-based models can learn effective cubing heuristics. We introduce a neuro-symbolic post-training framework for this task. We design an MCTS-based data curation pipeline that uses symbolic heuristics to explore splitting decisions over SAT competition formulas, producing preference data grounded in solver statistics and augmented with reasoning traces from a teacher model. Our two-stage post-training, supervised fine-tuning (SFT) followed by direct preference optimization (DPO), enables a 4B-parameter model to achieve a pass@5 score of 53 on 100 SAT competition benchmarks, surpassing frontier LLMs such as Claude-Sonnet-4 (50) and matching, with five attempts per benchmark, the best symbolic heuristic (53), which nonetheless remains preferable for a single attempt. Ablations show that SFT alone improves pass@5 from 46 to 51, with DPO adding 2 additional benchmarks; an entropy/agreement ablation on realized first-cube decisions further shows that SFT, not DPO, accounts for the root-level decision diversity that produces complementary per-run coverage over deterministic symbolic methods. This demonstrates that transformers can be trained to make effective cubing decisions in a domain traditionally dominated by symbolic methods.
We propose a novel definition of model exploitation in reinforcement learning. Informally, a world model is exploitable if it implies that one policy should be strictly preferred over another while the environment's true transition model implies the reverse. We analogize our definition with a prior characterization of reward hacking but show that the associated proof of inevitability does not transfer to exploitation. To overcome this obstruction, we develop a general theory of reward hacking and model exploitation that proves that exploitation is essentially unavoidable on large policy sets and yields the corresponding claim for hacking as a special case. Unfortunately, we also find that the conditions that guarantee unhackability in finite policy sets have no counterpart that precludes exploitation. Consequently, we introduce a relaxed notion of exploitation and derive a safe horizon within which it can be avoided. Taken together, our results establish a formal bridge between reward hacking and model exploitation and elucidate the limits of safe planning in world models.
Image degradations arise throughout acquisition, processing, and transmission, altering both visual appearance and downstream machine-perception performance. They are studied across synthetic corruption benchmarks, perceptual image quality assessment (IQA), low-level vision, and physically grounded imaging-system analysis. However, these communities rely on incompatible grouping schemes and backend-specific severity definitions, making results difficult to compare across datasets, degradation models, and tasks. We propose a causally grounded framework for organizing and interpreting image degradations. Rather than introducing new degradations or redefining existing benchmarks, we provide an interpretive representation and measurement layer that makes implicit assumptions explicit. Each degradation is characterized by two orthogonal axes: its dominant causal source in the imaging pipeline and its dominant perceptual effect. This dual-axis abstraction yields a compact taxonomy spanning algorithmic corruptions, perceptual distortions, low-level imaging artifacts, and physically motivated camera or system failures. To make severity semantics observable without modifying existing implementations, we quantify each native severity level using full-reference image quality metrics: PSNR, SSIM, and LPIPS. This separates causal origin, perceptual appearance, measured distortion strength, and downstream task impact while preserving native parameterizations. We demonstrate the framework through COCO-Degradation, a taxonomy-aligned benchmark for evaluating object detector robustness under diverse low-level imaging conditions. By connecting causal source, perceptual effect, and measured severity, the proposed framework supports more interpretable and reproducible evaluation of how low-level visual degradations affect machine perception.
Large Language Models (LLMs) are highly sensitive to their input contexts, motivating the development of automated context engineering. However, existing methods predominantly treat this as a global search problem, seeking a single context strategy that maximizes average performance across a dataset. This restrictive assumption overlooks the fact that different inputs often require distinct guidance, leaving substantial instance-level performance gains untapped. In this paper, we propose a paradigm shift by formulating context engineering as a recommendation problem. We introduce \textbf{Neural Collaborative Context Engineering (NCCE)}, a framework that transitions optimization from a static global search to dynamic, instance-wise routing. NCCE first bootstraps a diverse catalog of anchor contexts and then employs a novel \textbf{Context-CF Co-Evolution} mechanism. This stage establishes a synergistic feedback loop: a lightweight Neural Collaborative Filtering (NCF) model learns instance-context preferences to guide the generation of specialized context variants, while the newly evaluated contexts continuously refine the NCF model's understanding of latent preferences. At inference time, the trained NCF model acts as a context router, dynamically assigning the most suitable context strategy to each unseen instance. Theoretical Proofs and comprehensive experiments demonstrate that by matching individual inputs with their optimal contexts, NCCE significantly improves task accuracy, highlighting the critical importance of personalization in LLM context engineering.
Training large-scale deep neural networks (DNNs) is resource-intensive, making model compression a practical necessity. The widely accepted ''learning as compression'' hypothesis posits that training induces structure in network weights, which enables compression. Measuring this structure through Kolmogorov-Chaitin-Solomonoff (KCS) complexity is appealing, but existing estimators based on the Coding Theorem Method (CTM) and the Block Decomposition Method (BDM) are limited to small binary objects and do not scale to modern DNNs. We introduce the Quantized Block Decomposition method (QuBD), which extends algorithmic complexity estimation to any $k$-ary object. QuBD first quantizes the network weights to a finite alphabet, then estimates the KCS complexity by aggregating per bit-plane CTM estimates. We show theoretically that QuBD yields a tighter upper-bound on the estimation gap for ideal prefix KCS complexity under bit-plane independence than binarization-based methods. Using QuBD, we study how the algorithmic complexity of neural network weights evolves during training, showing that it decreases as models learn, scales with data budget, increases during overfitting, follows the delayed generalization observed during grokking, and correlates with generalization performance. We further show that algorithmic information resides predominantly in the most significant bit-planes, which can serve as a practical diagnostic for determining appropriate post-training quantization levels. This work offers novel insights into learning mechanisms in DNNs by providing the first scalable, tractable estimates of KCS complexity for large, non-binary objects such as DNN weights.
Layer pruning removes entire Transformer decoder blocks from large language models, but introduces a mismatch between the hidden state received by the next surviving layer and the distribution it was trained to process, leading to significant performance degradation. We propose Ghosted Layers, a training-free recovery module that addresses this issue by solving a boundary activation alignment problem. Our method derives a closed-form optimal linear operator from a small calibration set to reconstruct the activation discrepancy introduced by the pruned layers. We show that this solution corresponds to the unconstrained optimum of the alignment objective, whereas LinearPatch is restricted to a fixed basis symmetric operator family. Across multiple LLM backbones, pruning strategies, and pruning depths, Ghosted Layers outperforms prior training-free recovery methods in accuracy and perplexity in most settings while preserving the efficiency benefits of layer pruning.
Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves. However, current accuracy-based evaluations do not fully consider two central issues: (1) neural solvers incur substantial up-front costs for data generation, training, and tuning; and (2) classical solvers can also generate low-fidelity solutions at a sufficiently low simulation cost. To explicitly account for these realities and fully incorporate end-to-end costs, we propose an evaluation framework centered on breakeven complexity, a metric that counts the forward solves before a learned solver is cost-effective relative to an error-equivalent traditional solver. To evaluate this measure, we apply scaling laws to determine how much training budget to allocate to data generation and discuss how to achieve smooth error-matching in diverse settings. We evaluate the breakeven complexity of multiple neural PDE solvers on three PDEs on 2D periodic domains from APEBench and a novel benchmark of flows past multiple obstacles generated by the GPU-native PyFR code. Among other findings, our results suggest that neural PDE solvers become more effective as problems get harder in terms of cost, dimension, rollout, physics regime (e.g. higher Reynolds number), etc.