Papers

We present LARA (Lightweight Additive Residual Adaptation), a method for efficient adaptation that operates in the residual stream of a frozen model rather than in its weights. Where LoRA adds an update of low rank to weight matrices, LARA reads the hidden state at a small set of layers and adds a correction of low rank back to the residual stream, leaving all base weights untouched. On a code fine-tuning task and on preference optimization (DPO), LARA matches LoRA at equal parameter counts. Because adaptation is a frozen base plus a residual, LARA exposes a scale {\gamma}, applied at inference, that interpolates smoothly between base and adapted behavior, a form of graded control that adaptation in weight space does not offer. Finally, because each behavior is a small residual module over a shared frozen base, many behaviors can be held resident at once and routed automatically per token. We place seven behaviors, six fine-tuned and one optimized for preference, on one frozen 1.5B model for roughly 33 MB of overhead, against one full model for each behavior. Because the base is untouched, behaviors are trained separately and selected per token rather than loaded on demand, which suits hosting many behaviors, and adding new ones, on a single model on a device.

Recent work has shown that classifying large language models (LLMs)' responses can be distinguished by modeling token embeddings as trajectories of a black-box dynamical system (DS) and comparing prediction residuals of two DSs. Despite the empirical success of this dynamical approach, a theoretical understanding of why it works, how well it scales as a function of the token sequence, and when it transfers across embedding models remains lacking. We address these questions by formalizing the classification task as a binary hypothesis test between two stochastic linear DSs. We show that the total variation distance between the stationary marginal distributions of the two DSs can be arbitrarily small even when the dynamics differ substantially, which provides a fundamental accuracy floor for any classifier that ignores token dynamics. We then show that the misclassification probability of DS-based classification decays exponentially in the sequence length $L$, with the decay governed by a dynamical discriminability quantity $\delta^2$ that captures the spectral distance between the two DSs. We also characterize cross-embedding generalization by introducing an approximate intertwining condition between embedding models and establishing a lower bound on the transferable discriminability in terms of the intertwining map's smallest singular value. Together, these results explain the empirical performance of DS-based classification and motivate further investigation into using DS theory to analyze AI systems, in contrast to the more common approach of using AI to model dynamical systems.

Enterprise AI programmes stall at a rate that is widely quoted and poorly explained. This paper measures the mechanism. Six document-heavy workflows of the kind performed daily in regulated financial services were run across four model families and three tool configurations, three times each, producing 5,093 scored output elements across 72 configurations. Each configuration was assessed twice: against a demonstration bar, being a single correct run on a single case, and against a production bar requiring sustained accuracy, reproducibility across repeats, verifiable attribution, and a confidence signal that carries information. 57 of 72 configurations cleared the demonstration bar and 32 cleared the production bar, a survival rate of 56.1%. The paper then computes the review burden each configuration imposes, estimated out of sample rather than with hindsight. A tool that states no confidence requires review of 100% of its output, because it offers a reviewer no basis for triage. Requiring the tool to cite its sources and state a confidence reduces that to 49% while holding the residual error tolerance in 17 of 20 configurations. Adding a self-verification pass costs 2.3 times the latency of the plain configuration, reaches 44%, and is the only configuration that fails to hold the error tolerance. The practical implication is that the value of an AI workflow is set less by how often it is right than by how much of it a human must still check, and that the second property is measurable and rarely measured.

Automated driving systems (ADSs) are becoming ubiquitous. Future Software Defined Vehicles (SDVs) may be able to run multiple ADSs, both native and aftermarket such as Comma.ai's Openpilot. Monitoring systems to independently verify which automated driving system is active are important for safety monitoring, regulatory compliance, insurance assessment, and anomaly detection. In this paper, we first evaluate the effectiveness of three sequence-based classification models: Gated Recurrent Units (GRU), Long Short-Term Memory (LSTM) networks, and a Transformer encoder model for identifying Level 2 automated driving systems using vehicle telematics data alone: Comma Openpilot, Tesla Autopilot, and Cadillac Super Cruise, along with manual driving. All three models achieve strong clean-data performance with macro F1-scores of 0.92 (GRU), 0.90 (LSTM), and 0.93 (Transformer encoder model) when trained on clean data; threat-matched training yields 0.904-0.916 macro F1 with only a modest clean-data penalty. Second, we introduce a modular robustness evaluation framework that simulates realistic telematics degradation through five corruption families at five severity levels (L1-L5). Continuous channels are perturbed using additive white Gaussian noise with cumulative drift, correlated cross-channel noise, and temporal jitter. Binary event signals are subjected to burst loss, delayed transitions, spurious toggles and cross-feature inconsistencies inspired by communication errors. Robustness is measured using macro-F1, which gives equal weight to each class and is suitable for imbalanced multiclass evaluation. Our evaluation reveals a sharp failure-mode split: event-level corruptions reduce macro-F1 only slightly (greater than equal to 0.87 at L5), while temporal jitter collapses macro-F1 to 0.44-0.50 across GRU, LSTM, and Transformer encoder model.

Recent advances in large language models (LLMs) have enabled search agents to autonomously tackle complex tasks across extended search and reasoning horizons. However, training effective search agents remains challenging due to the lack of scalable and long-horizon tasks, and the difficulty of evaluating and correcting intermediate reasoning and tool-use behaviors. We introduce SearchArt, a scalable framework for training long-horizon search agents through verification-driven task synthesis and a multi-stage post-training pipeline. SearchArt constructs large-scale datasets for complex search-, research- and user-oriented tasks by synthesizing diverse information-seeking QA pairs and corresponding search trajectories from web documents and automatically generated evidence graphs. To ensure the reliability of the synthesized data, we design a verification pipeline that jointly evaluates QA consistency, trajectory quality, and the relevance of retrieved evidence. The verified trajectories are subsequently used in a multi-stage training process comprising supervised fine-tuning and reinforcement learning-based policy optimization. Search agents trained with SearchArt exhibit adaptive search planning, iterative evidence aggregation, and complex reasoning over extended interaction horizons. Experimental results demonstrate that, with only (Qwen3.5-) 27B parameters, SearchArt scores 74.39 on BrowseComp-ZH, 70.06 on BrowseComp, and 52.55 on Deepresearch-bench, matching or surpassing frontier closed-source agents on both deepsearch and deepresearch benchmarks.

Pretrained molecular encoders are commonly evaluated through downstream prediction, but predictive accuracy alone does not establish that a learned representation captures reproducible scientific structure, adds information beyond strong conventional baselines, or transfers out of distribution. We present a reliability-aware audit of generic molecular representations for human olfaction across four distinct claims: global perceptual geometry, incremental predictive value beyond chemistry, cross-dataset replication, and mixture transfer to unseen components. Using the Keller-Vosshall and Bierling single-molecule rating datasets and the Ma binary-mixture dataset, we compare MoLFormer and ChemBERTa against RDKit descriptors and Morgan fingerprints under identity-controlled and matched evaluations. Human three-attribute rating geometry, based on intensity, pleasantness, and familiarity, is reproducible across participant splits (median RSA 0.743 and 0.855), whereas model-human alignment is substantially weaker (RSA 0.019-0.158). Learned embeddings do not consistently outperform conventional representations in global alignment, and MoLFormer provides no clear incremental predictive value beyond a combined RDKit-Morgan baseline in either single-molecule dataset. Human geometry shows positive but incomplete agreement across 63 shared molecules (RSA 0.331; 95% bootstrap interval [0.204, 0.507]). Under one strict unseen-component mixture split, incremental effects are outcome- and representation-dependent, with all intervals crossing zero. These results establish empirical boundaries for the evaluated generic molecular encoders and motivate a broader evaluation principle: representation quality in scientific domains should be assessed separately for target reliability, structural alignment, incremental information, replication, and out-of-distribution transfer.

Music Source Separation (MSS), the task of recovering individual sound components (stems) from a polyphonic mixture, is central to applications ranging from karaoke and remixing to audio restoration and content production. The separation quality depends on engineering decisions across the entire pipeline: model choice, training data preparation and augmentation, loss function and metrics choice, training configuration, validation, and post-processing. This paper presents MSST (Music-Source-Separation-Training) - a universal open-source framework for MSS tasks, which unifies training, validation, and inference for a broad range of modern demixing model families under a single, configuration-driven interface. The framework supports various model architectures, data preprocessing and augmentations, multiple loss functions and evaluation metrics, which helps with fast iterations and ablation studies. Additionally, the framework supports a range of practical techniques that improve separation quality, such as sliding-window inference with cross-fading, test-time augmentation, model ensembling, and fine-tuning via Low-Rank Adaptation (LORA). Our ablation studies demonstrate improvements of MSS using the above techniques. By consolidating these components into a reproducible, YAML-configurable framework, MSST lowers the barrier to systematic experimentation and enables rapid iteration from idea to verifiable result.

When can additional low-bit residual computation replace missing numerical precision for a fixed input-output map? We model a quantized residual system over a fixed horizon as a pure schedule selecting fields from a declared low-bit operation library, and use relaxed controls to characterize its infinite-depth limit. The distance from the target to the closed relaxed reachable set is the exact structural floor: no increase in depth can remove it for that library. Pure schedules approach the relaxed class at rate $O(D^{-1})$ under bounded-variation time dependence and $O(D^{-\vartheta}+D^{-1})$ under Holder dependence of exponent $\vartheta$. Execution arithmetic can reverse this conclusion: full-state write-back introduces a $D\rho_z$ penalty and can freeze residual updates, whereas increment error feedback replaces this growth by a bounded carry term and obeys an exact common-lattice conservation law. A fixed-teacher converse makes this rate sharp: for coherent depth-$L$ first-order high-precision comparators, accuracy matching requires $D=\Theta(L)$. Learned codebooks add a metadata resource, while state-dependent routing introduces hybrid event conditions. Verified primal and dual bounds yield feasible, impossible, or unresolved decisions before training. Companion software implements the workflow, and Lean 4 machine-checks the exact discrete core. Depth replaces precision only relative to a declared library, horizon, execution semantics, and routing model.

Conventional CAPTCHAs pose puzzles that modern AI systems increasingly solve, while behavioral and cryptographic-attestation defenses carry privacy or enrollment costs. We investigate an orthogonal signal: the physical timing behavior of a client's GPU under a controlled WebGL rendering workload. Unlike WebGL fingerprinting, which hashes pixel output into a static device identifier, we measure render-timing dynamics to classify rather than identify, leaking no persistent identifier. We characterize the in-the-wild adversary with a 12-hour passive deployment (207 unsolicited requests; 86% automated; 85% of browser-claiming clients failed HTTP header-consistency checks). We then collect labeled GPU-timing samples through a single public endpoint exercised by real browsers (positive class, 13 distinct GPUs) and by keyed headless automation across a render-backend matrix (negative class). Software-rendered automation – empirically the dominant real-world adversary – separates from genuine GPUs by roughly 5x in mean render time. On a confound-controlled comparison (identical GPU family and browser engine, differing only in headless vs. interactive execution), headless automation on real hardware still exhibits a distinct timing signature, separating from human samples by 75-106% on frame jitter, timer-quantization ratio, and coefficient of variation. We report these as pilot-scale findings on a single GPU architecture and outline the cross-architecture collection required to establish generalization.

Constrained learning has been increasingly applied to various domains to ensure explicit feasibility requirements due to fairness, safety, robustness, regularization, and physics or logic constraints. Understanding how training samples influence the solution (e.g., learned parameters) of constrained learning is crucial for interpretability and robustness. The classical influence function may become unreliable in constrained settings: data perturbations can reshape both the objective and the feasible region, leading to estimates that violate feasibility. In response, we propose the Directional Influence Function (DIF), a new estimator that explicitly incorporates the constraints into influence estimation. DIF formulates the optimality conditions of constrained learning as a variational inequality (VI) and analyzes how perturbing training data affects this VI. We validate DIF in constrained linear regression and demonstrate that it recovers leave-one-out retraining results, whereas IF and penalty-based IF exhibit significant bias. We further apply DIF to fairness-constrained CNNs, where DIF accurately predicts test loss changes under data removal and aligns closely with actual retraining. Our results establish DIF as an efficient and reliable tool for data attribution in constrained learning.

Vascular segmentation is a standard procedure for clinical diagnosis, yet the specific visual features determining model decisions remain poorly understood. This paper investigates the visual cues Convolutional Neural Networks (CNNs) use to segment blood vessels across two distinct imaging domains: fluorescence microscopy and retinal fundus photography. We employ a series of experiments to quantify the influence of shape, texture, and receptive field on segmentation performance. First, we isolate texture and intensity by evaluating performance on patches subjected to pixel shuffling and normalization. Second, we assess global shape relevance by training models on sparse contours and centerlines. Lastly, we quantify the required spatial context by systematically varying the network's theoretical and effective receptive fields. Within the scope of the evaluated datasets, we found that pixel intensity is more relevant than texture, though networks maintain surprisingly high accuracy even when both cues are removed. Furthermore, CNNs struggle to extrapolate full vessel geometry from shape cues alone, typically relying on a relatively small effective receptive field of around 20 pixels, though global context provides a modest benefit for fundus images. While specific to the modalities studied, this methodology offers a quantitative foundation to audit and refine deep learning systems in vascular imaging.

Bitcoin price prediction on sub-daily timescales is a hard open problem in computational finance. Bitcoin exhibits fat-tailed returns, non-stationary dynamics, and a price discovery process influenced by social discourse on Reddit and Twitter. Conventional approaches fuse OHLCV technical features with sentiment via static concatenation, applying identical fusion weights regardless of market state. This is inconsistent with the behavioural finance literature, which shows that retail sentiment is most predictive during volatile periods and noisy during calm ones. This paper proposes Regime-Aware Multi-Modal Learning (RAML), which conditions fusion of sentiment and price features on a dynamically detected binary market regime. Rolling 24-hour volatility partitions observations into stable and volatile regimes; a learnable sigmoid gate adjusts the weight of the sentiment embedding relative to the price embedding, trusting sentiment more during volatility and price dynamics more during stable phases. The system is evaluated on 3,491 hourly observations (July 2024-September 2025), combining Bitcoin OHLCV data with Reddit /r/Bitcoin FinBERT sentiment. Four models are compared - price-only BiLSTM, sentiment-only classifier, static-concatenation BiLSTM, and RAML - across 3-hour and 6-hour horizons, with an ablation study isolating the sentiment branch, regime detection, and adaptive fusion. RAML achieves macro-F1 of 0.5474 (3h) and 0.5513 (6h), with the highest AUC at 3 hours (0.5084), indicating better calibration. Ablation confirms every component is necessary, and replacing adaptive weighting with concatenation causes recall collapse at 6 hours (F1: 0.14). These results establish regime-conditioned adaptive fusion as a necessary design principle for multi-modal financial forecasting.

Group Relative Policy Optimization (GRPO) is the dominant reinforcement learning algorithm for training reasoning capabilities in large language models, notably adopted by DeepSeek-R1. The recent improvement Dr. GRPO (COLM 2025) identifies the response-level length bias caused by per-trajectory length normalization in GRPO and proposes removing this normalization, claiming the resulting optimizer is "unbiased." We show that this claim is incomplete. Specifically, we establish an impossibility theorem: under the standard outcome reward + GRPO setting, no length-based weighting scheme can simultaneously achieve the following two properties. (P1) Gradient unbiasedness: the gradient estimator is an unbiased estimate of the true policy gradient. (P2) Length invariance: each trajectory's effective contribution to the gradient is independent of its token length. GRPO approximately satisfies P2 but violates P1; Dr. GRPO satisfies P1 but violates P2. We characterize the complete tradeoff spectrum via the parametric family f_alpha(L) = L^{alpha - 1}, where alpha = 0 recovers GRPO, alpha = 1 recovers Dr. GRPO, and provide quantitative analysis showing that Dr. GRPO's length bias can cause longer trajectories to dominate gradient updates by a factor proportional to the length ratio. Our results reveal that neither algorithm is universally "done right"; they occupy opposite ends of a fundamental and unavoidable tradeoff.

Language generation in the limit is an elegant model introduced by Kleinberg and Mullainathan [KM24] to formally study language generation by an algorithm that learns solely based on example strings. In this model, an algorithm is said to correctly generate from a language if it never makes an error after some finite time. In contrast, even sophisticated language models are known to regularly hallucinate in practice. In this paper, we initiate the study of language generation in the limit with (infinite) hallucination, i.e., the algorithm may generate incorrect strings infinitely often, but the errors occur at a limited rate (possibly even with 0-measure). We first show that hallucination, even at rate 0, makes generation in the limit strictly more powerful: there are language collections that cannot be generated with finite error but can be generated with infinite error, even when errors occur on a 0-measure set of time-steps. Furthermore, while all countable collections are generatable with finite error, we show a strict hierarchy of (uncountable) language collections characterized by the hallucination rate. This hierarchy extends to breadth, the fraction of the target language generated. While all countable collections can attain the optimal breadth of 1/2 [KW26b], we show strict separation at every breadth and hallucination rate. Finally, we study generation in the limit without repetition, where the algorithm may not repeat strings. This lets us compare the sets of correct and incorrect strings generated, rather than the fractions of correct and incorrect time-steps. Once again, we demonstrate a strict hierarchy at every hallucination rate and breadth. Taken together, these results reveal rich structure in language collections generatable in the limit with hallucination and establish hallucination rate as an important parameter in the theoretical study of language generation.

We study the generative capabilities of Boltzmann machines to recover systems governed by the majority rule under critical conditions. To this end, we train deep belief networks (DBNs) with different configurations, where the first layer can use Gaussian visible units with more than two states (i.e., non-binary units). We then allow the DBN to "dream" samples conditioned on visible units that we keep fixed, and we measure the deviation of this dreamed system from the real one. We also corroborate, using a discrete thermometer based on a convolutional network, that the reconstructions remain in a critical state. Across several training sessions with different architectures, we show that, despite the complexity of the problem, the DBN can recover samples that remain critical even under input noise, with a gradual degradation of physical observables relative to the original sample.

Mixed continuous–categorical data pose a representation problem for continuous generative models. Flow Matching and Gaussian diffusion operate in Euclidean spaces, whereas categorical laws lie on probability simplices and may be highly imbalanced. We study a logit-coordinate framework that encodes categorical variables as smoothed natural parameters and combines them with transformed numerical variables. This yields common formulations of Logit Flow Matching and Logit Diffusion. We introduce a mixed-distribution discrepancy separating categorical marginal error from conditional continuous Wasserstein error, and derive stability bounds and imbalance-aware nonparametric rates linking vector-field or drift error to decoded mixed-distribution error. Controlled simulations show that scaled-logit coordinates improve or match one-hot coordinates, especially under severe rare-cell imbalance. Across four real-data benchmarks and ten splits per dataset, Logit FM improves the primary distributional metrics on three datasets and is comparable on Churn2; Block-Conditional Logit FM consistently improves the flat model; and Logit Diffusion generally improves over or matches One-Hot Diffusion.

Modern deep neural networks are potent catalysts for scientific and industrial impact, yet excessive parameter counts impede deployment in low-compute settings such as hospital equipment and energy infrastructure. Predominant knowledge distillation (KD) methods favor replication: smaller students mimic teacher output logits, yet empirically yield low task performance, hamper convergence, and act merely as regularization rather than substantive knowledge transfer. We propose Saddle Point Recruitment for Knowledge Distillation (SPRKD), reframing distillation from replication to employing teachers as optimization-curvature and domain proxies, characterizing saddle points as regions of strong further-descent potential via embedding and basin-fractal properties. Using Hessian eigenvalue spectral density (ESD), SPRKD identifies low-loss saddle regions for student re-exploration; weak-teacher ensembles are aggregated into an Approximated Saddle Region (ASR), re-parameterized into the student via Transfer Learning by Injection, and approached with exponentially decaying Euclidean transformations, Negative Hessian Eigensteps, and Gaussian perturbations. On malaria blood smear classification with a 6,430-parameter CNN distilled from a weak 25,546-parameter teacher, SPRKD reaches 94.8% validation accuracy, outperforming Response KD by 24.70 percentage points (McNemar p = 6.3e-87) and matching scratch-trained baselines of the same architecture to statistical equivalence (p = 1.0). Across MNIST, CIFAR-100, and TinyImageNet, SPRKD exceeds scratch-trained baselines by up to 8 percentage points on preliminary benchmarks. Hessian ESD and 2-D loss landscape analysis show convergence to wider minima with substantially smaller Hessian trace and spectral radius than Response KD and control students, indicating smoother descent and greater noise robustness.

Named Entity Recognition (NER) for low-resource languages such as Marathi remains a challenging task due to limited annotated resources and linguistic complexity. Although recent Large Language Models (LLMs) have demonstrated strong performance across a wide range of natural language processing tasks, their effectiveness for language-specific NER in low-resource settings remains uncertain. In this study, we fine-tune MahaBERT-v2 on different variants of the MahaNER dataset and systematically compare the performance of these models with an existing MahaNER baseline and prominent general-purpose LLMs, including Gemini, LLaMA-3.3-70B, and Gemma models. All models are evaluated on a Marathi NER test dataset using standard metrics of precision, recall, and F1-score. The experimental results show that the fine-tuned MahaBERT-based models consistently outperform both the baseline and all evaluated LLMs, with the fine-tuned models achieving F1-scores ranging from 0.88 to 0.91, surpassing the existing MahaNER model (0.8843) and significantly exceeding the performance of LLM-based approaches, whose F1-scores range from 0.57 to 0.69. These findings demonstrate that task-specific, language-focused models trained on domain-relevant data remain more effective than general-purpose LLMs for Marathi NER, highlighting the continued importance of specialized architectures for low-resource language processing.

Graph compression reduces the computational cost of graph learning, but its effect on signal propagation remains largely underexplored. Existing work evaluates compression through downstream task performance or structural preservation, neither of which directly captures how propagation dynamics change after compression. We study two fundamental compression paradigms, coarsening and sparsification, and ask whether they preserve the propagation behavior of the original graph. Across five datasets, varying compression rates, and propagation depths, we measure signal behavior through three complementary metrics. Our results reveal a consistent tension between the two compression families. Sparsification retains higher signal diversity and mitigates oversmoothing, but its propagation trajectory progressively diverges from that of the original graph. Coarsening more faithfully preserves propagation behavior, but at the cost of stronger smoothing and rank collapse. These findings demonstrate that two propagation-centric objectives, preserving signal diversity and preserving propagation fidelity, are distinct and empirically at odds under graph compression, highlighting the need for evaluation protocols that jointly consider both dimensions. The code and results are available at: https://github.com/KawshikBanerjee/Compression-Propagation-Duality

Neural operators provide data-driven mappings for modeling dynamical systems. Extending them to families of systems typically requires explicit conditioning variables such as physical parameters, geometries, or boundary conditions. In many real-world settings, these quantities are unobserved. Here, we formulate neural operator discovery (NOD) as the problem of learning both shared solution operators and system-specific variation directly from heterogeneous trajectories without access to labeled governing factors. We introduce a factorized latent-conditioning formulation that jointly learns a neural operator and a low-dimensional latent representation through factorized prediction, trajectory-decoupled sampling, and dimension selection. Across diverse systems, the learned latent representation captures the intrinsic dimensionality of system variation and organizes system instances in a smooth and approximately invertible latent structure aligned with the underlying governing factors. This organization enables generalization to previously unseen system instances, including zero-shot extrapolation across regimes and stable long-horizon prediction. These results establish an interpretable paradigm for operator learning in the absence of explicit factor supervision.

We revisit the regret loss framework introduced in Park et al. (2025), which uses decision-theoretic regret as a direct loss function for training models to make better decisions, through the lens of probability-simplex policies. Our first result shows that a single-layer self-attention model trained with regret loss admits a stationary point whose forward-pass exactly matches smoothed fictitious play with the appropriate stepsize that ensures no-regret behavior-i.e., for any given policy input, the model outputs the same update that smoothed fictitious play would produce. In parallel, we also newly introduce a swap-regret loss function, which extends the regret-loss framework beyond external regret and enables models to directly optimize for swap-deviation robustness. We further show that this swap-regret loss admits a stationary point whose forward pass implements the corresponding swap-regret update induced by classical Blum-Mansour no-pass implementation algorithm, with each head implementing an external-regret update via smoothed fictitious play. Together, these results show that regret-trained attention can realize differentiable mechanisms whose deployment induces equilibrium behavior in games: external-regret dynamics lead to coarse correlated equilibrium, while swap-regret dynamics lead to correlated equilibrium. Thus, regret-based objectives steer minimal attention architectures toward online-learning dynamics with game-theoretic guarantees, without supervised traces of those algorithms.

Creating a reusable tool is an investment: an agent pays a fixed cost now in exchange for the potential of future reuse. Therefore, a user should prefer an agent that creates a small number of highly reusable tools, rather than many one-offs. We introduce a paired benchmark that tests whether LLM agents exhibit conscious allocation behavior under a fixed budget in two contexts: an abstract text-based formulation and a code-construction task. We find that every frontier model we test—Claude Haiku, Claude Opus, GPT-5.4-mini, and GPT-5.6 Sol—acts near-optimally in the abstract framing but fails to transfer this ability to script-writing. Through further experiments, we identify the particular failure modes for each model. Notably, the first three models fail even when the scripts are not evaluated, while GPT-5.6 Sol stays selective under that weaker manipulation and collapses only at full construction. Furthermore, an open-source Qwen model policy-trained for abstract allocation generalizes this ability across held-out lexical variations, but sees no improvement at script allocation. Together, these results establish online tool allocation as a significant capability boundary, even for modern frontier models.

Instruction tuning has become the standard method for adapting large language models to follow human intent, yet existing instruction datasets are dominated by English-language general-knowledge tasks and lack coverage of specialized pedagogical domains. This paper presents IKS-Instruct, a dataset of 24,795 instruction-response pairs for teaching language models to deliver educational content grounded in Indian Knowledge Systems (IKS). The dataset spans seven languages (English, Hindi, Sanskrit, Tamil, Telugu, Kannada, and Malayalam), covers 41 pedagogical techniques from the Vedic oral and mathematical traditions, and is aligned with the Central Board of Secondary Education (CBSE) curriculum for classes 6 through 12. The pairs are derived from six source types: classical text corpora (Bhagavad Gita, Thirukkural, Sangam literature, Vedic texts), curriculum-aligned pedagogical templates, Vedic mathematical sutra demonstrations, bilingual instruction pairs, technique-grounded multi-turn dialogues, and cross-tradition comparative analyses. Quality is assessed through a multi-judge evaluation framework in which independent language models score responses on 12 dimensions including technique fidelity, pedagogical quality, factual accuracy, and IKS cultural depth. Under a uniform five-judge external panel (median aggregation over 1,201 stratified items), the strongest IKS-Instruct fine-tune of a compact 7B model reaches a median judge score of 6.39, within 0.15 of a strong general-purpose reference model (Nemotron-Nano at 6.54) at a fraction of its deployment cost, while the base model without IKS fine-tuning scores near zero on the IKS-specific dimensions. Model quality does not increase monotonically with data curation, a result we report together with the corresponding data-quality gains.

Standard subword tokenization algorithms such as Byte-Pair Encoding (BPE) and SentencePiece are trained predominantly on modern language corpora and produce inefficient segmentations when applied to classical Indian languages. Sanskrit, Tamil, and other classical Indic languages exhibit agglutinative morphology, productive sandhi (phonological fusion at word boundaries), and domain-specific vocabularies absent from general-purpose training data. This paper presents BHARATI, a set of SentencePiece BPE tokenizers trained on a balanced 781 MB corpus spanning seven languages (English, Hindi, Sanskrit, Tamil, Telugu, Kannada, and Malayalam) with native script support for all languages. We describe three successive tokenizer versions: v1 (English and Sanskrit only, with broken byte-fallback for Tamil), v2 (four-language support with byte-level fallback for southern languages), and v3 (full seven-language native subword coverage). Subword fertility analysis demonstrates that v3 averages 2.6 tokens per Indian Knowledge System (IKS) technical term, compared to 5.25 tokens per term with GPT-2's tokenizer and 3.75 tokens with the multilingual SentencePiece baseline, with the largest gains on a set of reserved IKS terms that are represented as single tokens by construction. On a held-out test set of 490 IKS-domain sentences (70 per language across seven languages, released with the measurement script), v3 reduces sequence length by roughly 90% relative to GPT-2 and byte-level encoding (which lack native Indic subwords) and by approximately 25% relative to the mBART-50 multilingual baseline, averaged across the six Indic languages, directly translating to increased effective context length for downstream language models. The tokenizer models (32,000 vocabulary), training scripts, and evaluation benchmarks are released under open licenses.

We study an online variant of discrete fair division under generalized assignment budget constraints. Goods arrive one at a time and must be assigned irrevocably to a feasible agent or to charity, which holds all unallocated goods, while fairness is evaluated only against budget-feasible subsets of every recipient's bundle. We first show that, without additional structure, no deterministic online algorithm can guarantee any fixed approximation to feasible envy-freeness, even in highly symmetric instances. We then identify bounded density spread as a structural condition that restores meaningful guarantees, obtaining approximation algorithms for arbitrary item sizes and showing that, under common valuations and sufficiently small goods, these guarantees can be strengthened to an optimal deterministic frontier. We further study resource augmentation, where the online algorithm is allowed slightly larger budgets than the fairness benchmark, and characterize the resulting improvement in the achievable guarantees. Finally, we develop a learning-augmented framework based on predicting joint value-size types, proving consistency under perfect predictions, robustness to prediction error, and showing that separate predictions of value and size marginals are insufficient to recover strong fairness guarantees.

Modern predictive systems are expected to adapt their behavior to the specific situation they are facing. A clinical model should not treat every patient the same; a retrieval-augmented model should change its answer when given different evidence; a mixture-of-experts model should route different inputs to different experts. We call this capability context-adaptive inference: before predicting, the system uses information about the current context to specialize its parameters or computation for that instance. This article provides a unified view of context-adaptive inference across three traditions that are usually treated separately: (i) explicit adaptation in statistics (e.g. varying-coefficient models, local regression, hierarchical sharing), (ii) rapid task-specific adaptation in meta-learning and transfer, and (iii) implicit adaptation in large foundation models via prompting, retrieval, and expert routing. We formalize these approaches under a common objective: to map context $c$ to adapted parameters $\theta(c)$, then to predict via $f(x; \theta(c))$. Under squared loss, linear prediction heads, and fixed features, we prove that explicit parameter adaptation and implicit routing are mathematically equivalent to kernel ridge regression on joint features of inputs and context. Building on this bridge, we propose practical design principles and evaluation metrics including adaptation-efficiency, routing stability, and context-specific robustness to guide when to specialize, how to constrain that specialization, and how to audit context-adaptive models in deployment. Finally, we identify open problems in identifiability, robustness under distribution shift, and efficient large-scale adaptation, outlining design principles for methods that are scalable, reliable, and transparent in real-world settings.

In real-world machine learning applications, incomplete observations create a fundamental challenge. Researchers have come up with several ideas to address this crucial problem. However, current models still face challenges in balancing scalability and structural consistency. This study proposes a feature imputation method, called FILLER, that deliberately searches the two-dimensional latent space produced by a generative model and fills the missing values with appropriate entries. The generative model is trained on fully observed data to generate samples from the latent space, and FILLER uses this trained model to impute the values missing in the corrupted test samples. In this study, G-NeuroDAVIS serves the purpose of the generative model. This work also presents a mathematical proof on the convergence of the iterative search. Finally, FILLER has been evaluated on several image datasets under random and structured missingness patterns with varying levels of imputation complexities. In order to justify the efficacy of FILLER, it has been compared against existing state-of-the-art solution strategies in terms of RMSE, PSNR, and SSIM. In addition, Wilcoxon signed-rank test has been carried out to validate statistical significance. Moreover, downstream analyses (classification and clustering) have also established the quality of imputation in terms of standard metrics.

Image-source-method (ISM)-based room impulse response (RIR) simulation is a useful and physically interpretable tool for acoustic scene modeling, but full-order ISM becomes computationally expensive as the reflection order and room complexity increase. We propose a physics-guided framework for fast RIR simulation that preserves the geometric structure of ISM while learning to retain only acoustically important image-source paths during online traversal. To recover energy removed by pruning, the proposed PathRIR uses a lightweight compensation multilayer perceptron to predict the missing late-tail energy envelope and generate a compensation tail whose energy follows that envelope. Experiments on irregular 3D rooms show that PathRIR reduces image-source computation and improves runtime efficiency over a full-order ISM simulator, while achieving low waveform- and decay-related errors. Ablation results show that adding the compensation tail improves waveform fidelity and reduces energy-decay-curve error, reverberation-time error, and direct-to-reverberant-ratio error, with modest runtime overhead.

Gene regulatory network modeling often requires balancing predictive accuracy and mechanistic interpretability. In this work, we compare continuous surrogate models and a discrete mechanistic model on the same Arabidopsis thaliana induced systemic resistance (ISR) dataset, using both the raw continuous gene-expression measurements and their sign-binarized representation. The study considers eight defense-related genes measured over nine time points and evaluates two continuous predictors, Random Forest (RF) regression and a Multi-Layer Perceptron (MLP), against a threshold Boolean network (TBN). The models are assessed using rolling-origin one-step prediction, recursive multi-step rollout, and interpretability analysis. RF achieved the best average one-step numerical performance in the continuous domain, with an MAE of 1.910 and an RMSE of 2.836, compared with 2.089 and 3.106 for the MLP. In the binary domain, the TBN obtained the best average one-step qualitative performance, with a binary accuracy of 0.550 and a Hamming distance of 3.600, compared with 0.500 and 4.000 for RF, and 0.495 and 4.040 for the MLP. In recursive rollout, the TBN exactly reproduced the observed binarized trajectory, while the MLP also showed near-perfect fidelity, with a trajectory binary accuracy of 0.986, and RF accumulated substantially larger deviation, with a trajectory binary accuracy of 0.708. These results highlight that local numerical accuracy and global qualitative dynamical fidelity are not necessarily aligned, and suggest that continuous surrogates and threshold Boolean networks should be viewed as complementary tools for modeling biological regulation.

Photonic reservoir computing is a promising physical machine-learning approach for time-series prediction. Quantization of the reservoir response signal is an important consideration in the implementation of photonic reservoir computing, and the number of quantization bits and sampling frequency need to be optimized to achieve high prediction performance and low energy consumption. However, few studies have investigated the effects of the number of quantization bits and sampling frequency on both prediction performance and energy consumption. In this study, we introduce the concept of approximate reservoir computing with a semiconductor laser by quantizing the reservoir node states and output weights. We numerically evaluate the performance of a chaotic time-series prediction task and estimate the energy consumption per sample using a component-level model. By optimizing the number of quantization bits, the sampling frequency, and the injection current of the semiconductor laser, we achieve a significant reduction in the estimated energy consumption per sample while maintaining prediction performance. We also obtain model-based estimates of the throughput, energy efficiency, and energy per operation of the proposed reservoir-computing system.