HubRouter: A Pluggable Sub-Quadratic Routing Primitive for Hybrid Sequence Models

We introduce HubRouter, a pluggable module that replaces O(n^2) attention layers with O(nM) hub-mediated routing, where M << n is a small number of learned hub tokens. We demonstrate it in two from-scratch architectures: a Jamba-style hybrid and a 12-layer Transformer; retrofit into pretrained models is a tested negative case. HubRouter implements an encode-decode-score-council pipeline: M learned hubs cross-attend to all tokens, tokens project against hubs for routing fingerprints, a score head selects top-k tokens, and a sparse council attends only to the selected subset. We validate HubRouter in three settings. (1) Hub-Jamba yields a nominal 4.2% PPL improvement (200.2 vs 209.0, single seed; possibly within seed noise) and up to ~90x training throughput at sequence length 1024 in matched PyTorch-native baselines; an optimised baseline would narrow this to ~10-15x. (2) Graduated replacement of 25% of Transformer attention layers gives the best perplexity in our matched-budget sweep (268.0 vs 282.4 pure Transformer). (3) Hub-GPT provides strictly causal routing, achieving PPL 211.5 +/- 0.4 over 3 seeds (post council-causal fix); approximately 3 PPL worse than Jamba's 208.5 +/- 0.7, a measurable quality cost for avoiding O(n^2) computation. Post-fix, chunk size C has little effect; the pre-fix chunk-size benefit was an artifact of a bidirectional-council leak we found in adversarial review. A multi-seed hub-count sweep (~105 runs across M=1-32) reveals M=8-14 as the reliably-converging sub-band (4-5/5 seeds); M=6 is rescued to 5/5 by orthogonal regularization, while M>=20 shows increasing seed sensitivity. Companion paper arXiv:2603.20997 (Basu, 2026) defines the routing diagnostic task. Code and scripts will be released.

Transactional Attention: Semantic Sponsorship for KV-Cache Retention

At K=16 tokens (0.4% of a 4K context), every existing KV-cache compression method achieves 0% on credential retrieval. The failure mode is dormant tokens: credentials, API keys, and configuration values that receive near-zero attention but become essential at generation time. Because these tokens lack the statistical signals that eviction policies rely on, no method based on attention scores, reconstruction loss, or learned retention gates retains them. We introduce Transactional Attention (TA), a sponsorship mechanism in which structural anchor patterns (e.g., "key:", "password:") protect adjacent value-bearing tokens from eviction. TA achieves 100% credential retrieval at K=16 where six baselines (H2O, TOVA, SnapKV, StreamingLLM, PyramidKV, DynamicKV) achieve 0%, and sustains 100% accuracy across 200 function-calling trials. TA-Fast, an attention-free variant, reduces memory overhead by 52% and is compatible with SDPA and FlashAttention. TA is orthogonal to existing compression methods and adds less than 1% latency overhead.

Accelerated Dopant Screening in Oxide Semiconductors via Multi-Fidelity Contextual Bandits and a Three-Tier DFT Validation Funnel

Band gap engineering of oxide semiconductors through doping is critical for photocatalysis and optoelectronics, yet the combinatorial space of dopant elements, substitution sites, and co-doping combinations far exceeds typical density functional theory (DFT) budgets. We screen doped candidates across five oxide hosts (ZnO, TiO2, SrTiO3, SnO2, MgO), culminating in a 529-candidate ZnO co-doping campaign, and identify Cu-containing co-doped ZnO systems as consistently achieving visible-light-range band gaps (1.0-1.8 eV), with Y2Cu2 co-doped ZnO as the optimal candidate (1.84 eV). A three-tier validation funnel (PBE, PBE+U, ionic relaxation) reveals that no single level of theory suffices: V-doped ZnO shifts from near-metallic to wide-gap upon Hubbard U correction, while Cu-doped SrTiO3 enters the visible-light window only after correcting for d-electron localization. To make this screening tractable, we introduce a multi-fidelity screening strategy that replaces 81% of DFT evaluations with computationally inexpensive surrogate predictions, reducing a 529-candidate closed-loop Quantum ESPRESSO campaign from an estimated 440 to 62 CPU-hours while finding the global optimum in 100% of 50 independent trials (p = 5.0e-8 versus random screening, Wilcoxon signed-rank). Cross-host analysis of the dopant-host interaction matrix reveals that dopant performance is governed by just two latent chemical dimensions, enabling prediction of rankings in unseen hosts. All 583 DFT calculations, screening code, and stability proofs are released as an open benchmark.

The Coordinate System Problem in Persistent Structural Memory for Neural Architectures

We introduce the Dual-View Pheromone Pathway Network (DPPN), an architecture that routes sparse attention through a persistent pheromone field over latent slot transitions, and use it to discover two independent requirements for persistent structural memory in neural networks. Through five progressively refined experiments using up to 10 seeds per condition across 5 model variants and 4 transfer targets, we identify a core principle: persistent memory requires a stable coordinate system, and any coordinate system learned jointly with the model is inherently unstable. We characterize three obstacles -- pheromone saturation, surface-structure entanglement, and coordinate incompatibility -- and show that neither contrastive updates, multi-source distillation, Hungarian alignment, nor semantic decomposition resolves the instability when embeddings are learned from scratch. Fixed random Fourier features provide extrinsic coordinates that are stable, structure-blind, and informative, but coordinate stability alone is insufficient: routing-bias pheromone does not transfer (10 seeds, p>0.05). DPPN outperforms transformer and random sparse baselines for within-task learning (AULC 0.700 vs 0.680 vs 0.670). Replacing routing bias with learning-rate modulation eliminates negative transfer: warm pheromone as a learning-rate prior achieves +0.003 on same-family tasks (17 seeds, p<0.05) while never reducing performance. A structure completion function over extrinsic coordinates produces +0.006 same-family bonus beyond regularization, showing the catch-22 between stability and informativeness is partially permeable to learned functions. The contribution is two independent requirements for persistent structural memory: (a) coordinate stability and (b) graceful transfer mechanism.

When AI Shows Its Work, Is It Actually Working? Step-Level Evaluation Reveals Frontier Language Models Frequently Bypass Their Own Reasoning

Language models increasingly "show their work" by writing step-by-step reasoning before answering. But are these reasoning steps genuinely used, or decorative narratives generated after the model has already decided? Consider: a medical AI writes "The patient's eosinophilia and livedo reticularis following catheterization suggest cholesterol embolization syndrome. Answer: B." If we remove the eosinophilia observation, does the diagnosis change? For most frontier models, the answer is no - the step was decorative. We introduce step-level evaluation: remove one reasoning sentence at a time and check whether the answer changes. This simple test requires only API access -- no model weights -- and costs approximately $1-2 per model per task. Testing 10 frontier models (GPT-5.4, Claude Opus, DeepSeek-V3.2, MiniMax-M2.5, Kimi-K2.5, and others) across sentiment, mathematics, topic classification, and medical QA (N=376-500 each), the majority produce decorative reasoning: removing any step changes the answer less than 17% of the time, while any single step alone recovers the answer. This holds even on math, where smaller models (0.8-8B) show genuine step dependence (55% necessity). Two models break the pattern: MiniMax-M2.5 on sentiment (37% necessity) and Kimi-K2.5 on topic classification (39%) - but both shortcut other tasks. Faithfulness is model-specific and task-specific. We also discover "output rigidity": on the same medical questions, Claude Opus writes 11 diagnostic steps while GPT-OSS-120B outputs a single token. Mechanistic analysis (attention patterns) confirms that CoT attention drops more in late layers for decorative tasks (33%) than faithful ones (20%). Implications: step-by-step explanations from frontier models are largely decorative, per-model per-domain evaluation is essential, and training objectives - not scale - determine whether reasoning is genuine.

When Does Content-Based Routing Work? Representation Requirements for Selective Attention in Hybrid Sequence Models

We identify a routing paradox in hybrid recurrent-attention architectures: content-based routing - deciding which tokens deserve expensive attention - requires exactly the pairwise computation that routing is designed to avoid. Through 20+ controlled experiments across three tasks (a synthetic diagnostic, the Zoology MQAR benchmark, and HotpotQA), we map the routing landscape exhaustively. One layer of softmax attention creates a latent ~34-dimensional subspace enabling 98.4% routing precision; zero layers yield 1.2%. This subspace is invisible to cosine similarity, destroyed by random projections (98.4% to 2.6%), and cannot be created by contrastive pretraining - proving attention's role is writing pairwise match results into representations, not merely computing them. Twelve alternative mechanisms all cluster at 15-29%. Non-learned indices (Bloom filter: 90.9%; BM25 on HotpotQA: 82.7%) bypass the bottleneck entirely. The result is a sharp two-regime hierarchy with an empty middle ground. These findings provide the mechanistic explanation for the empirical observation that recurrent models fail at associative recall, and reframe attention as a representation constructor rather than merely a computation mechanism.

Structural Sensitivity in Compressed Transformers: Error Propagation, Lyapunov Stability, and Formally Verified Bounds

A single matrix out of 468 in GPT-2 Small can increase perplexity by 20,000x when compressed, revealing that transformer compression sensitivity spans five orders of magnitude. We map this sensitivity landscape across five architectures (117M-8B parameters), finding a consistent hierarchy: early-layer MLP up-projections are catastrophically sensitive while value projections compress nearly for free. This hierarchy is stable across compression levels, evaluation scales (2K-51K tokens), and datasets (WikiText-103, C4). Using Lyapunov stability theory, we show that residual connections contract compression errors by growing the hidden state faster than the error. Error contraction is necessary but not sufficient for compression tolerance: architecture-specific redundancy plays an equally important role, as demonstrated by the hybrid LFM2-2.6B degrading only 7x despite higher amplification than the fully-contracting GPT-2 Small (120x). Ten machine-checked Lean 4 theorems formalize per-matrix error bounds with no sorry markers; all bounds produce zero violations across 14,040+ configurations. We validate with downstream task evaluation (HellaSwag, ARC-Easy, Winogrande), activation-aware pruning on two architectures, and a Compression Fragility Index that rank-orders model robustness.

ICE: Intervention-Consistent Explanation Evaluation with Statistical Grounding for LLMs

Evaluating whether explanations faithfully reflect a model's reasoning remains an open problem. Existing benchmarks use single interventions without statistical testing, making it impossible to distinguish genuine faithfulness from chance-level performance. We introduce ICE (Intervention-Consistent Explanation), a framework that compares explanations against matched random baselines via randomization tests under multiple intervention operators, yielding win rates with confidence intervals. Evaluating 7 LLMs across 4 English tasks, 6 non-English languages, and 2 attribution methods, we find that faithfulness is operator-dependent: operator gaps reach up to 44 percentage points, with deletion typically inflating estimates on short text but the pattern reversing on long text, suggesting that faithfulness should be interpreted comparatively across intervention operators rather than as a single score. Randomized baselines reveal anti-faithfulness in one-third of configurations, and faithfulness shows zero correlation with human plausibility (|r| < 0.04). Multilingual evaluation reveals dramatic model-language interactions not explained by tokenization alone. We release the ICE framework and ICEBench benchmark.

When Names Change Verdicts: Intervention Consistency Reveals Systematic Bias in LLM Decision-Making

Large language models (LLMs) are increasingly used for high-stakes decisions, yet their susceptibility to spurious features remains poorly characterized. We introduce ICE-Guard, a framework applying intervention consistency testing to detect three types of spurious feature reliance: demographic (name/race swaps), authority (credential/prestige swaps), and framing (positive/negative restatements). Across 3,000 vignettes spanning 10 high-stakes domains, we evaluate 11 LLMs from 8 families and find that (1) authority bias (mean 5.8%) and framing bias (5.0%) substantially exceed demographic bias (2.2%), challenging the field's narrow focus on demographics; (2) bias concentrates in specific domains -- finance shows 22.6% authority bias while criminal justice shows only 2.8%; (3) structured decomposition, where the LLM extracts features and a deterministic rubric decides, reduces flip rates by up to 100% (median 49% across 9 models). We demonstrate an ICE-guided detect-diagnose-mitigate-verify loop achieving cumulative 78% bias reduction via iterative prompt patching. Validation against real COMPAS recidivism data shows COMPAS-derived flip rates exceed pooled synthetic rates, suggesting our benchmark provides a conservative estimate of real-world bias. Code and data are publicly available.

Budget-Sensitive Discovery Scoring: A Formally Verified Framework for Evaluating AI-Guided Scientific Selection

Scientific discovery increasingly relies on AI systems to select candidates for expensive experimental validation, yet no principled, budget-aware evaluation framework exists for comparing selection strategies -- a gap intensified by large language models (LLMs), which generate plausible scientific proposals without reliable downstream evaluation. We introduce the Budget-Sensitive Discovery Score (BSDS), a formally verified metric -- 20 theorems machine-checked by the Lean 4 proof assistant -- that jointly penalizes false discoveries (lambda-weighted FDR) and excessive abstention (gamma-weighted coverage gap) at each budget level. Its budget-averaged form, the Discovery Quality Score (DQS), provides a single summary statistic that no proposer can inflate by performing well at a cherry-picked budget. As a case study, we apply BSDS/DQS to: do LLMs add marginal value to an existing ML pipeline for drug discovery candidate selection? We evaluate 39 proposers -- 11 mechanistic variants, 14 zero-shot LLM configurations, and 14 few-shot LLM configurations -- using SMILES representations on MoleculeNet HIV (41,127 compounds, 3.5% active, 1,000 bootstrap replicates) under both random and scaffold splits. Three findings emerge. First, the simple RF-based Greedy-ML proposer achieves the best DQS (-0.046), outperforming all MLP variants and LLM configurations. Second, no LLM surpasses the Greedy-ML baseline under zero-shot or few-shot evaluation on HIV or Tox21, establishing that LLMs provide no marginal value over an existing trained classifier. Third, the proposer hierarchy generalizes across five MoleculeNet benchmarks spanning 0.18%-46.2% prevalence, a non-drug AV safety domain, and a 9x7 grid of penalty parameters (tau >= 0.636, mean tau = 0.863). The framework applies to any setting where candidates are selected under budget constraints and asymmetric error costs.