每天知道
你的领域
出了什么

Omni-modal LLMs jointly process audio, video, and text, but long multimodal sequences incur substantial prefill and KV-cache costs. Existing omni-modal compression methods primarily focus on pre-LLM token reduction, leaving modality-specific compression across the LLM boundary underexplored. We propose A-PACK, a two-stage framework that defers audio pruning until query-conditioned multimodal interactions emerge. Our analysis shows that audio exhibits higher task-relevant information density and representational diversity per token than video. We further find that local audio-visual dynamics provide a more effective cue for visual selection than token-wise matching. We therefore preserve audio and compress video with local dynamics before the LLM, then progressively prune low-relevance audio and visual tokens and their KV-cache entries inside the LLM. Across four benchmarks on Qwen2.5-Omni-7B/3B, A-PACK achieves the strongest average performance among the evaluated prior methods while reducing prefill FLOPs by up to 78% and improving decoding throughput by up to 2.21x.

Recent advancements in Speech Large Language Models have demonstrated remarkable capabilities in understanding complex audio tasks. Despite this progress, their long-context inference remains severely bottlenecked by prohibitive KV cache memory demands. Existing text-centric compression methods struggle here, often disrupting speech continuity or discarding crucial semantic cues. To address this, we propose VoxZip, a train-free, two-stage semantic-anchored KV cache compression framework. The first stage uses automatic speech recognition (ASR) transcriptions as explicit semantic anchors to temporally align, compress, and fuse audio tokens, significantly reducing the initial KV cache while elevating token information density. To further improve the compression ratio, the second stage employs a dynamic filtering strategy based on temporally decayed accumulated attention to evict non-essential tokens while mitigating early-token bias. Comprehensive evaluations on Qwen3-Omni across six diverse audio benchmarks demonstrate the superiority of our approach. VoxZip excels in long-audio reasoning and consistently maintains high-fidelity perception on short-form tasks. Notably, it sustains over 90% of the uncompressed baseline performance even under an aggressive 20x KV cache compression in long-context scenarios. Furthermore, at a 4x compression ratio, VoxZip yields a 1.9x increase in inference throughput alongside a 3.3x reduction in peak memory overhead. Code and models will be available at https://github.com/MM-Speech/VoxZip.

Transformer-based large language models (LLMs) achieve strong performance across many tasks, but their Key-Value (KV) cache grows linearly with sequence length, creating a severe memory bottleneck for long-context inference. Existing heuristic eviction methods (e.g., H$_2$O and SnapKV) rely on static attention or positional signals that often fail to capture a token's future predictive influence. We propose DistillCache, a reinforcement learning framework that formulates KV-cache eviction as a sequential decision problem. DistillCache learns a lightweight policy network using rich internal model signals (attention statistics, value norms, entropy, and position) and trains it with REINFORCE via a per-step KL-divergence reward to preserve the full-cache output distribution. On a 7B-parameter instruction-tuned Transformer (Mistral-7B-Instruct-v0.3), DistillCache retains 94.2% of full-cache accuracy on LongBench at a 25% cache budget, outperforming both strong heuristic baselines (H$_2$O, SnapKV) by up to 2.7 absolute points and, under our re-implementations, concurrent RL-based methods (ForesightKV, RLKV) by up to 1.4 points on long-context tasks. On reasoning benchmarks, DistillCache is competitive with the best concurrent method and surpasses it under aggressive compression. It also delivers up to 2.1x full-cache throughput while maintaining competitive practical efficiency. These results highlight the effectiveness of learned, distribution-aware policies for memory-efficient long-context LLM inference.

Emotion is central to human communication, and its expression varies across languages. Large audio-language models (LALMs) achieve strong performance on multilingual speech tasks, yet it remains unclear whether they encode emotion through language-specific correlations or language-agnostic representations. We present the first neuron-level interpretability study of this question. We define Multilingual Emotion Neurons (MLENs) as functional units exhibiting stable emotional selectivity and aligned causal effects across languages, and introduce Consistency-Regularized Fusion (CR-Fusion) to identify them. Across four modern LALMs and 12 typologically diverse languages, emotion-sensitive neurons identified independently per language show minimal overlap, and additional monolingual identification data saturates quickly without isolating more transferable units, motivating identification from pooled cross-lingual evidence. Causal interventions demonstrate that MLENs identified by CR-Fusion provide more precise and transferable affective control than monolingual neuron sets in both zero-shot and low-resource settings. Leave-one-out ablations further reveal asymmetric transfer: individual identification languages, including low-resource ones, contribute non-redundant evidence, while several low-resource languages benefit most from the resulting cross-lingual transfer. Together, our findings provide the first causal, neuron-level account of how LALMs encode emotion across languages, and establish multilingual neuron identification as an effective mechanism for understanding cross-lingual affective behavior.

A central obstacle in building graph foundation models is the input heterogeneity in terms of feature space dimensionality, semantics, and structure. Such heterogeneity limits the capability of graph neural networks to generalize to new graphs with unseen feature spaces. We address the transferability challenge with SIGIL, a framework that maps any attributed graph to a unified representation space of fixed dimension. Given a graph, SIGIL lifts it to a structural interaction graph, where nodes are the input feature dimensions and weighted, typed edges encode feature alignment across multiple orders of the graph's connectivity. A relational message-passing network embeds each feature dimension into a shared space, transforming the original node features, of arbitrary dimensionality, into representations transferable to any downstream graph. By construction, SIGIL is equivariant to permutations of nodes, feature dimensions, and labels. Additionally, when the input features are one-hot indicators of discrete relations, SIGIL recovers and strictly generalizes existing foundation models for knowledge graph reasoning. A single SIGIL model, pretrained on one graph, delivers strong fully-inductive link prediction. Also, SIGIL can be used to implement existing knowledge graph foundation models. As such, SIGIL unifies several existing regimes in graph foundation model design under a single framework

Large Language Models are deployed to multiple types of environments, from internet browsers to edge devices, and WebGPU serves as a modern cross-platform standard. The engines for browser-based LLM inference have proliferated, yet the overhead of WebGPU per-operation dispatch remains poorly characterized. In this work, we introduce a sequential-dispatch measurement method and show that naive single-operation measurements overestimate per-dispatch cost by conflating dispatch with synchronization. Using our method, we measure the per-dispatch cost and show that it is independent of data type used. We show that the dispatch overhead, not kernel quality, is the bottleneck at batch size 1, and isolate the dispatch count as the cause. Therefore, we conclude that at batch size 1, the effective approach to LLM inference optimization in WebGPU is reducing dispatch count. Our findings point to dispatch amortization, in the inference engines and in the WebGPU specification, as a path to practical browser-based inference.

The Model Context Protocol (MCP) standardizes how servers expose data and tools to Large Language Models (LLMs). A common server design embeds frequently used reference data, such as identifier lookup tables, directly in the server instructions: the system-prompt text a server hands to the host application. When a query concerns an entry of the embedded table, the model can act on it immediately instead of re-discovering the same information through a search tool. We test whether client LLMs actually consume such instruction-embedded data, reporting a 54,000-trial study across 24 LLMs (9 Claude, 6 Gemini, 9 GPT) on a production legal-information MCP server. A diagnostic condition that removes the competing search tool shows that failures are dominated by behavioral preference rather than missing capability. With search unavailable, 23 of 24 models read the embedded data reliably (hit ratio at least 98%); with a search tool merely present, 9 models drop below 15%. A 2^3 factorial analysis of three instruction-level interventions reveals strong interaction effects: combining all three restores at least 86% for 20 of 24 models, but individual interventions can backfire for specific model families. Per-server prompt engineering is therefore a workaround rather than a fix; we argue that MCP host applications should provide an explicit mechanism that places server instructions ahead of tool selection in the client LLM's deliberation.

Current LLM safety guardrails face a fundamental tension: fine-tuning distorts pre-trained representations while generative judges incur prohibitive inference costs. We challenge the prevailing paradigm by asking: can safety be achieved through pure geometric reasoning over frozen semantic representations? We present HoloAegis, a minimally parametric topological inference framework that decouples representation from reasoning. We term our approach minimally parametric because the only free parameters are the anchor count K and the temperature tau, both fixed after construction and requiring no gradient-based training. An un-fine-tuned encoder maps text to a unit sphere, after which all decisions are purely geometric. We formalize safety evaluation as a Gibbs-Boltzmann Free Energy computation over a pre-computed System Topology Anchor Bank, and we introduce Dual Time-Scale Exponential Moving Averages to detect progressive multi-turn semantic drift. Our key theoretical insight is a Topological Boundary Stability Conjecture: we provide theoretical motivation and strong empirical evidence that sparse anchor centroids stabilize the decision boundary against high-frequency lexical perturbations far better than full vector space methods. Evaluated across 8 benchmarks, HoloAegis achieves state-of-the-art accuracy (1.0000 AUC on AuthenHallu, 0.9802 on HarmBench) with sub-millisecond latency, zero cold-start data, and cross-lingual transfer (0.9758 AUC on Chinese CHIFRAUD).

Cognitive decision-making research depends on diverse scenarios with carefully controlled complexity, yet manual production is slow, inconsistent, and biased. We developed an automated pipeline that uses LLms to generate structured decision scenarios and validates their complexity through a composite framework rooted in established task-complexity theory. We evaluated 4,238 scenarios across multiple domains and complexity tiers. Measurement validation met rigorous psychometric standards. Agreement among five independent model families was nearly perfect, with an intraclass correlation coefficient of 0.997 and a kappa of 0.971. Known-groups validity demonstrated large separation between tiers, with an eta-squared of 0.587 and all pairwise comparisons significant at p less than .001. Factor analysis revealed a dominant complexity construct, with loadings between 0.87 and 0.96 across three frameworks, while interactivity formed a weaker secondary dimension at 0.34. Discriminant validity was limited by a strong relationship between complexity and text length that persisted after controlling for tier, yielding a partial correlation of 0.86. This constrains construct purity but does not undermine the instrument's tier-grading function. Model analyses showed a negative association between throughput and schema pass rate (r = -0.967, p = .007, n = 5), suggesting a speed-quality trade-off, though largely driven by one high-throughput model. Llama 4 Maverick generated scenarios fastest at 134 per minute versus 25 for DeepSeek Chat V3.2, but underproduced complex-tier scenarios, whereas DeepSeek Chat V3.2 balanced domain coverage with high schema compliance. The system demonstrated strong psychometric properties, enabling reliable classification into Simple, Moderate, and Complex tiers and providing the measurement infrastructure needed for downstream cognitive assessment of AI systems

We independently reproduce two recent methods for making large language model (LLM) reasoning more reliable, and stress-test them across domains and models (RPC across four new task domains with Qwen3-8B, LCF across four 7-8B models). The first, RPC, aggregates token probabilities and self-consistency at inference; the second, LCF, trains projectors that split hidden states into "content" and "logic" and edits the logic part toward a valid region. Validating such reliability claims matters because the original evaluations are run by each method's own authors and were never independently reproduced or stress-tested across models and domains, and LCF shipped no public code. We re-run RPC's published-path aggregation and re-implement LCF's projector, contrastive, and intervention pipeline, then extend both to text-to-SQL, legal extraction, fallacy identification, and precedent grading, and probe LCF's representation directly. RPC reproduces the original grid exactly on the authors' released reasoning paths; on four new domains its edge over self-consistency is never significant (ties or small mixed differences, paired p >= 0.28), and on BIRD, the one domain where we vary the budget, the edge grows with K as predicted but its largest gap (+2.5 accuracy at K=32, p=0.16) reverses to -0.25 when we enlarge the sample to n=200. LCF's logic-validity direction is real but weak (0.82 separability at the single best sub-layer versus 0.95 for a semantic-attribute control); its one positive effect (Qwen3 $Δ$Prob) is not significant (p=0.56), while it significantly reduces $Δ$Prob on two of the other three models.

Scientific named entity recognition (SciNER) plays a crucial role in information extraction and knowledge discovery from scientific texts. Recently, large language models (LLMs) have demonstrated the capacity to achieve competitive SciNER performance with minimal human effort. Existing research highlights the importance of incorporating candidate entity type information for accurate entity recognition and classification by LLMs. However, when too many candidate entity types are provided in the prompt, LLMs struggle to accurately recognize and label entities in scientific texts, where entity types are more complex than in general domains. To address this challenge, we propose TdSciNER, a type-driven approach that effectively leverages entity type information to enhance SciNER performance. In TdSciNER, we first design an entity type filter model to identify the most likely entity types present in a given sentence. Subsequently, we introduce an auxiliary multi-class entity typing task within a multi-task learning framework alongside SciNER to obtain richer contextual representations. Then, we develop a novel demonstration selection strategy based on sentence similarity and entity type diversity to activate the in-context learning capabilities of LLMs, thereby improving entity recognition accuracy across diverse scientific domains. Experiments on three datasets demonstrate that our method achieves performance comparable to fully supervised models. Further analysis validates that each entity type-driven component in TdSciNER contributes to the improvement of SciNER performance. This work provides valuable insights for future advancements in SciNER and broader information extraction tasks in scientific text mining.

Large language models (LLMs) increasingly serve as data-driven reasoners, yet their chains-of-thought (CoT) can be unfaithful even when final answers are correct. Most existing ``verification'' signals are not diagnostic: answer matching observes only the outcome, LLM-as-judge provides subjective and non-verifiable critiques, and scalar rewards (e.g., PRMs/RMs) offer little insight into where a multi-step derivation fails.We propose SymDiag, a neuro-symbolic framework that reframes reasoning verification as structured failure diagnosis. SymDiag translates natural-language CoT into symbolic constraints and performs step-level satisfiability/entailment checks to (i) localize failing steps and (ii) produce verifiable diagnostic evidence, including counterexamples, inconsistency witnesses, and missing-premise indicators. A central challenge is that apparent ``logic violations'' can be caused either by genuine reasoning defects or by neural-to-symbolic translation noise. SymDiag therefore incorporates a Self-Auditor that disentangles TranslationError from ReasoningError via dual symbolic encodings consistency checks, enabling robust diagnosis under partial observability. Across diverse mathematical, logical, scientific, and general reasoning benchmarks, SymDiag improves detection of unfaithful reasoning and provides substantially more effective feedback for multi-round reasoning repair than outcome-only verification and LLM-based judging, offering a principled foundation for trustworthy and scalable reasoning diagnosis.

Simulation-ready 3D assets are central to robotics and embodied AI. Generating them from a single image is usually framed as a vision-language model that emits a serialized asset for a decoder to turn into geometry and physical fields, leaving the image-to-3D reasoning implicit. We argue the limiting factor is this output-centric view: part placement and local shape are entangled in one global-coordinate token stream, and the intermediate physical states are never exposed for supervision, conditioning, or verification. PhysX-CoT instead casts single-image asset generation as an explicit structured physical reasoning process, an ordered and machine-parseable trajectory of part-level states covering decomposition, 2D and 3D grounding, relations, coarse geometry, and surface cues that we separately supervise, use to condition geometry, and treat as reward targets. Geometry is factorized so that 3D boxes carry placement and local codes carry shape, and CoT-aligned GRPO optimizes parse validity, grounding, geometry, placement, and physical consistency. Under a unified protocol that retrains all learned baselines on the same backbone, data, and frozen decoder, PhysX-CoT outperforms the closest full-task baseline across geometry, scale, and physical-attribute metrics. Oracle, token-matched, and state-order controls show the explicit states are functional rather than cosmetic, and in Unreal Engine~5 the generated assets parse, collide, and articulate at high validity.

Reinforcement learning with verifiable rewards (RLVR) has emerged as an effective approach for improving multimodal reasoning. However, most existing methods evaluate an entire response using a binary reward based only on final-answer correctness, thereby discarding the supervision available in intermediate reasoning steps. Process reward models offer finer-grained feedback, but they typically rely on separately trained verifiers, costly chain-of-thought annotations, or online judging by large language models (LLMs). In this work, we introduce StructReward, a compute-efficient framework that provides dense reinforcement signals through structured step-level reward alignment. StructReward represents each generated solution as a sequence of reasoning steps and aligns them with process-labeled reference steps using lightweight numerical, symbolic, and lexical matching rules. The aligned labels are aggregated into a dense process reward and combined with final-answer consistency and output-validity rewards through a gated Group Relative Policy Optimization (GRPO) objective. We further recycle policy rollouts into complementary supervision for response comparison and reflective self-correction, rather than discarding them after policy updates. Separately, we use a strong LLM to rewrite sampled correct trajectories into reflection-oriented training instances, further strengthening the policy's ability to evaluate and refine its reasoning. Since reward computation is performed online without an additional learned verifier or external LLM judge, StructReward substantially reduces the computational overhead of multimodal reinforcement learning. Experimental results show that structured process supervision and rollout recycling provide an efficient path toward self-improving multimodal reasoning.

Permutation optimization arises whenever the components of a system are fixed but their ordering affects performance. We introduce PRISM, a predictive protocol for permutation optimization that measures a fitness landscape before selecting a search strategy. PRISM uses inexpensive landscape diagnostics, including one-step move autocorrelation and fitness-distance correlation, to predict useful mutation operators, identify when structured search is likely to outperform random sampling, and detect regimes in which search provides little advantage. Across synthetic permutation landscapes, neural architecture benchmarks, scientific machine learning pipelines, and large-language-model instruction ordering, the protocol makes testable predictions about search behavior before optimization begins. Exhaustive instruction-ordering experiments reveal substantial performance variation induced solely by permutation, while cross-model experiments show that useful ordering structure can transfer across model families and task difficulty. Additional experiments demonstrate that instruction ordering remains consequential after prompt wording is optimized, indicating that content optimization and ordering optimization are complementary. The results position PRISM not as a universally superior optimizer, but as a framework for determining when permutation search is useful, which representation and operator should be used, and when simpler alternatives are preferable.

On-policy self-distillation (OPSD) adapts a language model by distilling guidance from a frozen teacher on trajectories sampled from the student. Its effectiveness, however, depends critically on the quality of those trajectories. We show that when student rollouts drift from target trajectories, conditioning the teacher on off-target prefixes substantially weakens its task-relevant supervision. Controlled prefix-corruption experiments expose this failure mode, which we term rollout-conditioned signal degradation. To address this problem, we propose a unified training framework that separates two complementary supervision pathways. The first retains rollout-conditioned distribution matching, providing guidance on states the student actually visits. The second applies supervised cross-entropy on canonical ground-truth contexts, avoiding the incompatibility of imposing target tokens on erroneous rollout prefixes. Token-level rollout-target alignment is used to adapt the strength of the canonical-context anchor, emphasizing it during cold start and relaxing it as rollout quality improves. Experiments across multiple model scales, two task families, and general-reasoning benchmarks show that the proposed approach improves task acquisition over OPSD while preserving general capabilities, resulting in a more favorable empirical plasticity-stability trade-off. These findings identify context quality as a central bottleneck in on-policy self-distillation and demonstrate the value of separating rollout-conditioned guidance from canonical supervision.

Knowledge distillation trains a smaller student to match the outputs of a larger teacher. Feature-based methods also align intermediate representations, but this extra constraint may affect students differently. We study this question on CIFAR-100 using a ResNet-50 teacher, a width-controlled CustomResNet family and MobileNetV2 as a cross-design comparison. For each student, we evaluate each feature method against a matched logit-KD run using the same teacher, optimizer settings, training schedule and seed. We repeat the main comparisons across multiple seeds. Logit KD improved every tested student over its scratch baseline. Attention Transfer showed no clear relationship with size inside the CustomResNet family, but its average effect was negative for that family and positive for MobileNetV2. FitNets was below logit KD in all 15 paired runs. Within the constant-depth width sweep, its gap increased for wider students, although the different-depth w=48 student did not follow this trend. Finally, the same auxiliary coefficient produced different gradient scales across students, showing that a fixed coefficient does not create a uniform training condition.

On-policy self-distillation (OPSD) improves the reasoning abilities of LLMs by internalizing privileged context into model parameters through self-distillation. Two recent research lines promote vanilla OPSD by choosing which tokens to learn from and by controlling how much privileged information the teacher receives, respectively. However, we show that each line optimizes one variable while holding the other fixed, which leads to a suboptimal solution. We argue that the two variables are coupled through the student's learning capacity: the privileged information sets the per-token divergence the teacher prescribes, while token weighting selects which of these the student must absorb. We formalize the two lines of work into a unified optimization framework, which maximizes the aggregate teacher--student divergence, subject to a budget on the aggregate learning difficulty the student can absorb. Under this modelling, we propose Unified On-Policy Self-Distillation (USD), a lightweight online algorithm to solve the Lagrangian. USD reveals that a single dual variable governs both decisions: at one price for learning difficulty, it simultaneously sets the token-selection threshold and the direction of privileged-information adjustment, keeping supervision matched to the student's evolving capacity. Through extensive experiments, USD consistently demonstrates superior performance over OPSD and token- and PI-side baselines across various model scales on various reasoning benchmarks. Code is available at https://github.com/lauvlalala/USD.

Building on recent advances in world models, World Action Models (WAMs) jointly model video prediction and action generation. However, they typically represent videos in 2D pixel space, creating a representation gap with 3D space in which robotic actions are executed. Recent 3D approaches introduce 3D information, but fail to fully exploit the dynamics of 3D structures. In this work, we propose 4D-WAM, a model-agnostic training strategy that injects spatiotemporal knowledge from 3D trajectory fields into WAMs through representation alignment. To this end, we introduce two complementary objectives: 1) motion alignment, which aligns temporal feature variations across adjacent frames and encourages the model to build local 4D awareness during training, and 2) destination alignment, which guides the model to infer the final destination from the source frame by minimizing the gap between their attention-like similarity distributions. Together, these objectives provide both local motion supervision and long-horizon goal guidance, enabling WAMs to learn trajectory-level spatiotemporal representations. Extensive in-distribution and out-of-distribution experiments across different base models demonstrate the model's improvements in spatial understanding, execution precision, robustness, generalization, and versatility.

Streaming world models predict future visual states online while maintaining physically coherent dynamics over long horizons. However, their rollouts often violate basic physical constraints. A common approach distills pretrained bidirectional DiTs into few-step causal generators. However, this paradigm suffers from two fundamental limitations: generic bidirectional teachers acquire limited physical priors from visually oriented pretraining, and the limited priors suffer further loss during bidirectional-to-causal distillation. We present PhyS, a three-stage framework for distilling physical priors into streaming world models. To acquire physical priors from real-world interactions, we construct PhyS-120K, a dataset of 120K real-world physical-interaction videos spanning rigid-body dynamics, soft-body deformation, fluid phenomena, and phase transitions. Each video is annotated with structured descriptions of object properties and causal state transitions. Physics-aware supervised fine-tuning injects the physical priors into a bidirectional 14B DiT teacher, which we then distill into a lightweight 1.3B causal DiT for few-step autoregressive streaming generation. Finally, we use online reinforcement learning to incentivize the distilled model to generate physically plausible rollouts and further propose Temporal Credit Routing (TCR) to address temporal credit assignment. TCR evaluates physical consistency over overlapping temporal windows and routes the resulting group-relative advantages to temporally aligned denoising actions. On PhysicsIQ, PhyS improves the Wan2.1-14B teacher by 18.2% and the Self Forcing, Rolling Forcing, and Causal Forcing by 23.7%, 14.8%, and 31.4%, respectively. Results also improve the physics-aware video benchmarks VideoPhy, VideoPhy2, and PhyGenBench. The dataset, code, and more sample videos are available on our Project Page.

Recent advances in generative models have achieved remarkable performance in text- and image-conditioned editing. However, preserving the content of a given image while referencing style patterns from another remains challenging, often leading to uncontrollable stylization results. In this paper, we approach image stylization from the perspective of continuous control, aiming to enable modern Diffusion Transformer (DiT)-based multi-reference editing models to (1) faithfully preserve the semantic structure of the content image, (2) render strong stylization effects, and (3) smoothly transition between the two. To this end, we propose a simple yet effective two-stage training strategy along with a style-strength-aware spline formulation. Specifically, in the first stage, the model is trained to produce strongly stylized outputs while preserving the content semantics as much as possible. In the second stage, with the base model frozen, we learn a set of anchor projectors that map various stylization strengths into the model parameter space. During inference, by performing style-strength-aware spline interpolation in a low-rank space, our method enables continuous control over stylization strength, even though the model is trained with only a few discrete strength levels. Extensive experiments demonstrate that our method supports precise and continuous manipulation of stylization strength while generating high-fidelity results with modern DiT models. Project page: https://reychiaro.github.io/StyleController.

In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs). Perforated microstructures induce complex boundary conditions and fine-scale flow features that are difficult for standard neural networks to resolve. Conventional PINNs, even when combined with advanced training techniques, can suffer from a loss of accuracy and efficiency as the number of perforations increases. One important source of this difficulty is the soft enforcement of boundary conditions through penalty terms, which can lead to stiffness, gradient conflicts, and poor resolution of near-boundary flow structures. Hard constraints provide an alternative by encoding boundary conditions exactly into the network ansatz, but may introduce undesirable non-local effects due to the global nature of the approximation. To address these challenges, finite basis PINNs (FBPINNs), which are based on domain decomposition and localisation principles, are used together with hard boundary constraints that efficiently encode perforation-related boundary conditions. This approach helps mitigate spectral bias, improves overall accuracy, and exhibits convergence that is only weakly affected by the number of perforations, thereby providing an efficient and highly parallelisable neural network framework. The proposed approach is further supported with theoretical arguments, specifically focusing on the localisation and approximation properties of FBPINNs.

As firms increasingly deploy machine learning for strategic decision-making, understanding algorithmic interactions has become central to operations research and economics. This paper studies learning in infinite-horizon, nonzero-sum linear-quadratic stochastic games under a radically uncoupled information structure, where players are either unaware of opponents or strategically oblivious, observing only a common state and their own action history. Under this minimal information, we analyze an asynchronous decentralized learning process in which each player independently runs a single-agent $ε$-greedy iterated least-squares algorithm. We prove that, despite being unable to identify the system parameters, players' learning dynamics converge almost surely to the complete-information Nash equilibrium and characterize the convergence rate. We then apply the framework to a dynamic Cournot competition with sticky prices. Numerical experiments validate the theoretical results and show that learning under limited information reduces firm profits under both low and high price stickiness, while total surplus declines and market concentration increases when price stickiness is high. Publicly revealing aggregate market output substantially accelerates convergence and mitigates these welfare losses.

Tool-using language-model agents face constraints whose meaning changes with observations and prior actions. We study exact sampling from the model distribution conditioned on a hard stateful validator while reusing invalidity certificates across histories. Stateful CARS freezes a bank of sound state--continuation schemas within each attempt and removes every trajectory containing a certified continuation at a matching abstract state. An exact residual Doob transform samples from the resulting proposal. We give a checkable future-validity bisimulation condition, prove schema soundness, adaptive exactness, i.i.d.\ outputs, almost-sure termination, monotone acceptance, and compression invariance, and characterize computation by the number of reachable full-history product states. This number can be exponential for a history-dependent language model; the evaluated method therefore makes no generic finite-trie scalability claim. On enumerable workflows, its analytic law matches the valid conditional to $10^{-16}$ at validity probability $6\times10^{-8}$, whereas state-aware local decoding can be $0.97$ away. A matched comparison is negative: observation-keyed official CARS is cheaper in sampler steps (root/Stateful ratio $0.942$ $[0.934,0.951]$), and the Qwen comparison is null ($0.99$ $[0.90,1.08]$). Cross-history transfer helps only in an internal matched-key ablation ($1.27\times$). Thus the evidence supports exact schema-induced conditioning, not a systems advantage over CARS.

We argue that learning visual representations without labels requires a training signal jointly complete across three non-overlapping objectives: semantic invariance across augmented views, patch-level spatial prediction, and representational non-degeneracy. We formalize these as the observation, prediction, and regularization principles and prove (i) that combining observation and prediction without regularization admits the constant encoder as a global minimizer under negative-free alignment; (ii) that the two objectives are gradient-complementary and structurally non-conflicting at the encoder output; and (iii) that the momentum encoder converges to the same fixed point as the online encoder and provides no collapse guarantee at convergence. Contrastive alignment provides only self-limiting collapse resistance, formalized via an explicit gradient-decay argument. Dropping prediction withholds the spatial training signal by construction; dropping observation forfeits cross-view semantic invariance by construction; at the scale we study, no pair substitutes for the third. Every major self-supervised method is a special case of a single unified energy decomposition. We pair every theoretical claim with a controlled experiment, including a patch-retrieval evaluation for the spatial consequence of prediction.

Generative AI has emerged as one of the most transformative forces in modern artificial intelligence, reshaping how we create, imagine, and interact with digital content. From photorealistic images to coherent text, from immersive videos to novel molecular structures, generative models now power applications that were once confined to science fiction. This book is designed to guide readers through the foundational principles, mathematical underpinnings, and practical architectures that underpin this revolution.

This work proposes deep nonparametric Instrumental variable quantile regression (IVQR), a two-stage estimator that combines conditional diffusion modeling with a kernel-smoothed conditional moment formulation. In the first stage, we estimate the joint conditional distribution of the outcome and endogenous covariates given the instrument using a variance-preserving conditional diffusion model. In the second stage, we approximate the conditional moment operator through Monte Carlo sampling and a kernel-smoothed surrogate for the indicator function, and then estimate the structural quantile function by empirical risk minimization over deep neural networks. We establish an excess-risk bound for the proposed estimator and derive end-to-end total variation guarantees for the conditional diffusion model under unbounded support, explicitly accounting for score estimation, early stopping, and discretization errors. Our theory is developed under a polynomial-tail envelope on the data distribution and degenerates continuously to the exponential setting: as the tail index grows, the obtained excess-risk rate converges to the minimax-optimal rate of nonparametric regression, thus our heavy-tailed theory covers the classical light-tailed nonparametric guarantees as a limiting case. Simulation studies and a real-data application demonstrate that the proposed method outperforms existing nonparametric IVQR approaches, with gains that become increasingly pronounced as the dimensionality of the covariates and instruments increases.

Tropical cyclones are growing more destructive in a changing climate, and efficient forecasting of their structure and track has become a necessity. Deep generative models promise an alternative to computationally expensive numerical weather prediction (NWP), yet current systems produce either satellite imagery or atmospheric fields, never both; they need many sampling steps, putting them out of reach of modest hardware; and their storm tracks come from regression heads with no physical link to the generated atmosphere. This work presents a single-pass model that jointly forecasts GRIDSAT-B1 infrared imagery and four ERA5 atmospheric fields (U-wind, V-wind, air temperature, and surface pressure) out to nine hours. A five-channel variational autoencoder compresses each 5 x 256 x 256 frame to a 4 x 64 x 64 latent, and a conditional rectified-flow UNet with a factorized temporal-attention module predicts the next three frames from three past frames, their best-track coordinates, and timestamps. The model is then reward-fine-tuned (DRaFT) against a differentiable track error derived from the predicted winds through a steering-flow calculation. On held-out 2022 storms the model reaches 16.35 dB PSNR and 0.759 SSIM, ahead of a reproduced cascaded-diffusion baseline at every lead time (+0.84 dB at +9 h) while sampling ~30x faster (56 ms vs. 1673 ms). Track error at +9 h is 62.4 km, 15% below the baseline, and a reward fine-tuning study demonstrates a further 8-11% track-error reduction across sampler budgets.

Large vision-language models have achieved strong performance in multimodal reasoning, but they remain unreliable on fine-grained spatial tasks that demand both precise spatial perception and fine-grained geometric computation beyond end-to-end generation. Tool augmentation offers a natural solution, while existing methods either plan tool calls from scratch without explicit dependency constraints or rely on fixed pipelines that are redundant and generalize poorly across spatial tasks. An effective spatial reasoning agent should instead accumulate reusable experience and adaptively compose it for new problems. To this end, we propose NeSy-Spatial, a neuro-symbolic framework for self-evolving spatial skills. NeSy-Spatial abstracts tool interactions and geometric operations into typed executable atomic instructions and composes them into two complementary skill types: Tool-Use Skills for organizing tool execution and Geometry Skills for structured geometric reasoning. During inference, NeSy-Spatial retrieves and executes relevant skills in a closed-loop process. During evolution, it analyzes buffered successful and failed trajectories to refine skill structures and prune unreliable or inactive entries. Experiments on three spatial reasoning benchmarks show that NeSy-Spatial consistently improves reasoning accuracy with more precise tool utilization.

Multimodal large language models (MLLMs) have demonstrated significant potential in complex spatial scene understanding and reasoning tasks. However, their open-ended reasoning process is prone to decision errors and error accumulation, leading to instability in answer quality. To address this, we propose an advantage-guided gating framework that dynamically intervenes in and corrects deviations during the reasoning process. Specifically, we model step-by-step reasoning as a finite-horizon decision process and introduce Monte Carlo value evaluation on the reasoning tree to provide intermediate supervision signals. The framework includes Step-Advantage Gate and Trajectory-Advantage Gate, which dynamically select high-value reasoning steps and high-quality complete reasoning trajectories, respectively. During training, we perform supervised learning for the gates using reasoning trees generated via multi-branch sampling, and combine shared-parameter initialization with task-specific heads to achieve cross-task robustness and diversity. During inference, the model greedily selects high-value prefix reasoning steps while choosing the optimal reasoning head based on the problem type, thereby significantly improving the accuracy of the final answer. Furthermore, we constructed the Reasoning-Tree-160k dataset and performed two-stage learning on it. Extensive experiments demonstrate that this advantage-guided gating framework effectively enhances the performance of benchmark MLLMs in visual-based spatial understanding and reasoning tasks. The code is open to the public for research: https://github.com/LingLin-ll/Advantage-Guided-Gate.