Batched Contextual Reinforcement: A Task-Scaling Law for Efficient Reasoning

Large Language Models employing Chain-of-Thought reasoning achieve strong performance but suffer from excessive token consumption that inflates inference costs. Existing efficiency methods such as explicit length penalties, difficulty estimators, or multi-stage curricula either degrade reasoning quality or require complex training pipelines. We introduce Batched Contextual Reinforcement, a minimalist, single-stage training paradigm that unlocks efficient reasoning through a simple structural modification: training the model to solve N problems simultaneously within a shared context window, rewarded purely by per-instance accuracy. This formulation creates an implicit token budget that yields several key findings: (1) We identify a novel task-scaling law: as the number of concurrent problems N increases during inference, per-problem token usage decreases monotonically while accuracy degrades far more gracefully than baselines, establishing N as a controllable throughput dimension. (2) BCR challenges the traditional accuracy-efficiency trade-off by demonstrating a "free lunch" phenomenon at standard single-problem inference. Across both 1.5B and 4B model families, BCR reduces token usage by 15.8% to 62.6% while consistently maintaining or improving accuracy across five major mathematical benchmarks. (3) Qualitative analyses reveal emergent self-regulated efficiency, where models autonomously eliminate redundant metacognitive loops without explicit length supervision. (4) Crucially, we empirically demonstrate that implicit budget constraints successfully circumvent the adversarial gradients and catastrophic optimization collapse inherent to explicit length penalties, offering a highly stable, constraint-based alternative for length control. These results prove BCR practical, showing simple structural incentives unlock latent high-density reasoning in LLMs.

Ouroboros: Dynamic Weight Generation for Recursive Transformers via Input-Conditioned LoRA Modulation

Recursive transformers reuse a shared weight block across multiple depth steps, trading parameters for compute. A core limitation: every step applies the same transformation, preventing the model from composing distinct operations across depth. We present Ouroboros, a system that attaches a compact Controller hypernetwork to a recursive transformer block. The Controller observes the current hidden state, produces a per-step diagonal modulation vector, and applies it to frozen SVD-initialized LoRA bases, making each recurrence step input-dependent. We combine this with gated recurrence (bias-initialized to 88% retention) and per-step LayerNorm for stable deep iteration. On Qwen2.5-3B split into a Prelude/Recurrent/Coda architecture (17 of 36 layers retained), Ouroboros reduces training loss by 43.4% over the unmodified 17-layer baseline, recovering 51.3% of the performance gap caused by layer removal. The full system adds only 9.2M trainable parameters (Controller, gate, and per-step norms) yet outperforms equivalently-sized static per-step LoRA by 1.44 loss points at depth 1 and remains ahead across all tested depths (1, 4, 8, 16) and ranks (8, 32, 64). We also find that gated recurrence is essential: without it, recursive layer application makes the model strictly worse. These gains are measured on the training distribution; on held-out text, the Controller does not yet improve over the baseline, a limitation we attribute to frozen downstream layers and discuss in detail. Code: https://github.com/RightNow-AI/ouroboros

Homogenized Transformers

We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a discrete-time interacting particle system on the unit sphere. We prove that, under suitable joint scalings of the depth, the residual step size, and the number of heads, this dynamics admits a nontrivial homogenized limit. Depending on the scaling, the limit is either deterministic or stochastic with common noise; in the mean-field regime, the latter leads to a stochastic nonlinear Fokker--Planck equation for the conditional law of a representative token. In the Gaussian setting, the limiting drift vanishes, making the homogenized dynamics explicit enough to study representation collapse. This yields quantitative trade-offs between dimension, context length, and temperature, and identifies regimes in which clustering can be mitigated.

Investigating Permutation-Invariant Discrete Representation Learning for Spatially Aligned Images

Vector quantization approaches (VQ-VAE, VQ-GAN) learn discrete neural representations of images, but these representations are inherently position-dependent: codes are spatially arranged and contextually entangled, requiring autoregressive or diffusion-based priors to model their dependencies at sample time. In this work, we ask whether positional information is necessary for discrete representations of spatially aligned data. We propose the permutation-invariant vector-quantized autoencoder (PI-VQ), in which latent codes are constrained to carry no positional information. We find that this constraint encourages codes to capture global, semantic features, and enables direct interpolation between images without a learned prior. To address the reduced information capacity of permutation-invariant representations, we introduce matching quantization, a vector quantization algorithm based on optimal bipartite matching that increases effective bottleneck capacity by $3.5\times$ relative to naive nearest-neighbour quantization. The compositional structure of the learned codes further enables interpolation-based sampling, allowing synthesis of novel images in a single forward pass. We evaluate PI-VQ on CelebA, CelebA-HQ and FFHQ, obtaining competitive precision, density and coverage metrics for images synthesised with our approach. We discuss the trade-offs inherent to position-free representations, including separability and interpretability of the latent codes, pointing to numerous directions for future work.

ContextBudget: Budget-Aware Context Management for Long-Horizon Search Agents

LLM-based agents show strong potential for long-horizon reasoning, yet their context size is limited by deployment factors (e.g., memory, latency, and cost), yielding a constrained context budget. As interaction histories grow, this induces a trade-off between retaining past information and staying within the context limit. To address this challenge, we propose Budget-Aware Context Management (BACM), which formulates context management as a sequential decision problem with a context budget constraint. It enables agents to assess the available budget before incorporating new observations and decide when and how much of the interaction history to compress. We further develop BACM-RL, an end-to-end curriculum-based reinforcement learning approach that learns compression strategies under varying context budgets. Experiments on compositional multi-objective QA and long-horizon web browsing benchmarks show that BACM-RL consistently outperforms prior methods across model scales and task complexities, achieving over $1.6\times$ gains over strong baselines in high-complexity settings, while maintaining strong advantages as budgets shrink, where most methods exhibit a downward performance trend.

A Simple Baseline for Streaming Video Understanding

Recent streaming video understanding methods increasingly rely on complex memory mechanisms to handle long video streams. We challenge this trend with a simple finding: a sliding-window baseline that feeds only the most recent N frames to an off-the-shelf VLM already matches or surpasses published streaming models. We formalize this baseline as SimpleStream and evaluate it against 13 major offline and online video LLM baselines on OVO-Bench and StreamingBench. Despite its simplicity, SimpleStream delivers consistently strong performance. With only 4 recent frames, it reaches 67.7% average accuracy on OVO-Bench and 80.59% on StreamingBench. Controlled ablations further show that the value of longer context is backbone-dependent rather than uniformly increasing with model scale, and reveal a consistent perception-memory trade-off: adding more historical context can improve recall, but often weakens real-time perception. This suggests that stronger memory, retrieval, or compression modules should not be taken as evidence of progress unless they clearly outperform SimpleStream under the same protocol. We therefore argue that future streaming benchmarks should separate recent-scene perception from long-range memory, so that performance improvements from added complexity can be evaluated more clearly.

TRU: Targeted Reverse Update for Efficient Multimodal Recommendation Unlearning

Multimodal recommendation systems (MRS) jointly model user-item interaction graphs and rich item content, but this tight coupling makes user data difficult to remove once learned. Approximate machine unlearning offers an efficient alternative to full retraining, yet existing methods for MRS mainly rely on a largely uniform reverse update across the model. We show that this assumption is fundamentally mismatched to modern MRS: deleted-data influence is not uniformly distributed, but concentrated unevenly across \textit{ranking behavior}, \textit{modality branches}, and \textit{network layers}. This non-uniformity gives rise to three bottlenecks in MRS unlearning: target-item persistence in the collaborative graph, modality imbalance across feature branches, and layer-wise sensitivity in the parameter space. To address this mismatch, we propose \textbf{targeted reverse update} (TRU), a plug-and-play unlearning framework for MRS. Instead of applying a blind global reversal, TRU performs three coordinated interventions across the model hierarchy: a ranking fusion gate to suppress residual target-item influence in ranking, branch-wise modality scaling to preserve retained multimodal representations, and capacity-aware layer isolation to localize reverse updates to deletion-sensitive modules. Experiments across two representative backbones, three datasets, and three unlearning regimes show that TRU consistently achieves a better retain-forget trade-off than prior approximate baselines, while security audits further confirm deeper forgetting and behavior closer to a full retraining on the retained data.

Reinforcement Learning for Speculative Trading under Exploratory Framework

We study a speculative trading problem within the exploratory reinforcement learning (RL) framework of Wang et al. [2020]. The problem is formulated as a sequential optimal stopping problem over entry and exit times under general utility function and price process. We first consider a relaxed version of the problem in which the stopping times are modeled by the jump times of Cox processes driven by bounded, non-randomized intensity controls. Under the exploratory formulation, the agent's randomized control is characterized via the probability measure over the jump intensities, and their objective function is regularized by Shannon's differential entropy. This yields a system of the exploratory HJB equations and Gibbs distributions in closed-form as the optimal policy. Error estimates and convergence of the RL objective to the value function of the original problem are established. Finally, an RL algorithm is designed, and its implementation is showcased in a pairs-trading application.

Multi-Mode Pinching-Antenna Systems: Polarization-Aware Full-Wave Modeling and Optimization

Millimeter-wave and terahertz communications face a fundamental challenge: overcoming severe path loss without sacrificing spectral efficiency. Pinching antenna systems (PASS) address this by bringing radiators physically close to users, yet existing frameworks treat the waveguide as a mere transmission line, overlooking its inherent multi-mode capabilities and the critical role of polarization. This paper develops the first polarization-aware, full-wave electromagnetic model for multi-mode PASS (MMPASS), capturing spatial radiation patterns, modal polarization states, and polarization matching efficiency from first principles. Leveraging this physically grounded model, we reveal fundamental trade-offs among waveguide attenuation, atmospheric absorption, and geometric spreading, yielding closed-form solutions for optimal PA placement and orientation in single-user scenarios. Extending to multi-user settings, we propose a modular optimization framework that integrates fractional programming with closed-form polarization updates, scaling gracefully to arbitrary numbers of waveguides, PAs, and users. Numerical results show that MMPASS achieves up to a 167% increase in spectral efficiency compared with single-mode PASS. Moreover, when comparing MMPASS with its polarization-ignorant counterpart, polarization awareness alone improves the sum rate by up to 23%. By bridging rigorous electromagnetic theory with scalable optimization, MMPASS establishes a physically complete and practically viable foundation for future high-frequency wireless networks.

Cognitive Friction: A Decision-Theoretic Framework for Bounded Deliberation in Tool-Using Agents

Autonomous tool-using agents in networked environments must decide which information source to query and when to stop querying and act. Without principled bounds on information-acquisition costs, unconstrained agents exhibit systematic failure modes: excessive tool use under congestion, prolonged deliberation under time decay, and brittle behavior under ambiguous evidence. We propose the Triadic Cognitive Architecture (TCA), a decision-theoretic framework that formalizes these failure modes via cognitive friction. By combining nonlinear filtering, congestion-dependent cost dynamics, and HJB optimal stopping, TCA models deliberation as stochastic control over a joint belief-congestion state, explicitly pricing information by tool signal quality and live network load. TCA yields an HJB-inspired stopping boundary and a computable rollout-based approximation of belief-dependent value-of-information with a net-utility halting condition. We validate TCA in two controlled environments (EMDG and NSTG) designed to isolate stopping quality, action selection under congestion, and temporal urgency. TCA improves resource outcomes while reducing time-to-action without degrading accuracy, gaining 36 viability points in EMDG and 33 integrity points in NSTG over greedy baselines. Ablations show that selection and stopping must be optimized jointly, as stopping rules alone recover at most 4 viability points. Sensitivity sweeps over alpha, beta, and lambda_S yield stable accuracy and interpretable trade-offs, and a continuation-value sweep over eta values 0, 0.1, 0.3, and 0.5 finds eta equal to zero is optimal under high temporal urgency. Finally, we demonstrate an illustrative instantiation around a black-box LLM on a memorisation-free corpus, where the same stopping principle executes using empirically computable uncertainty and value-of-information proxies.