每天知道
你的领域
出了什么

LLM serving is increasingly constrained by memory capacity as model weights, KV caches, and the number of served model variants continue to grow. This report examines High-Bandwidth Flash (HBF) as a capacity-oriented extension to HBM-based serving systems. We first discuss how HBF can be integrated into the GPU memory hierarchy without undermining the bandwidth expected by the compute die. We then model the system-level value of added capacity as expanded residency for read-mostly model-state objects. Under this view, HBF can improve MoE serving by enabling more expert replicas and can improve multi-model serving by reducing model loading and supporting hot-model replication. Our simulation results show that these benefits depend on preserving the HBM-resident execution path while using HBF to expand the resident set of model weights.

Edge AI deployment demands neural architectures that are simultaneously accurate, computationally efficient, and hardware-deployable - a challenge addressed by hardware-aware Neural Architecture Search (NAS). While recent works incorporate quantization directly into the NAS loop, these approaches expand search complexity and tightly couple architecture and quantization design. The simpler post-search quantization strategy has received little analytical attention: the effects of Post-Training Quantization (PTQ) on the NAS-discovered Pareto structure remain uncharacterised, and no framework combines quantized architecture mapping onto reconfigurable accelerators with automated hardware exploration. This paper addresses both gaps. First, a three-stage pipeline is proposed: a hardware-agnostic Pareto rank surrogate frontend on NAS-Bench-201, a quantization bridge with Pareto-aware filtering and feedback control, and an evolutionary Domain Space Exploration (DSE) backend on CGRA4ML for optimal hardware mapping. Second, an empirical study characterises how INT4 PTQ perturbs the NAS-Bench-201 Pareto space through formal stability metrics on ground-truth data for all 15,625 architectures, and demonstrates that an FP32 zero-shot surrogate outperforms a dedicated INT4-trained surrogate in Pareto space coverage across two standard search strategies.

In expert-parallel (EP) MoE serving, every layer synchronizes at the slowest GPU. Dispatchers balance token counts (EPLB, LPLB, UltraEP) or activated-expert counts (METRO), assuming expert time is linear in one. Measurements on two datacenter GPU generations show it is neither: below $n^* \approx 156$--$168$ tokens, HBM weight streaming dominates---cost attaches to $activated replicas$, not tokens; above it, grouped GEMM rounds tokens to 128-tile $M$-tiles, so $splitting$ an expert adds padded compute. A max-affine profile $t=\max(a+bG,\,c+βN)$ captures both regimes. Realistic decode batches hold hot experts in the linear regime and cold in the flat $simultaneously$; recorded batches show proxy dispatches differ by $1.4$--$1.6\times$ in modeled block time (p95 up to $1.7\times$), and $which$ proxy wins flips with the regime. We formalize per-batch dispatch as a fixed-charge makespan problem---NP-hard on two fully replicated GPUs, polynomial in degenerate limits---and present TEMPO, a makespan-aware dispatcher solving it in milliseconds off the critical path; its SGLang integration runs out-of-process and fuses dispatch with count collection into one in-graph kernel. Anchored by an 8-GPU Testbed A microbenchmark, TEMPO stays within $1%$ of the best fixed baseline everywhere and wins by up to $15.5%$ where regimes mix. End-to-end on Testbed B, Qwen3-235B (inside the win region) gains $4$--$6%$ throughput and cuts p99 latency by $\sim 15.6%$; DeepSeek-V3 (outside, communication-dominated) shows only mechanism cost. A phase diagram, not a universal win, is the claim: it predicts both outcomes before deployment.

Interactive world models must support persistent memory, responsive interaction, and long-horizon generation, yet these requirements place conflicting demands on the model. Maintaining history in the denoiser context or key-value cache incurs growing cost, forcing a trade-off between session length and retained memory, while low-latency interaction relies on few-step generation whose capabilities are bounded by its teacher. Alaya-EVOKE (Evoke) addresses both limitations by externalizing persistent world state and redesigning the teacher for long-horizon interactive generation. Scene geometry is maintained in an external, camera-indexed world state bank, from which only view-relevant information is retrieved, keeping the denoiser context bounded as the session grows. Rather than treating the teacher as a fixed generator, we design it for long-horizon supervision: its sparse attention combines chunk-wise grouping, retrieval of selected distant frames, and a linear-attention global state, yielding linear growth in memory and compute while enabling supervision over long horizons. Such supervision exposes content drift that stays locally plausible within short windows, while per-chunk conditioning enables prompt changes and event control throughout the sequence. A 30-second distribution-matching objective, applied under self-forced rollouts, transfers both capabilities to a three-step student that uses no classifier-free guidance, improving resistance to long-term drift while preserving responsive conditioning. With bounded context and recurrent external memory, Evoke supports open-ended, continuously evolving generation; on a single H200 at $384\times 640$, each $1.5\,\mathrm{s}$ chunk is generated in $2.11\,\mathrm{s}$. As a three-step world model, Evoke achieves state-of-the-art performance on WBench while remaining competitive on VBench-Long and VBench-2.0.

As edge-side vision services continue to expand toward low-latency, high-throughput scenarios, reducing the inference cost of vision models without sacrificing reliability has become a central concern. Existing semantic caching methods largely rely on empirical similarity thresholds; while such thresholds improve hit rates, they tend to introduce silent misclassifications near decision boundaries. To address this, we propose LipCache, a certified semantic caching framework for image classification. Without modifying the existing deployed main model, MainNet, the framework introduces a lightweight network, GuardNet, that maps inputs into a low-dimensional feature space subject to a Lipschitz constraint. It then computes a per-sample certified reuse radius from the local classification margin and the spectral norm of the classification head. At runtime, a cached result is reused only when the query feature falls inside the certified reuse ball; otherwise, the query falls back to MainNet. Thus, cache hits are transformed from empirical threshold tests into geometric certification decisions with explicit theoretical boundaries. Across standard image classification tasks like CIFAR, Tiny-ImageNet, and SVHN, LipCache achieves a measured speedup of up to $1.65\times$ with limited end-to-end accuracy degradation, while all accepted cache hits satisfy the GuardNet-side certified-consistency condition. Furthermore, an enhanced GuardNet training recipe substantially improves cache hit rates in the Tiny-ImageNet multi-class extension while maintaining a certified-consistency rate of $100%$. These results demonstrate that per-sample certified reuse can reduce main-model fallback while preserving theoretical consistency, providing a feasible approach to reliable cache-assisted inference at the edge.

Large language model serving faces a critical memory bottleneck: the KV cache grows with sequence length and batch size. PagedAttention uses fixed-size memory blocks to reduce allocator-level fragmentation, but recent KV eviction algorithms operate at a token granularity finer than block-level management. This mismatch causes intra-block fragmentation, leaving a large fraction of allocated KV memory unreclaimable. We present vToken, a lightweight token-level virtualization layer that decouples logical token liveness from physical block placement. vToken maintains a stable logical token view through token-table indirection and realizes physical reclamation by repacking live tokens asynchronously. The design preserves PagedAttention kernels and CUDA Graph compatibility. We implement vToken in vLLM and evaluate it with H2O, Random, and Scissorhands across models. Compared with a paired Naive-Evict baseline, vToken reduces retained KV blocks per request by 27.2%--72.3% and improves SLA-constrained throughput by up to 1.37$\times$. Under a constrained active-KV budget, it extends the maximum feasible concurrency by up to 2$\times$, while reducing the per-policy integration footprint from 500+ lines to under 50.

Vision-Language-Action (VLA) models promise to bring end-to-end reasoning to autonomous driving, but their computational cost remains far too high for real-time control. The core challenge is structural: VLA inference is not a single bottleneck but a cascade of four. Visual encoding wastes compute on overlapping video frames; language-model prefill recomputes context that could be carried over from the previous timestep; reasoning tokens are generated serially despite low entropy; and flow-matching denoising applies uniform compute to a non-uniform velocity field. Addressing any one stage in isolation leaves the others untouched. We propose FlashDrive, an algorithm-system co-design framework that targets all four stages simultaneously. Our key insight is that each bottleneck admits a distinct, lightweight algorithmic shortcut: temporal overlap enables streaming KV-cache reuse across frames; the low per-token entropy and strong intra-block correlations of driving-domain reasoning make a non-autoregressive diffusion drafter highly effective for speculative decoding; and the velocity field's structure---sharp at the endpoints, flat in the middle---permits adaptive step caching that concentrates compute where it matters. Layered on system-level CUDA Graph compilation and kernel fusion, these techniques compound. Applied to Alpamayo 1.5-10B with W4A8 quantization, FlashDrive reduces end-to-end latency from 717ms to 151ms (4.7x) while leaving accuracy essentially unchanged: minADE6@6.4s shifts by only 0.08m, minADE1 improves, and closed-loop collision and off-road rates improve in simulation. By raising a 10B-parameter reasoning VLA from 1.4~Hz to 6.6~Hz on a single GPU, FlashDrive moves end-to-end autonomous driving substantially closer to real-time deployment.

Schedulability analysis is essential for certifying real-time systems, but existing tests are often developed through pen-and-paper proofs that are difficult to scale, validate, and maintain. Mechanized verification in PROSA/ROCQ offers a rigorous alternative, yet manually constructing such proofs requires substantial domain expertise and proof-engineering effort. Recent successes of large language models (LLMs) across a wide range of tasks make them promising candidates for generating PROSA/ROCQ scripts for mechanized theorem provers. However, state-of-the-art LLMs often lack the PROSA-specific knowledge required to correctly use its modeling abstractions and proof patterns. This paper introduces PROVE-RT, an LLM-assisted framework for generating PROSA/ROCQ scripts to mechanize schedulability analyses in real-time systems literature. PROVE-RT guides generation through dependency-aware informal sketches, retrieval from processed PROSA documentation, staged skeleton generation, and proof completion. We construct a mechanization-oriented corpus from 1, 191 real-time systems papers, containing 13, 134 informal sketches with dependency information. On a curated evaluation set, direct prompting of state-of-the-art LLMs fails to reliably generate valid PROSA mechanizations, whereas PROVE-RT achieves a success rate of 44.7%. These results show that retrieval-guided and staged LLM assistance can improve automated mechanization of schedulability analysis in PROSA/ROCQ.

Visual classifiers are expected to generalize under data shifts, target shifts, and their combinations, yet most existing methods focus on domain invariance while failing to address intra-image predictive sufficiency. We investigate the structural hypothesis that each image contains a sample-adaptive oracle intra-image predictive subset sufficient for label prediction, while the remaining patches form non-essential complementary context that may correlate with the label. The theoretical analysis shows that restricting prediction to this oracle subset preserves the Bayes risk achievable by the full-patch representation while admitting a complexity bound that tightens with the oracle-subset size. Based on this view, we propose PatchGen, a text-free module that learns a sample-dependent soft predictive-subset mask as a task-driven proxy for the unobserved oracle subset mask. Specifically, histopathology visualizations suggest that PatchGen assigns higher scores to tumor-consistent regions than to some frequently co-occurring inflammatory context. Extensive experiments on natural and histopathological image benchmarks spanning all three shift settings show that PatchGen improves average performance over matched-backbone baselines in most evaluated configurations, enhances generalization to unknown classes, and remains competitive with vision-language methods without text supervision.

Implicit multimodal in-context learning compresses demonstrations into internal interventions, ranging from static task vectors to query-conditioned transformations and attention routing. Despite their common goal, these methods differ substantially in how the intervention depends on the query and where it modifies the model, leaving unclear which additional complexity is necessary for a given task. We propose the Selection--Realization Hypothesis. It views demonstrations as inducing a compact family of internal changes from which the query selects, while the model's computation constrains how the selected change can be implemented. We evaluate this account using controlled multimodal tasks in which query dependence varies without changing the underlying task primitives or prompt format. By contrasting correct demonstrations with matched counterfactuals, we measure the structure of explicit M-ICL and test whether it predicts intervention behavior. We find that the success of a static task vector is closely tied to how much of the demonstration-induced change is shared across queries. Additional intervention complexity becomes useful when explicit M-ICL contains query-specific or distributed structure that a local additive shift cannot recover. These relationships extend to natural VQA benchmarks and support cost-aware method selection without access to test performance. Our results provide a unified empirical theory of when demonstrations can be compressed into a task vector and when a more expressive intervention is warranted.

Current large language model development relies on massive, often non-permissible datasets, creating a high barrier for researchers committed to open-source and ethically sourced data. We introduce Mimir v1, a 1-billion-parameter language model based on the Hierarchical Reasoning Model (HRM) architecture, that is trained from scratch and delivers highly competitive performance for English and sets a new state of the art for Danish using only permissible post-training data. Trained on a mixture of 161 datasets, Mimir v1 outperforms the original HRM-Text 1B and competes with larger frontier models like Qwen 3.5 4B and Gemma 4 E2B, tested across 20 benchmarks for English, Math & Code and Danish. The model is available on the Hugging Face Hub: https://huggingface.co/danish-foundation-models/DFM-Mimir

Multi-layer transformers form the critical component of essentially all large language models (LLMs) in use today. Because of their ubiquity and computational capability, there is a rapidly growing body of work that aims to precisely calibrate the expressive power of transformers as language recognizers by comparing them against standard models of computation studied for decades by the theoretical computer science community. In this endeavor, circuit complexity has by and large emerged as the "correct" branch of computational complexity to analyze the expressive power of transformers; the reason is that parameterizing transformers by the various resources they use, such as attention and precision, leads to direct comparisons with different classes of circuits parameterized by resources such as type of gates, size, and depth. Here, we present an overview of selected results that delineate the expressive power of transformers using concepts and methods from circuit complexity.

Local chemical perception and property reasoning are both essential for understanding how molecular structure determines properties. Current LLM-based chemical reasoning methods either receive SMILES/molecular images together with descriptions of local motifs, or reason directly from molecular images. Neither approach enables the model to focus on chemically meaningful regions before reasoning. To address this gap, we propose Visual Latent Structural Reasoning (VLSR), an end-to-end framework that jointly learns localization and reasoning from molecular images. Central to our approach is a localize-then-reason strategy. VLSR first learns to locate chemically meaningful regions in a molecular image. It then reasons about their property effects in a compact latent workspace before producing the final answer. Under the same inference setup, this design achieves 9.6X higher throughput than a comparable textual-reasoning baseline.

Routing each query to a cost-effective large language model (LLM) is critical for balancing quality and cost, yet most routers rely on a centralized task center to predict model performance, creating an information-risk mismatch and a scalability bottleneck as the model pool grows. We propose a market-based routing paradigm that shifts ex-ante prediction to LLM providers via a reverse auction, where providers bid with self-predicted success probabilities and execution costs. To account for inherently noisy provider predictions and center evaluations, we introduce the Error-Aware Reverse Auction Mechanism (EA-RAM), which explicitly models this inherent Dual Error. We prove that EA-RAM is Bayesian incentive compatible and individually rational under the Dual Error, establish sufficient conditions for center rationality, and derive an explicit welfare-loss bound. We further identify robustness effects: opposite-signed errors can cancel, vanishing-tail link functions (e.g., logistic) stabilize clear-cut cases via saturation, and extra noise smooths belief maps, reducing the gains from marginal manipulation. Experiments on simulations and real-world benchmarks show that EA-RAM is robust to the Dual Error and achieves a better cost--performance Pareto frontier than centralized baselines, with additional gains when providers contribute local information, validating its practical effectiveness.

The extent to which large language models for code rely on memorization over genuine understanding remains highly debated. While current literature frequently reports widespread memorization, evaluating the underlying probing techniques across dense architectures reveals a severe breakdown in their utility at scale. Traditional encoder-style probes using perturbations such as synonym fuzzing or dead-code insertion struggle to expose memorization in scaled models, even on known-contaminated benchmarks, and decoder-style probes that rely on log probabilities show similar performance degradation. The specific mode of failure for these probes, particularly why such techniques disrupt smaller models but fail to impact larger ones, motivates us to untangle representation load from memorization rather than treating them as a single phenomenon. By applying invertible mathematical transforms to numeric problems, we isolate these two factors and reveal that scaled encoders successfully absorb substantial representation load while still converging on the correct family of solutions. In practical software engineering, this ability to adapt to varying surface forms is what truly matters for usability and generalizability in LLM and agentic applications. Whether a specific solution was seen during training becomes a much less pressing question because although memorization inflates scores on contaminated benchmarks, factoring out representation load makes it debatable how much we should truly care if a functional answer was originally memorized. Future evaluations must therefore be built around separating these phenomena rather than relying on methodologies that quietly entangle them.

The OWL 2 EL profile is used in some of the largest production ontologies, including the Gene Ontology and SNOMED CT. Existing neuro-symbolic (NeSy) learning methods accept propositional theories or Datalog, and reasoning-shortcut (RS) awareness has not been investigated in ontology settings. We present Moose, a method that compiles an $\mathcal{EL}^{++}$ TBox and finite ABox to a Sentential Decision Diagram (SDD). The SDD acts as a differentiable weighted-model-counting layer, and we add closure clauses outside the $\mathcal{EL}^{++}$ profile on declared exhaustive families to overcome the limited expressivity of $\mathcal{EL}^{++}$ under partial supervision. We show termination, soundness, completeness, and polynomial intermediate sizes, and validate the proofs in Lean. We then define the first formal partial-supervision latent-concept-learning task over an OWL EL ontology, i.e., learning per-individual classifiers for latent concepts from observed ABox literals, and evaluate Moose on MNIST-with-ontology and Pizzaïolo. Moose improves over propositional-NeSy, fuzzy-logic, and ontology embedding baselines, and presents the first reasoning-shortcut analysis in an OWL EL setting.

We address the use of large language models (LLMs) to help discover Isabelle proofs. An Isabelle build establishes that the submitted theory is accepted, but not that an LLM changed only what the developer authorised. We present CAPRI, a contract-aware repair workflow in which Isabelle checks the proof and an independent checker enforces a machine-readable edit contract. Prompts, proposals, candidate repositories, diagnostics, verdicts, and hashes are retained for audit. We evaluate five workflows on twelve failed proofs from four developments, with three replicates per task and condition, giving 180 runs and 138 valid repairs. Of 144 terminal candidates accepted by Isabelle, six had modified protected text; all arose in iterative workflows that could edit a complete theory. A proof-body-only interface produced 29/36 valid repairs and no contract violations, compared with 31/36 for the corresponding full-theory workflow. One-shot repair produced 22/36, while a later prospectively frozen iterative workflow produced 32/36; these figures compare complete workflows rather than individual mechanisms. A separate post hoc OpenRouter campaign found no improvement in the designated Luna comparisons. A Sol configuration with matched demonstrations produced 33/36 repairs, compared with 29/36 in the frozen OpenAI Responses condition, but the difference was not statistically significant in a one-sided exact McNemar test ($p=0.0625$).

Watermarking LLM-generated text is an important task for tracing its provenance. Existing LLM watermarks preserve provenance under editing, but this same robustness allows an adversary to alter critical content while retaining attribution, a vulnerability known as piggyback spoofing. We introduce an innovative watermark that jointly provides provenance and tamper evidence. It co-embeds a robust signal and a fragile signal into each generated token. The signals share the same mechanism but use independent keys and different seeding windows over normalized text, making one resilient to edits and the other sensitive to reader-visible changes. Multiple rounds of unbiased tournament reweighting preserve the expected generation distribution, while a periodic round-allocation pattern controls the trade-off between the two signals. At detection, their scores form a two-dimensional space supporting three decisions: Intact, Tampered, and No-Watermark. Across two large language models and two prompt datasets, our method demonstrates the highest tamper-detection rate among the evaluated methods while maintaining competitive attribution robustness and perplexity. Ablation studies show that reliable three-state detection requires a well-defined notion of intactness, co-embedding of the two signals, and complementary sensitivity to edits.

Modern LLMs excel at reasoning and instruction following, enabling users to express complex and diverse information needs. However, conventional retrievers largely rely on surface-level matching between queries and documents, resulting in a growing gap between how users express their needs and how retrievers interpret them. In this paper, we present GEM, a generative embedding model that augments retrieval through its own knowledge by explicitly reasoning about user intent and relevance criteria. GEM unifies generation and embedding within a single model: it first reasons over the query, then appends an embedding token to encode the enriched context for retrieval. Evaluated on reasoning-intensive and instruction-following retrieval tasks, GEM demonstrates the effectiveness of its reasoning-augmented retrieval, outperforming its non-reasoning variant and matching baselines using substantially larger models. Furthermore, GEM's generative nature allows test-time compute scaling via prompting to further enhance retrieval performance. Our code is available at: https://anonymous.4open.science/r/GEM.

Multi-parametric magnetic resonance imaging (mpMRI) is a cornerstone for brain tumor diagnosis and treatment, yet current AI models face critical limitations: their lack of natural language interaction and interpretability impedes spatial information integration and cross-modal reasoning required clinically. Key challenges arise from significant physical meaning differences across modalities, spatial misalignment due to scan intervals, and the need for complex multi-feature interpretation in tasks like glioma grading. While visual-language models (VLMs) show promise in cross-modal understanding, existing methods focus mainly on 2D image modeling, neglecting direct perception of 3D volumetric space. Although 3D VLMs have been proposed for report generation and feature alignment in 3D CT imaging, mpMRI applications demand collaborative inference across multiple imaging modalities-a requirement unmet by current solutions. To address this, we introduce Mr3D-VL, a dedicated visual-language foundation model for multi-parametric 3D MRI. With 4 billion parameters, it employs an unsupervised pre-trained shared 3D encoder and 4D rotational positional embedding for dual modality-spatial integration. Its cross-modal projection layer uses a multi-resolution feature implantation strategy to enhance feature perception across resolutions. Experimental results show significant improvements over existing 4B/7B/30B domain-specific and general-purpose models in text generation tasks, achieving a BERTScore of 0.856 for report generation, with question-answering accuracy at 0.713 and multiple-choice accuracy at 0.912.

Formal verification provides strong guarantees of software correctness, but its adoption is limited by the high cost of writing precise formal specifications. While recent large language models (LLMs) have shown strong capabilities in theorem proving and verified code generation, their true ability to generate program specifications remains unclear. Existing evaluations require either verifying implementation conformance or proving semantic equivalence between specifications, both of which are formidably difficult and may conflate proof difficulty with specification quality. To address this problem, we introduce Coins, a Rocq based evaluation framework that assesses specification quality by instantiating specifications under evaluation on trusted test cases and generating concrete proof obligations. This design aligns with the asymmetric nature of formal reasoning, where successful proofs provide reliable evidence while proof failures are inherently ambiguous. Using Coins, we conduct a large scale study on HumanEval with a curated set of human written Rocq specifications. Our results show that specification generation remains a formidable challenge, and that verification complexity can obscure genuine differences in specification quality. Overall, we find that accurate specification evaluation, rather than model scaling alone, is central to understanding the power of LLMs for specification synthesis, and that test case based formal reasoning offers a more faithful and discriminative measure of progress.

Self-referential prompting has been shown to reliably induce large language models to produce first-person reports resembling subjective experience, but no prior work measures how consistent these reports are across repeated, independent trials, or how that consistency compares to the model's behavior on other kinds of open-ended questions. We measure response instability, defined as one minus the mean pairwise cosine similarity of sentence embeddings computed over a compressed core claim extracted from each response, for three groups of questions: self-referential prompts eliciting a subjective-experience report, unresolvable philosophical questions unrelated to self-reference, and questions with a verifiable correct answer. Using 30 independent responses per question (360 responses total, Gemini API, temperature 0.7) across four questions per group, we find that self-referential questions show the highest instability (0.343 +/- 0.047), unresolvable philosophy questions show intermediate and tightly clustered instability (0.192 +/- 0.008), and verifiable questions show the lowest instability (0.105 +/- 0.058). This provides a quantitative baseline for the induced subjective-experience report, showing that it occupies a distinct, less stable position in the model's output distribution than ordinary open-ended philosophical uncertainty.

Deep representation learning has primarily focused on how features evolve across network layers, while largely overlooking the structured geometry embedded in network parameters. We introduce a dual-manifold perspective in which each convolutional layer contains two coupled geometric spaces: a Kernel Manifold induced by convolutional filters and a Data Manifold characterized by intermediate feature representations. Because these manifolds share the same channel space, parameter geometry can provide complementary structural information to guide feature evolution. Based on this insight, we propose Kernel-Guided Feature Transform (KGFT), a lightweight module that derives a geometric guidance matrix from the kernel Gram matrix and uses it to transform the covariance structure of feature representations. Unlike conventional attention mechanisms that reweight feature responses, KGFT explicitly reshapes feature relationships by transferring geometric information from the kernel manifold to the data manifold. To accommodate network hierarchy, we further introduce Exploit and Explore modes with a depth-aware scheduling strategy and a learnable guidance strength that adaptively controls the contribution of geometric transformation. This design promotes geometric alignment in shallow layers while encouraging feature diversity in deeper layers, without imposing excessive constraints on representation learning. Theoretical analysis establishes the validity of the proposed transformation and characterizes its effect on feature covariance. Extensive experiments across CNN- and Transformer-based architectures, including ResNet, ViT, and LLaMA-7B, demonstrate consistent improvements on image classification and arithmetic reasoning tasks, validating the generality and effectiveness of kernel-guided dual-manifold representation learning. Code will be publicly available.

Transformer-based language models achieve strong performance but incur substantial inference cost due to repeated high-dimensional matrix multiplications. We propose Reduced Matrix Multiplication (RMM), a training-free, input-adaptive inference method that reduces Transformer matrix products by selecting informative slices along their contraction dimensions, without modifying model weights. Under a simple retention-ratio control, RMM provides a smooth and predictable accuracy-efficiency trade-off. Across language models ranging from 1B to 70B parameters, we find that reduction tolerance depends on the model family, task, component, and retention ratio, although it often improves with model scale. Under moderate reduction, RMM remains robust across the evaluated discriminative, autoregressive generation, and long-context settings. We further show that the same principle extends to multimodal vision-language inference. Mechanistic ablations reveal a structural asymmetry within Transformers: attention-side computations are substantially more reducible than MLP components. Finally, wall-clock benchmarks with custom kernels on an NVIDIA A100 show that these computational savings can translate into practical runtime gains, especially at longer sequence lengths. Together, these results position RMM as a scalable direction for input-adaptive inference-time optimization.

Transformer-based language models are known to sometimes generalize to sequences longer than seen during training, but we lack a precise characterization of which tasks admit length generalization. It is not even known which regular languages transformers length-generalize on — and this is a foundational class of languages. Our contributions are to establish the first complete characterization of which regular languages transformers length-generalize on and provide a decision algorithm running in polynomial time in the size of the language's syntactic monoid. These results rely on an effective characterization of the regular languages in C-RASP, a recently-established formalism that expresses which languages transformers length-generalize on. This characterization is challenging because classical tools like Krohn-Rhodes decomposition theory for finite semigroups are insufficient for C-RASP. Firstly, the basic building blocks of Krohn-Rhodes theory — flip-flop and simple groups — are not expressible in C-RASP. Secondly, the basic building block of C-RASP (unbounded counting) is not expressible by the finite semigroups of Krohn-Rhodes theory. Thus, length generalization on regular languages is controlled by an algebraic property that is invisible to classical finite decomposition theory. We generalize classical decomposition theory from finite semigroups to the infinite additive group on the integers, allowing us to characterize C-RASP in terms of iterated wreath products of the integers and derive a provable polynomial-time decision algorithm for regular language membership. Experiments across a broad test suite of regular languages confirm that our theory captures transformers' length-generalization behavior more accurately than existing classifications.

In this work, we introduce DMDIntel which uses dynamic mode decomposition (DMD) to make the predictions made by LLMs in a classification task interpretable. It develops an input attribution pipeline, that first decomposes the hidden states of an LLM into prominent patterns, also known as modes, and then associates ranks to the input tokens based on the projection values on those modes. Rigorous experiments across three datasets and three model families consistently show that the ranked attribution of input tokens obtained using DMDIntel by far outperforms state-of-the-art techniques such as principal component analysis, integrated gradients and SHAP.

Modern language models are trained on heterogeneous web-scale text corpora. Consequently, studying knowledge and skill acquisition is difficult, as prior exposure to related content is hard to characterize. To address this challenge, we introduce LITTLECURRICULUM, a curated 88B-token pretraining corpus tailored to U.S. elementary school material, explicitly excluding concepts, facts, and vocabulary taught above Grade 5. Training a 5B-parameter LLM from scratch on LITTLECURRICULUM yields LITTLELEARNER, a model with sufficient language competence for open-ended evaluation, yet with clear knowledge and capability boundaries mapped to interpretable curriculum guidelines. We release LITTLECURRICULUM and LITTLELEARNER as a developmentally restricted sandbox to study how models acquire, represent, and use data under a well-defined training scope. We illustrate the sandbox's utility in a first suite of experiments on injecting new knowledge through post-training and in-context learning. These methods let LITTLELEARNER better utilize existing knowledge, but do not raise out-of-scope capabilities. Our findings underscore the value of this controlled environment for future investigations.

We study a large language model (LLM) service in which a provider chooses a per-token price and a default reasoning-token allocation, while a user may accept the default, customize the allocation, or exit. Larger allocations can improve accuracy but increase token cost and latency. We model this interaction as a Stackelberg game and derive the user's unique optimal customized allocation in closed form. For any price, the acceptable defaults form either an empty set or a compact interval. We characterize the provider's optimal default through a three-regime rule, reduce equilibrium computation to a one-dimensional price optimization, and prove the existence of the equilibrium. We further show that defaults affect the implemented reasoning allocation only when users value the convenience of avoiding customization; otherwise, every service-providing outcome implements the user's optimal customized allocation. Experiments with two compact open-weight reasoning models on five mathematics and science benchmarks support the accuracy-token model and show how model and task characteristics determine equilibrium prices, defaults, and reasoning allocations.

Few-shot in-context learning (ICL) with multi-modal large language models (MLLMs) enables task adaptation without parameter updates, but its performance is highly sensitive to the quality and coverage of the selected demonstrations. While unlabeled multi-modal data is abundant, it remains elusive how to exploit them for ICL. We propose MAG (MAnifold-Guided semi-supervised in-context demonstra- tion selection), an efficient framework that leverages unlabeled data to improve multi-modal ICL. MAG formulates demonstration selection as a semi-supervised propagation problem on a multi-modal graph and adopts a two-stage strategy: (i) relevance score propagation identifies a compact set of high-impact unlabeled samples for pseudo-labeling, reducing MLLM inference cost; (ii) multi-modal relevance is used to select the final demonstrations. We show that textual represen- tations are more effective for relevance propagation, while both visual and textual modalities are crucial for high-quality demonstration selection. Experiments on eight multi-modal benchmarks demonstrate that MAG consistently outperforms strong baselines in label-scarce regimes, achieving significant gains with a limited pseudo-labeling budget.

Large language models (LLMs) remain vulnerable to harmful requests and jailbreak attacks. Parameter-efficient safety alignment methods based on prompt tuning typically rely on a single global prompt or externally selected prompt modules. Such static designs struggle to maintain a cross-category safety boundary while generating constructive responses tailored to specific risks and avoiding over-refusal of benign inputs. To address these limitations, we propose HiRoute, an input-adaptive hierarchical prompt-tuning framework that separates category-agnostic safety control from category-specific response guidance. HiRoute first trains a lightweight hierarchical router on representations extracted from a frozen LLM to jointly detect harmful intent and predict multi-label risk scores. It then freezes both the backbone model and the router and uses preference optimization with alternating gradient updates to learn a shared coarse-grained prompt and a set of fine-grained prompt experts as continuous embeddings. At inference time, benign inputs bypass the safety branch, whereas risky inputs are processed using the shared prompt together with a router-weighted mixture of risk-specific prompt experts. Experiments across three instruction-tuned models show that HiRoute achieves high safety rates across multiple safety benchmarks while preserving safe-response helpfulness, reducing over-refusal, and maintaining competitive performance on general-purpose tasks.