Papers

Patient knowledge graphs from bedside monitoring should type their relations and state whether the data support their signs. In anesthesia and intensive care, clinicians titrate drugs and ventilation in response to the physiology, so temporal relations mix the patient's response with the clinician's policy. We introduce ClosedLoopBench: 29 relations with signs fixed by physics, pharmacology or clinical practice, on 3,442 VitalDB surgical cases (12,653 h) with negative-control action streams. When each patient's actions are replaced by another patient's, six of 12 estimators declare on average 11-18 of their 19-29 distinct relation estimates significant without calibration, and after calibration cross-correlation and Granger tests still assign ventilator rate -> end-tidal CO2 the sign of the clinician's policy. We propose feedback-robust patient graphs that combine concept nodes with evidence pointers, typed relations admitted against negative controls, and beat-level couplings. On VitalDB under null streams, our graphs contain 0.06-0.10 false concept-level relation instances per graph, versus 10-12 for correlational construction. Patient-specific estimates of 11 slow drug and ventilator responses predict later data no better than population estimates, whereas the pulse-arrival-time-systolic-pressure slope is negative in 94.3% of 2,884 cases and patient-specific (early-late correlation 0.67 [0.63, 0.70]).

Posterior sampling for reinforcement learning (PSRL) is one of the simplest and most effective exploration methods, but a basic question has remained open: does unmodified PSRL achieve minimax regret without structural assumptions on the prior? We answer yes. Exact vanilla PSRL is minimax optimal in leading-order Bayesian regret under arbitrary correlated priors. The difficulty is that a posterior-sampled transition model is coupled with its own continuation value. We overcome this with a common empirical transition reference that isolates the resulting value mismatch and a Bellman-based variance argument that controls it without an extra leading-order state-space factor. For finite-horizon, time-inhomogeneous tabular MDPs with unknown stochastic rewards, this yields the minimax $\widetilde{O}(\sqrt{SAH^3K})$ regret rate under arbitrary joint priors over rewards and transitions. The same proof principle gives the minimax $\widetilde{O}(d\sqrt{H^3K})$ rate for linear-mixture MDPs under arbitrary joint parameter priors.

The Forward-Forward Algorithm (FFA) replaces backpropagation (BP) with layer-wise local contrastive objectives, eliminating the backward pass and the need to retain intermediate activations, yet suffers a persistent performance gap with BP that worsens with depth. This paper diagnoses two structural failure modes: an optimization floor arising from concurrent local updates; and a geometric collapse of layer representations driven by the local update mechanism. On the optimization side, we prove that the FFA loss satisfies the Polyak–Lojasiewicz inequality at each layer; however, simultaneous layer updates induce inter-layer representation-distribution drift, so each layer optimizes against a moving input distribution and incurs an error floor. On the representational side, the pairwise similarity kernel of layer representations contracts exponentially toward rank one as depth increases, collapsing the diversity of per-layer error signals. This collapse bounds FFA's effective learning capacity, which measures the diversity of gradient information across layers, independently of depth, whereas BP's chain-rule signal preserves per-layer diversity, yielding a capacity that scales with depth.

Diffusion policies represent multimodal action distributions, but an advantage-weighted update does not specify how to sample from the resulting target distribution. We propose Schrödinger–Föllmer Actor–Critic (SFAC), an offline-to-online reinforcement learning (RL) method for Kullback–Leibler (KL)-regularized policy improvement through conditional diffusion. A minimax Bellman critic estimates the advantage function, which defines an exponentially tilted target policy. A Doob $h$-transform expresses this update as a correction to the reference diffusion drift. We derive a posterior-mean representation of the correction and estimate it using paired self-normalized importance sampling (SNIS). Supervised regression on these drift targets updates the neural actor without critic action gradients. In the small-update regime, the KL-regularized update follows the natural policy-gradient direction, and the Doob correction represents the same local change in the space of diffusion drifts. Under suitable conditions, we derive finite-sample bounds that separate the effects of critic estimation, neural drift regression, finite-sample SNIS, diffusion discretization, and inherited actor error on expected average policy suboptimality. Synthetic experiments assess the accuracy of approximation to prescribed advantage-tilted targets and sensitivity to sampling budgets. On six offline-to-online continuous-control tasks, a reference-anchored implementation achieves higher final-window returns than those of its corresponding offline initialization.

Continuous-time sensing and monitoring with timely and accurate decision-making are critical for many real-world applications. In healthcare monitoring systems, physiological signals are often available or sampled at irregular time intervals, hence requiring continuous-time processing to provide accurate prediction. Moreover, such systems often need to solve multiple detection/prediction tasks to provide a comprehensive patient review from different physiological aspects for more accurate decision-making. To solve this, continuous-time neural networks (CTNNs) can be employed. However, state-of-the-art works typically solve only one task at each network, thereby limiting their efficiency gains. To address this limitation, we propose MTLiquid, a novel methodology to enable efficient multi-task learning in continuous-time processing for healthcare monitoring systems through effective network design and training strategy. MTLiquid employs: (1) multiple input and output heads to accommodate different tasks, while sharing the same backbone network across tasks; as well as (2) an effective training strategy that leverages a loss-weighting technique to balance learning updates across different tasks and a proportional data presentation technique to address imbalanced dataset sizes. Experimental results for mortality prediction (P12) and sepsis early detection (P19) tasks for ICU patients show that, MTLiquid achieves strong performance (AUROC: 0.84 for P12 and 0.94 for P19) comparable to the state-of-the-art single-task learning in both continuous-time networks (AUROC: 0.84 for P12 and 0.95 for P19) and discrete-time networks (AUROC: 0.79-0.82 for P12 and 0.92-0.94 for P19), while incurring significantly smaller memory cost by 44%-94%. These results highlight the potential of our MTLiquid methodology to enable lightweight continuous-time healthcare monitoring systems for better decision-making.

Reinforcement Learning from Human Feedback (RLHF) is a powerful technique for aligning large language models (LLMs) with human preference. However, it often suffers from the reward hacking issue, where policy optimization improves the proxy reward model while actually degrading performance with respect to the true human preference, due to the imperfection of the proxy. To address this, we propose Reward Model Boosting (RMB), a novel approach that enhances the robustness and reliability of the reward signal for RLHF. RMB first trains a set of reward models with a diversity-promoting regularizer. This encourages each model to learn complementary aspects of the reward landscape. Then, RMB learns a lightweight aggregator in the principle of boosting to aggregate the outputs of the diverse reward models into a more accurate and robust reward signal. Our extensive experiments demonstrate that RMB significantly improves reward accuracy on both in-distribution and out-of-distribution datasets, substantially mitigating the reward hacking issue and ultimately improving RLHF performance.

Outcome-based reinforcement learning can produce models with similar task performance but very different ways of communicating about their mistakes. We study failure disclosure: whether a model admits that an attempted solution failed rather than staying silent or presenting it as successful. Across repeated outcome-only GRPO training runs, failure disclosure varies far more than task accuracy. The pattern extends to a second reasoning task and stabilized PPO, persists at 7B, and also appears in an instruction-conditioned 32B setting. We also find that small floating-point and sampling differences during training can redirect reporting behavior even when the task objective and earlier training history are held fixed. Additional tests show that failure disclosure is not a single decision: Checking the answer, entering a report, and completing the admission can separate, and the weak point depends on the task and response format. Further, experiments with neutral controls show more broadly that behaviors left weakly constrained by training are especially likely to vary across runs, of which failure disclosure is an example. We can reduce variability in failure disclosure by discouraging the model from drifting from its starting policy on failed, well-formed responses. This makes reporting substantially more consistent, though its effect on task performance depends on the setting. Stable task accuracy therefore does not guarantee stable safety-relevant behavior: Researchers should measure these behaviors directly across runs and design training methods that keep them reliable.

Typed-decision models such as TypeSafe's Jev answer a declared yes/no or multiple-choice question about a state with a probability instead of text, and their evaluations report accuracy and calibration. Neither requires that the probabilities a model gives to logically related questions fit together item by item, which is what a system that acts on those probabilities needs. We test this property, coherence, with a battery of logically linked questions that needs no labels. For 160 items from ChaosNLI and PubMedQA, each with three mutually exclusive labels, we ask whether the label is X, whether it is not X, whether it is one of the other two labels, and which label applies. On 480 negation pairs, Jev's probabilities for "the label is X" and "the label is not X" miss summing to one by 0.064 on average (95% CI 0.055 to 0.072). Qwen3.8-27B, run from its official BF16 weights, misses by 0.293 with first-token probabilities and by 0.122 with verbalized probabilities. The gap to the first-token readout persists on pairs where both systems give similar probabilities, without double-negation labels, and after averaging Jev's repeated calls. Jev is not coherent either: its violations are about five times its repeat noise, and it over-endorses statements about single labels, so that its three single-label probabilities sum to 1.14 on average. The two systems also fail differently. Qwen3.8-27B's first-token readout under-endorses the complement of a label whether or not the question contains "not", rejecting both a statement and its negation in 196 of 480 pairs, and it does not become more coherent where it is more confident, whereas Jev's violations concentrate where its answer is uncertain. Because the checks need no labels, they expose biases that appear only when question forms are compared, and inconsistencies within items.

Spiking Vision Transformers (SViTs) are developed as an energy-efficient alternative to conventional ViTs for computer vision tasks at the edge. However, huge parameter counts and complex multi-head self-attention (MHSA) operations make it challenging to achieve high energy efficiency in SViT inference, especially in tightly constrained applications. To maximize efficiency gains of SViT processing, we propose MorphAtt, a novel digital accelerator that expedites SViT inference through streamlined processing. Specifically, it processes MHSA operations using cascaded hardware modules: a Spiking Query-Key-Value generator (SpikeQKV), a low-complexity Spiking Multi-Head Self-Attention engine (SpikeAtten), and Reparameterization Convolution (RepConv) modules. To mitigate traffic congestion in on-chip memory accesses and data reuse, specialized inter-module buffers are integrated within the dataflow. Under synthesis using 32nm CMOS technology, MorphAtt achieves 792-1605 GOPS of throughput, while incurring ~39-55 mW of power consumption and 1.5 mm^2 of area, which lead to 20.3-29.1 TOPS/W of energy efficiency. These results also demonstrate that our MorphAtt offers better performance and efficiency trade-offs than state-of-the-art, thereby enabling highly energy-efficient vision-based AI systems at the edge.

High-fidelity simulations of time-dependent partial differential equations (PDEs) are computationally expensive, motivating data-driven reduced-order surrogates for many-query tasks such as uncertainty quantification, design optimization, data assimilation, and optimal control. However, existing surrogate models often exhibit poor temporal stability, which can lead to unstable rollouts and exploding gradients during backpropagation, especially in multistep long-horizon forecasting. To address this, we propose SMORE, a mesh-agnostic framework for model order reduction of time-dependent PDEs. Its latent dynamics are trained with Lyapunov-guided stability regularization, which promotes stable long-horizon rollouts. We provide theoretical guarantees under the stated structural assumptions. Beyond forecasting PDE evolution, the learned latent dynamics, which are interpretable and linear or linear-quadratic, could bring benefits for downstream tasks such as data assimilation and optimal control. Moreover, our framework is capable of predicting continuous PDE solution fields from sparse measurements of the initial condition. We evaluate SMORE on a range of problems, including wave propagation, the Navier-Stokes equations, and the shallow water equations. Our results show that it improves long-horizon rollout generalization and empirical robustness, and achieves competitive accuracy at comparable parameter budgets relative to competitive baselines including DINo, FNO, CNO, and Transolver.

On-policy self-distillation trains reasoning models on their own trajectories using dense token distribution guidance from a privileged teacher with access to a verified solution. This supervision transfers what the teacher predicts without directly transferring where it attends within the preceding context. We introduce On-Policy Attention Self-Distillation (OPASD), which complements token-level supervision with solution-conditioned attention distillation. Because the privileged teacher can attend to verified solution tokens unavailable to the student, OPASD projects teacher attention onto student-visible positions and renormalizes the resulting distribution before alignment. Across three model sizes and four competition-level mathematics benchmarks, OPASD consistently outperforms token-only OPSD, improving average accuracy by 4.98 to 8.40 percentage points. OPASD also avoids the response-length inflation and performance degradation observed with token-only distillation, reducing generated rollout tokens by 73.9% and estimated model compute by 72.6% while training 1.53x faster. These results show that solution-conditioned attention provides a complementary supervision signal that makes on-policy self-distillation more accurate, stable, and compute-efficient.

Matrix-valued optimizers such as Muon exploit the spectral structure of neural network updates through Newton–Schulz orthogonalization, but their near-flattening of the singular spectrum discards relative magnitude information across gradient modes. We introduce Soren (Spectral Orthogonal Reshaping), a matrix-valued optimizer that preserves the singular subspaces of the gradient while applying a bounded, monotone sigmoid transformation to its singular values. This smoothly compresses dominant modes without fully flattening the spectrum. We interpret Soren as a positive-definite preconditioned gradient method and establish convergence guarantees under relative smoothness and metric Polyak–Łojasiewicz geometry. To avoid explicit singular value decomposition, we further develop a finite-depth Soft Newton–Schulz (SNS) polynomial realization of the sigmoid spectral map and characterize how its spectral approximation affects the induced convergence geometry. Experiments across LLM pre-training, supervised fine-tuning, and direct preference optimization demonstrate the effectiveness and robustness of Soren against established optimizers.

How many directions in weight space does training need? The intrinsic dimension answers this with the smallest number of random directions in which training still reaches a target accuracy, and small values have motivated parameter-efficient methods such as LoRA. We measure it for variational Monte Carlo (VMC), which trains a neural network to represent the ground state of a quantum many-body system. VMC is a demanding test, because the network generates its own training samples and every gradient is noisy, and a revealing one, because the exact answer is known and every run can be scored. We train only a small latent vector that a frozen random map turns into the network's weights, with no change to the standard natural-gradient optimizer. We find that a small dimension can be misleading, while the stability it brings is real. On a magnet with a hard sign pattern, a network that cannot represent signs reaches its best energy in 8 of 28,642 directions, but only because no such network can go lower; once signs are learnable, neither the signs nor the magnitudes are cheap. The dimension rises across a quantum phase transition, so it tracks how difficult a state is at far less compute than fitting a scaling law, yet it never falls below a floor set by the random subspace itself, even where the ground state is nearly trivial. Training in the subspace, in contrast, never diverged in our experiments, whereas full-parameter training with the same settings did, and a control with matched solvers attributes the difference to the reduced dimension.

Scientific code generation can produce executable programs that fail to compute the intended scientific object. We study this problem in language-model synthesis of Clifford circuits, which prepare the stabilizer states used in quantum error correction and admit exact classical verification. In our target-conditioned framework, each target is given as compact signed stabilizer generators, and an exact verifier checks the generated OpenQASM circuits. We supervise models with Aaronson-Gottesman chain-of-thought (AG-CoT) traces checked by the verifier, and continue training on model generations that the verifier accepts. Across two independently trained model families (3B and 7B), AG-CoT supervision multiplies greedy-decode state-equivalence accuracy by four to six times over circuit-only baselines, and verifier-filtered continuation training adds a further consistent gain atop both. A complementary 32B study shows that supervised models achieve near-perfect syntax and Clifford validity while the strongest direct model reaches 6.14% state equivalence per target, rising to over 10% under verifier-guided selection with multiple candidates. These results show that algorithmic trace supervision gives a large, statistically significant gain in both model families and that verifier-filtered continuation adds a further repeated gain. The persistent gap between Clifford validity and state equivalence confirms that exact verification is necessary: a circuit can be syntactically and physically valid yet prepare the wrong quantum state.

When the human reference scores zero on a metric, the released GTRS-Dense label generator for NAVSIM marks every candidate trajectory in the scene as passing it. NAVSIM's authors introduced this human-reference forgiveness to avoid penalizing contextually justified maneuvers when scoring one trajectory, and warned that it could overlook important failures. In label generation it sets a whole column of 16,384 candidate targets to passing. To measure the consequences for supervision, we re-run the generator with the overwrite disabled and compare the pre-overwrite targets with the released labels on all 103,288 navtrain scenes. The rule erases a candidate distinction that the training loss reads on 11,237 of them (10.8793%). Firing usually changes most of a column: lane keeping carries 9,982 of the 13,042 forgiven loss columns, and its median forgiven column had 14,391 of 16,384 candidates failing before the overwrite. On held-out navtest scenes forgiven on lane keeping, the released lane-keeping head's median AUC against the pre-overwrite outcome is 0.7095; on unforgiven scenes matched on failing-candidate count it is 0.9807. For the Hydra-MDP checkpoint released with GTRS, whose configuration takes the same label file, the two values are 0.6627 and 0.9761. Continuing the released GTRS-Dense checkpoint for 300 optimizer steps with three paired seeds, we observe the forgiven-scene AUC 0.1086-0.1251 higher with pre-overwrite than with published targets, and a narrower gap between matched groups, still above zero. Scoring with forgiveness disabled, we observe lane keeping higher by 2.478-3.524 points on navtest scenes forgiven on any of five loss metrics, with lower adjacent-frame plan consistency. Both changes are larger there than on the rest. EPDMS, scored the same way, does not separate the two target sets.

Evaluating a target policy using data generated by a different behavior policy remains a fundamental challenge in reinforcement learning. While most existing work relies on the standard one-step Bellman residual, we consider a convex combination of one-step and two-step residuals with a fixed mixing weight. In ideal settings, this mixed Bellman formulation can provide a natural bias–variance trade-off between approximation error under a restricted value-function class and the increased variance arising from multi-step importance weighting. To solve this mixed residual optimization, we adopt a minimax formulation involving a critic function. Unlike standard approaches that rely on a fixed functional class, we construct a data-dependent critic representation using predicted future feature directions which effectively induces a kernel adapted to the underlying transition dynamics. This allows the critic to focus on directions that are most relevant for the estimated Bellman error. To control overfitting, we use sample splitting to construct the critic and estimate the value function on separate data subsets. Simulation studies and MetaWorld tasks illustrate the effect of the mixing parameter and show that intermediate residual combinations can improve value estimation in challenging settings.

Large Language Models (LLMs) suffer from temporal misalignment, often due to the contradictory nature of their training corpora. While current mitigation strategies rely on computationally expensive fine-tuning or context-heavy retrieval augmented generation (RAG), the internal mechanisms governing time-sensitive recall remain under-explored. Unlike prior studies that identify temporal components such as attention heads and MLP layers, we provide the first feature-level map of temporal recall by isolating individual MLP features via transcoder circuit tracing. We identify three node categories (common temporal, common to the year, and chrono-semantic) which interact to generate a temporal filter during factual recall. By analysing Gemma 2 2B, LLaMA 3.2 1B, and Qwen3-4B, we show that these features do not follow a simple linear pipeline but represent time through a parallel and mixed syntactic-semantic interplay across layers. We additionally discover a class of higher-layer temporal components invisible to existing EAP-IG methods, establishing transcoders as a more complete lens for temporal interpretability in time-sensitive factual recall. These findings present MLP components for potential targeted interventions in time-sensitive factual recall

As recursive self-improvement (RSI) rapidly advances, reliable evaluation becomes critical for guiding adaptive search. RSI typically relies on finite evaluation resources, such as fixed benchmarks, to determine which modifications are retained and what is proposed next. However, when these finite resources are repeatedly reused, new candidates are proposed based on feedback from the same evaluation set, so the search trajectory can adaptively overfit and empirical improvement may not reflect genuine population improvement on the underlying task distribution. Some existing methods account for multiple comparisons but assume that candidates are chosen independently of the evaluation set, and therefore do not control this adaptive dependence. To address this, we propose REUSE (Risk-controlled Evaluation Under Sequential Evolution), a certified evaluation and promotion framework that allows a fixed evaluation set to support repeated adaptive decisions while providing statistical guarantees. For a user-specified error level $\alpha$, with probability at least $1-\alpha$, every promoted modification is a genuine population improvement on the underlying task distribution. REUSE achieves this by strictly limiting the evaluation feedback returned to the search process and accounting for possible promotion histories within the error budget. We develop detailed statistical theory for RSI evaluation in this setting, including simultaneous error control, valid lower bounds on cumulative improvement, and a characterization of the fundamental limits of adaptive evaluation reuse. In live self-improvement experiments, REUSE commits substantially fewer false promotions than evaluation frameworks from current RSI systems and error-controlled baselines, reducing the proportion of false promotions from up to 20.7% to 0%, while achieving final true population performance comparable to the best baselines.

Constrained-option scoring reads a model's probabilities for a fixed set of permitted answers, so it returns a score even when the model is about to write something else. We study a prompt that quotes a multiple-choice item, ending in the item's own answer instruction, and asks for a forecast of whether a reader model given only a short note will answer it correctly. The model can begin answering the quoted item: on three Qwen3 checkpoints an answer letter is the most probable token on nearly every passage, and the forecast ranks the reader's correctness indistinguishably from chance. Beyond prior work's argmax check and prefill repair, we contribute a label-free diagnostic of the declared options' support, their first-token mass in context; a deletion test tracing the Qwen3 answer-letter start to the quoted instruction; and rendering and tokenisation checks for dropped separators and coinciding first tokens. Prefilling an answer stem lifts the median option mass from below to above one half on all nine checkpoints scored with this prompt and, with options and renormalisation unchanged, raises the Qwen3-averaged AUC from 0.4929 to 0.6152. lm-polygraph's default P(True) estimator shows a related failure: it reads True where Qwen3 without thinking favours an answer letter (MMLU) or the prompt's (A)/(B) label (TriviaQA), and its Qwen3-averaged AUROC is indistinguishable from chance on MMLU and below chance on TriviaQA. Scoring and renormalising the (A)/(B) labels after an answer stem raises it to 0.632 and 0.868, renormalising True against False in place reaches 0.660 and 0.860, and on TriviaQA both exceed all fourteen default single-answer library estimators. The original forecast is renormalised too, yet stays indistinguishable from chance: option mass flags low support in both settings without labels, and only checking the intended target shows which score still ranks.

World-Action models (WAMs) trained on static demonstrations often fail to manipulate moving targets even when they possess the required manipulation skills. We attribute this failure to target-response collapse: as execution advances, the policy becomes increasingly biased toward the learned continuation of its ongoing behavior and less responsive to target relocation. To bridge the gap between what the model has learned and what it can generate from the current context, we formulate dynamic manipulation as counterfactual planning by decoupling the context used for plan generation from the physical state used for execution. Our framework, Dynamic Predictive Planning (DPP), first uses the WAM's predictive rollout to estimate when an interaction is expected to occur, and combines this timing estimate with observed target motion to predict the target's future interaction position. DPP then constructs a counterfactual observation that places this predicted target position in a familiar robot context, allowing the model to invoke an existing manipulation skill rather than generate a recovery behavior from an unfamiliar robot-target configuration. The resulting plan is connected to the robot's actual state during execution. DPP enables real-time dynamic manipulation on a single consumer GPU without additional training on dynamic data. Experiments in simulation and on a real robot demonstrate consistent improvements across diverse target motions, with simulation performance surpassing all evaluated baselines, including methods additionally trained on dynamic data. Project page: https://methoder00.github.io/DPP/

Latent diffusion models serve as powerful priors for solving inverse problems in image restoration, such as deblurring, inpainting, and super-resolution. Current methods have a trade-off between generality and efficiency. Solvers that are restricted to a fixed set of degradation operators are fast and efficient. Methods that support arbitrary degradation operators are slow and require gradients through the diffusion network. To break this bottleneck, we introduce PASEO (Perturb-And-Solve for Efficient Operator conditioning), a method that uses a small (1M parameters) learned network to degrade diffusion model predictions in latent space. PASEO supports learned degradation operators without back-propagating through the diffusion network. We efficiently sample reconstructions from an approximate posterior by combining the diffusion model's prediction with the observed image. We do this by adding noise and solving linear equations based on a local linear approximation of the learned network, without building or inverting large covariance matrices. Across super-resolution, deblurring, and inpainting on FFHQ and COCO, PASEO achieves strong perceptual quality while running up to 9x faster and using up to 34% less peak memory than the tested baselines, with the same or fewer model evaluations.

When a policy with memory is trained through a differentiable simulator, credit can reach what it stores along two routes: representation credit teaches the network that writes the memory what to summarize, while closed-loop credit travels back through the physical states that earlier actions produced and that the memory later stored. Stopping gradients at stored history, as truncated backpropagation and Transformer-XL do, removes both routes at once. Keeping every forward computation identical and removing one route at a time, we trained Transformer policies for quadrotor tracking to determine when each route matters. Credit through memory improved learning only when velocity observations were noisy or hidden. When velocity was hidden, mildly decaying the gradient between consecutive physical states ($\gamma = 0.8$) eliminated the truncation cost of removing closed-loop credit while leaving representation credit essential, a separation that held in 14 of 16 new seeds. Two further systems bound this result: in a fixed-wing aircraft, representation credit could replace closed-loop credit on its own, leaving no cost to separate, and in a cart-pole, training with full state-edge credit was too unstable to compare the routes. In both the quadrotor and a fully observed vessel model, static gradient norms failed to predict which cut cost more, so memory truncation choices are best guided by short training runs.

In-context reinforcement learning (ICRL) enables large language model agents to adapt to new environments using their interaction history without updating model parameters. However, repeatedly conditioning on growing histories can lead to substantial token cost. We propose a bounded-history context-management framework that predicts the task-dependent downstream effect of removing historical interactions to guide history selection and determine a decision-dependent context budget. Formally, our framework uses the full rolling history as a reference. The predictor evaluates removal effects, defines a deletion ordering, and applies a shared selection criterion to determine how much history to retain at each decision. We evaluate the method in closed-loop SUMO driving under held-out in-distribution, unseen-domain, and unseen-route settings, and in ScienceWorld under a continual ICRL protocol. Relative to a baseline using the full context, our method reduces total token usage by 25.7%, 25.8%, and 23.2% across the three driving settings while maintaining comparable closed-loop driving performance. In ScienceWorld, it reduces total token usage by 52.1% compared to full context and uses 30.2% and 37.8% fewer tokens than the Recent and Similarity baselines, respectively, while maintaining performance.

In these notes, we view control as a dynamically constrained sampling problem on the state-space of a control system. With this viewpoint, we extend methods from generative modeling, such as flow matching, normalizing flows and denoising diffusions to control problems. Concepts such as controllability, optimal control and trajectory planning play an important role in guiding the extension and understanding well-posedeness of the corresponding algorithms, with application to steering systems to target states or distributions and sampling from reachable sets. The notes are intended as an accessible introduction for readers with a background in control theory and robotics.

We study episodic continuous-time control with an unknown vector control gain, scalar state, quadratic action cost, and smooth convex terminal cost. In the scalar Gaussian experiment, let $\Delta(H)$ denote the minimax improvement over zero control and set $\delta=\sqrt2H^2-1$. We prove the critical law $$ \Delta(H)\asymp \delta^4\sqrt{\log(1/\delta)} \qquad (\delta\downarrow0), $$ with a matching lower and upper bound. The lower bound follows from a uniform deficit–energy inequality valid for fully adaptive controls with unbounded amplitudes, while a moving soft-threshold feedback attains the rate. For local parameters $\theta=N^{-1/4}h$, $|h|\le H$, we show that the normalized minimax regret over $N$ episodes is within $O(N^{-1/2})$ of a fixed-horizon Gaussian sequential control problem, without an additional dimension factor. The terminal task enters the limit only through $c_g=\operatorname{Var}(g(Z))$. The Gaussian problem exhibits an exact no-learning phase transition: $$ C_d^T(H)=TH^2/2 \iff H^4T\le d^2/2, $$ yielding the asymptotic task boundary $c_gH^4=d^2/2$.

Muon is emerging as a promising alternative to AdamW for large-scale neural network training, yet theoretical understanding of its practical implementation remains incomplete, as existing analyses often simplify or omit two key components: (i) practical Newton–Schulz iterations with empirically tuned polynomial coefficients $(3.4445,-4.7750,2.0315)$; and (ii) decoupled weight decay for regularization. In this paper, we provide an optimization interpretation and establish convergence for practical Muon, jointly accounting for both components. Specifically, we interpret practical Muon as right-preconditioned optimization of the original loss with a dynamic weighted $\ell_2$ regularizer that vanishes as stationarity is approached, so that the optimization target remains the original objective. We then establish, to our best knowledge, the first convergence guarantee for practical Muon in the stochastic nonconvex setting, with an $\mathcal{O}(T^{-1/4})$ convergence rate in terms of the expected Frobenius norm of the gradient, improving the dimension dependence of the best known AdamW's convergence rate by a factor of $\sqrt{d}$, where $T$ is the iteration horizon and $d$ is the parameter dimension. Experiments further support the theoretical convergence results.

Federated low-rank adaptation (LoRA) enables collaborative fine-tuning of large language models without centralizing private client data. Its factorized update, however, creates a structural mismatch in federated averaging: averaging the two LoRA factors separately does not equal averaging their products. Existing exact methods resolve this issue mainly by freezing an entire factor or alternating factors across rounds, but none can update factors simultaneously without aggregation errors or expanding communication ranks. To address this fundamental problem, we present CFLoRA, a federated LoRA scheme that partitions latent LoRA channels into two complementary sets in every communication round. By ensuring that columns and rows are complementary across factors, we eliminate bilinear terms in matrix multiplications, making federated aggregation exact. Crucially, our framework also supports clients with heterogeneous rank budgets. Convergence analysis validates CFLoRA achieves $\mathcal{O}(1/\sqrt{T})$ convergence rate of the original LoRA objective in homogeneous-rank cases. Extensive experiments with RoBERTa on the GLUE benchmark and with LLaMA-3.2-3B-Instruct on commonsense reasoning tasks demonstrate that CFLoRA achieves superior performance and training efficiency compared to state-of-the-art federated LoRA baselines.

Looped Transformers can generalize to reasoning chains longer than those encountered during training, but the computations enabling this behavior and limiting its extent remain unclear. We mechanistically compare two looped-Transformer configurations, which we call the Matched-Recurrence Looped Transformer (MR-Loop) and Decoupled-Recurrence Looped Transformer (DR-Loop), reflecting their respective recurrence-training schemes. We evaluate polynomial iteration, finite-state composition, and knowledge-graph traversal using detailed mechanistic analysis. Attention analysis, intermediate-state decoding, and causal interventions reveal distinct mechanisms learned under final-answer supervision. MR-Loop updates an intermediate state at a fixed readout while advancing relation selection through adjacent-token interactions and a transferable progress cue. DR-Loop instead propagates intermediate states across relation positions, forming an advancing computational frontier. However, both mechanisms become unreliable at greater depths: MR-Loop exhibits degradation of its readout state and progress cues, while DR-Loop exhibits declining reliability of state propagation. Limited self-correction allows local errors to persist and compound. Across both models, we uncover a common representational principle: recurrent states encode not only task-relevant content but also its computational status, whether that content remains in a form that can support subsequent computation. Transferable live-consumed and fresh-aged residual directions causally control whether represented information can participate in subsequent computation, including beyond the training horizon. We further show that length generalization need not rely on faithful step-by-step reasoning, as Looped Transformers can exploit task structure without explicitly representing every intermediate state.

Quarter-ahead revenue forecasting requires company-scale numerical accuracy, strict temporal validity, and company-specific interpretation of narrative disclosures. LLMs can distill textual evidence but can produce scale-misaligned forecasts, whereas history-based anchors are stable but miss forecast-time signals such as product transitions, supply constraints, and management guidance. We introduce CAME (Company-Aware Evidence-Memory Experts), a residual-forecasting framework that refines a no-leakage statistical anchor when current semantic evidence and prior error patterns justify an adjustment. On a development-inclusive rolling backtest of 336 company-quarters from 12 large public technology and platform firms, CAME achieves the lowest aggregate point-estimate error among the reported methods, with statistically supported macro-sMAPE gains over the matched Statistical Anchor, and outperforms History + Guidance on all six aggregate metrics. CAME also links adjustments to source-linked evidence cards and guarded memory traces, supporting forecast inspection, provenance, and failure localization.

On-policy distillation (OPD) trains a student to match a teacher's next-token distributions on student-generated trajectories. However, privileged information supplied to the teacher for OPD training may contain sensitive data. Whether the student leaks private information about the records supplied to the teacher during distillation remains poorly understood. To the best of our knowledge, we present the first systematic study of membership inference in this setting. We find that fresh student trajectories expose sparse membership signals that fixed reference-answer losses often miss. These signals are mixed with probability changes caused by training on other records. We introduce Leaky, which samples fresh trajectories from the target model and compares its token log-probabilities with the maximum across matched reference models trained without the candidate records. It applies Leaky ReLU to the resulting gaps, preserving positive gaps and downweighting negative gaps as an approximate correction for incidental positive gaps in non-members. Across fifteen targets spanning mathematics, medical question answering, and code generation, Leaky outperforms all evaluated baselines and achieves mean AUROC 0.875, compared with 0.614 for the strongest baseline on each target in the main evaluation. On the same sampled trajectories, the strongest baseline achieves mean AUROC 0.826. These results show that students trained through OPD can expose the membership of records used for teacher supervision, even when fixed reference-answer losses provide little evidence of membership.