Papers

Multi-reward reinforcement learning trains large language models to satisfy multiple behavioral objectives simultaneously. Reward-wise normalization, as used in GDPO, preserves reward-specific relative information within rollout groups, but different objectives can still exhibit uneven learning progress. We study this behavior through advantage energy, the sum of a reward's squared advantages over a batch. Under idealized GDPO normalization, we show that this energy is proportional to active-group density: the fraction of rollout groups in which the reward provides nonzero relative advantages. This reveals a residual batch-level signal imbalance and provides a basis for calibrating reward contributions. Based on this relation, we propose Density-Aware Reward Aggregation (DARA). We derive an inverse-square-root density correction that gives greater weight to signals from less frequently active rewards. DARA computes its weights from each rollout batch, adapting to changes in reward activity throughout training without modifying the underlying policy optimization objective. Experiments on tool calling and mathematical reasoning show that DARA learns the targeted behaviors faster than GDPO, reaching high format compliance in up to 26% fewer training steps on tool calling and near-saturated length compliance in up to 65% fewer steps on mathematical reasoning, while remaining competitive in final performance. Our code is available at https://github.com/zhaihaotian/DARA.

Large reasoning models (LRMs) have achieved substantial improvements in solving complex mathematical problems, but often produce lengthy, repetitive, or erroneous reasoning trajectories. In this work, we introduce a new interpretability framework, SLIDER, to evaluate the quality of the reasoning process. SLIDER leverages an emerging body of work from information theory called Partial Information Decomposition to disentangle the information about the final answer between two consecutive reasoning steps into non-negative components: unique information (in preceding steps or current step), redundant information, and synergistic information. Building on this decomposition, we propose the *Step-wise Repetitive Reasoning Index (Step-RRI)*, a theoretically grounded measure that assesses whether the answer-relevant information in the current step $S_i$ is predominantly redundant with the past steps $S_{<i}$, relative to its unique and synergistic contributions. To evaluate the effectiveness of Step-RRI in detecting repetitiveness, we apply SLIDER to the redundancy class of the PRMBench dataset where Step-RRI improves step-level redundancy identification accuracy by over $10$ points compared to embedding-similarity and information-gain baselines. Next, we define *Trajectory-RRI*, an aggregate measure of repetitiveness for an individual reasoning trajectory. To demonstrate its practical relevance, we show that average Trajectory-RRI strongly correlates with actual reasoning length across QwQ-32B, DeepSeek-R1-Distill-Qwen-32B, and GPT-4.1, motivating its use as a signal for improving reasoning efficiency. Finally, we introduce *Trajectory-RRI-guided data selection for fine-tuning*, demonstrating that selecting training data based on Trajectory-RRI can improve a fine-tuned model's reasoning efficiency while largely preserving its task performance.

Full detector simulation and reconstruction of collider events are projected to become major bottlenecks at the High-Luminosity Large Hadron Collider, motivating the development of fast, ML-based surrogates. At the same time, LLMs have driven fast progress in generative discrete modeling: autoregressive transformers trained on tokenized data now represent the state of the art across a range of generative tasks. We extend the discrete modeling paradigm by introducing a particle-level generative model trained on residual-quantized full-event data. We demonstrate the ability of this model family to perform conditional generation from detector-stable particles; we study its scaling behavior across a range of dataset and model sizes, characterize the effects of repeated data exposure and demonstrate that token-level loss systematically predicts downstream physical fidelity. These results provide an empirical framework for scalable collider full-event generation based on residual-quantized representations.

Operator learning on probability measures can be accomplished with transformers. For measures with polynomial tails, the exponential weighting in softmax can make the corresponding measure-level attention integrals diverge. This motivates replacing the exponential with slower-growing functions. We construct two benchmarks for operator learning on measures with closed-form targets. We use these benchmarks to study attention kernel growth and data transformation in post-norm transformers. Without data transformation, the softmax models exhibit ensemble collapse on both heavy-tailed benchmarks, while the three slower-growing kernels avoid collapse. Symlog preprocessing allows softmax to avoid collapse on the matrix inverse task but not on the sheared swap task. On the Gaussian control, all four kernels perform similarly. We also examine how sample size affects the sensitivity of empirical energy and Wasserstein distances to tail differences. These results support slower-growing attention kernels as an effective design choice for post-norm transformers learning from heavy-tailed ensembles.

This paper presents a preliminary study of an alternative to the affine transformation underlying conventional neural-network layers. In the proposed Soft Dominance Layer, each output unit compares input coordinates with a learnable reference vector and aggregates smooth inequality responses. A sigmoid relaxation makes the comparisons differentiable, while a sharpness parameter $\alpha$ controls their transition toward hard threshold decisions. The aim is to examine the trainability and direct threshold interpretation of this primitive, not to claim a replacement for affine layers. In single-run MNIST experiments, the highest observed Soft Dominance accuracy is $0.9061$ without annealing and $0.9173$ with annealing, compared with $0.9827$ for the MLP baseline. These descriptive results do not establish reliable configuration rankings or a statistically supported annealing benefit. Learned reference vectors exhibit spatial structure, providing qualitative evidence of structured learning. Repeated-seed experiments and broader datasets are required to assess robustness and practical relevance beyond this proof of concept.

Longitudinal clinical reasoning requires large language models (LLMs) to identify and integrate relevant evidence distributed across extended patient histories. Although long-context models can process increasingly large amounts of information, providing more history does not necessarily make relevant evidence more accessible or improve reasoning. We compare five context strategies (Full, Recent, Episodic, Semantic, and Hybrid) on MedLoCoMo across four open-weight LLMs, examining answer correctness, robustness to query-evidence distance, and abstention on questions with unsupported premises. Episodic and Hybrid generally achieve the strongest overall accuracy, while Recent Context degrades most as supporting evidence becomes more distant; Episodic and Hybrid maintain the highest accuracy at long distances. Analysis of adversarial questions further shows that strong performance on answerable questions does not necessarily translate to successful abstention when the available history does not support the requested conclusion. These findings show that reliable longitudinal reasoning depends not only on how much history an LLM can access, but critically on how relevant evidence is selected and presented for reasoning.

While Mixture-of-Experts (MoE) models effectively scale model capacity through sparse activation, their deployment is often bottlenecked by prohibitive memory requirements. Extracting a compact subset of experts presents a promising solution. However, existing expert selection heuristics predominantly rely on Top-k ranking, which isolates the evaluation of individual experts and ignores the intricate inter-expert dependencies introduced by the MoE gating network. In this paper, we propose DS-MoE, a theoretically grounded framework that redefines expert selection via difference-of-submodular (DS) optimization. By analyzing the second-order Taylor expansion of the loss degradation, we reveal functional duality within expert combinations: redundancy (where experts encode overlapping representations) and synergy (where experts provide complementary error cancellation). To navigate this duality, we mathematically decouple redundancy reduction from synergy maximization by formulating the selection objective as a DS function. Furthermore, we devise a tailored majorization-minimization (MM) algorithm with provable monotonicity guarantees to efficiently identify the optimal expert subset. Extensive experiments demonstrate that DS-MoE effectively preserves indispensable expert combinations, achieving superior performance compared to the state-of-the-art baselines.

We evaluate hybrid quantum-classical machine learning for the reduced-order prediction of spatiotemporal brain deformation fields. To mitigate the computational intractability of high-dimensional displacement fields, we employ Proper Orthogonal Decomposition (POD) to project the data into a compact latent space. Within this framework, we formulate two distinct learning objectives: static temporal-to-latent regression and autoregressive latent state forecasting. We systematically benchmark compact classical baselines against both minimal and enhanced hybrid quantum architectures. Our results demonstrate that classical networks provide the strongest baselines in the present setting. For static regression, a classical POD-MLP outperforms all evaluated quantum variants, although an enhanced Variational Quantum Circuit (VQC) substantially improves upon a minimal VQC baseline. For temporal forecasting, a classical POD-LSTM delivers superior predictive accuracy and statistical robustness compared to an enhanced Quantum LSTM (QLSTM) across varying history windows and random initializations. Overall, this study establishes reduced-order physical field learning as a rigorous testbed for near-term QML, highlighting that while hybrid enhancements successfully recover expressivity in weak quantum circuits, classical architectures retain a definitive advantage in both fidelity and stability.

Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar $t^{1/3}$ coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.

We study adversarial online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed sets. A learner commits each action before observing its objective and competes with the best fixed action in hindsight. We prove a comparator-uniform first-order inequality that gives coefficient $4/9$, improving the online $0.401$ benchmark, with one gradient query and one projection per round and $O(\sqrt T)$ expected approximate regret. If $\zeta {\bf 1} \in K\subseteq[0,1]^d$, the coefficient improves to $\underline\alpha(\zeta)=\tfrac12-(1-2\zeta)_+^2/[2(3-2\zeta)^2]$. The proof is a direct ordered-coordinate argument with an objective-independent rational action. Conversely, a three-group symmetry-gap construction yields an offline oracle upper bound $\beta_*=0.470438681380894\ldots$ at $\zeta=0$, even with exact value and full-gradient responses. A parameterized extension and exact finite-instance bounds define an upper function for every $\zeta$. The lower and upper bounds match at $1/2$ for $\zeta\ge1/2$, and show that the optimal deficit from $1/2$ is $\Theta((1/2-\zeta)^2)$ as $\zeta\uparrow1/2$. For coefficient-revealed polynomials we obtain $1/2$ for quadratics and a geometry-dependent cubic coefficient starting at $8/17$, including $0.49$ at $\zeta=1/5$. A constant objective sequence yields an offline $(4/9-\varepsilon)$ approximation with polynomially many first-order queries on the cube and projections, without requiring a supplied positive lower bound on the optimum. We also give nonanticipating adaptive-adversary and value-feedback guarantees, including $O(T^{3/4})$ regret with one noisy value per round.

Recursive models create computational depth through parameter reuse, offering a parameter-efficient alternative to increasing model size. However, most recursive models repeatedly apply one learned transformation or a prescribed sequence of transformations, restricting computation to a fixed layer order. We introduce the Random Recursive Model (RRM), which maintains a pool of $L$ learned layers and performs $T$ recursive steps by sampling one layer independently with replacement for each example and step. This enables flexible layer reuse while retaining the parameter efficiency of recurrence. We evaluate RRM on challenging reasoning tasks, where it matches or exceeds the baselines, often with 50-75 % fewer parameters. RRM can vary its depth at inference, including beyond that seen during training, without retraining or adding parameters, improving tasks that benefit from deeper iterative computation. RRM also supports Monte Carlo inference and probabilistic test-time scaling, both of which improve performance without retraining. These insights may open new directions in neural network architecture design.

Uncertainty quantification is critical in scientific machine learning, where black-box, image-based models are increasingly deployed in high-stakes settings. In many such applications, model outputs inform costly decisions, yet most methods provide only point estimates without quantifying predictive uncertainty. This challenge is compounded by the limited accessibility and interpretability of model internals, making it difficult to assess reliability across different regions of the input space. As a result, there is a growing need for methods that can provide input-dependent uncertainty estimates to guide both model development and downstream experimentation. To address this need, we propose Adaptive Conformal Prediction using Nearest Neighbors (ACPNN), an input-adaptive conformal framework for image regression. ACPNN leverages information from neighboring samples to produce locally adaptive uncertainty estimates while maintaining low computational cost. The neighborhood structure is defined using a scaled distance metric learned via a Gaussian Process with an automatic relevance determination (ARD) kernel. We demonstrate the effectiveness of ACPNN on a diffusion model for emulating inertial confinement fusion (ICF) simulations, showing that it achieves reliable and adaptive uncertainty quantification.

Vision-language-action (VLA) models often struggle to generalize to skill combinations absent from their fine-tuning demonstrations, even when every constituent skill has been demonstrated. We focus on a vision shortcut as one failure mode: during fine-tuning, visual observations can serve as a proxy for the instruction, so a policy may execute a demonstrated combination associated with similar observations rather than the instructed combination. This motivates training with counterfactual pairs formed by holding a demonstration observation fixed while changing the instruction to specify an undemonstrated combination. These pairs, however, lack corresponding demonstrated action targets. Crucially, the currently required skill has already been demonstrated, but actions from those executions cannot serve as direct targets because the same skill can require different actions across observations. We propose CRAFT, which transfers supervision from demonstrated executions of the required skill to counterfactual pairs using skill representations that can be reused across executions of the same skill. Across three VLA models and two simulation benchmarks, CRAFT improves success on undemonstrated combinations while maintaining high success on demonstrated ones; it also improves compositional generalization on a real robot. Project website: https://taegeunyang.github.io/craft/

Conformal prediction guarantees marginal coverage, but a single calibration threshold can still spread that coverage unevenly, over-covering easy regions and under-covering hard ones. SimplexUQ is, to our knowledge, the first benchmark and reproducible protocol for measuring this allocation problem on simplex-valued predictions; it compares existing conformal wrappers rather than proposing a new one. Its task suite, SimplexTasks-12, combines six controlled synthetic regimes with six frozen-predictor real tasks spanning class probabilities, topic mixtures, spectral abundances, cell-type fractions, age distributions, and emotion mixtures. Each comparison fixes the predictor, score, and response-free stratification map, varies only the wrapper, and reports marginal coverage, worst-stratum coverage, max disparity, and within-task radius and compute. Global calibration can look valid while failing badly: on CIFAR-10 it attains 0.900 marginal coverage but only 0.542 in the worst entropy stratum, and Mondrian calibration raises that stratum to 0.886 while reducing max disparity from 0.358 to 0.022. No wrapper dominates, however. Under smooth synthetic heterogeneity, several repairs are competitive; fixed-map analyses show that rankings depend on the evaluation groups and protocol; and in a 12-task comparison, Mondrian has lower disparity on its single target partition for all 12 tasks, whereas BatchMVP has lower disparity over overlapping groups on five. These are empirical comparisons, not new coverage guarantees. A controlled predictor-bias sweep shows that removing predictor bias only partly reduces global-threshold disparity. We release task cards, result provenance, permitted derived arrays, and rebuild instructions, and treat wrapper selection as a diagnostic comparison rather than a universal ranking.

One-step generative models construct a static generator through iterative training-time transport. Existing transport objectives primarily assess distributional motion, although a neural generator needs to realize the requested sample displacements jointly through shared parameter updates. The training-time construction raises the question: once training becomes the iterative process that constructs the final one-step map, what to optimize: the next distributional move, or the route by which the finite generator learns the final map? To address the question, we introduce Training Dynamics Action (TDAction), which selects transport targets according to local shared-parameter realization cost while retaining a prescribed level of distributional progress. We formulate the cost as a soft-terminal control problem and derive a closed-form Batch Tangent Action-to-Go value that accounts for parameter effort and terminal mismatch. The criterion captures cross-sample interactions omitted by independent pairwise costs; under isotropic mobility, the criterion agrees with quadratic Euclidean assignment for deterministic balanced couplings. Randomized tangent probes provide a low-rank implementation that constructs shared detached targets without adding an inference-time trajectory. Controlled studies examine the relationship between generator geometry, transport selection, and realized local action. On ImageNet $256\times256$, TDAction attains an FID below $1.1$ without distillation.

Neural operators learn maps between function spaces, while hereditary network dynamics are described by Volterra resolvents with non-rational Laplace symbols. We introduce a fractional Laplace neural operator (fLNO) that embeds this structure in the learned map. For commuting excitation–Laplacian pairs, one block graph-spectral layer represents the full linear Volterra solution operator exactly. We establish an expressivity frontier for finite rational realizations: they approximate fractional memory geometrically on compact frequency windows, but cannot reproduce the non-integer critical asymptotics generated by a branch point, and on the half-line the best rational rate is root-exponential. The same theory yields trainable parametrizations that enforce a prescribed stability margin by construction, and a graphon-transfer theorem separates genuine operator consistency from parameter sharing. In a common-data benchmark, positive rational operators can match or exceed fLNO accuracy on finite horizons, whereas in controlled near-critical experiments fLNO recovers the branching coordinate more faithfully with far fewer parameters; unconstrained rational fits can cross the stability boundary, while certified parametrizations cannot. A four-parameter spectral law transfers without retraining from graphs of size 48 to 192 with 0.51–0.62% relative error. Applications to Chilean aftershock sequences and to renewal models for Chile and 21 Italian regions illustrate structured inference with explicit uncertainty. The contribution is an operator-learning architecture in which exact memory structure, physical coordinates and stability guarantees coexist with competitive accuracy.

As diffusion large language models (dLLMs) become more capable, they are moving from research settings to real-world serving, where request management (such as scheduling and resource allocation) relies on accurate estimation of per-request inference cost. However, common cost proxies fall short for dLLMs: output length ignores that one forward pass can unmask multiple tokens, and denoising-step count ignores the heterogeneous per-step costs. We observe that the block-autoregressive generation mechanism induces a two-dimensional execution structure over output blocks and within-block denoising steps, whereas these proxies collapse it into a scalar, discarding information essential for characterizing the cost. Motivated by this insight, we propose the Denoising Workload Surface (DWS), which preserves this two-dimensional block-step structure as a probability surface to weight the heterogeneous per-step costs. We then design a coarse-to-fine training scheme that enables a lightweight prompt-only predictor to accurately predict the complex DWS. This predictor runs efficiently even on a single CPU core, avoiding GPU contention with the serving model. Since DWS decouples request-dependent execution behavior from deployment-specific cost factors, the predictor transfers across hardware configurations without retraining. In real-world serving experiments, DWS reduces cost-prediction error by up to $2.50\times$ over scalar-based predictors, while the DWS-guided shortest-job-first scheduler reduces end-to-end latency by up to $1.92\times$ for online chatbots.

When minimizing the squared-error loss, the popular CP decomposition can be interpreted as parameter inference in a Gaussian model with a low-rank mean tensor and constant variance across the tensor entries. We introduce heteroskedastic-CP (HCP), which models entrywise variability with a non-constant, low-rank precision tensor, and develop an alternating block-coordinate ascent method to recover both the low-rank mean and precision tensors from noisy observations. Our procedure is computationally competitive, with the same leading-order factor-update complexity as CP-ALS. We demonstrate HCP on synthetic experiments and an EEG application.

We present Gumbel Straight Flow (GSF), a continuous flow map language model that leverages the noise-data coupling of a pretrained autoregressive language (AR) model. We theoretically demonstrate that the coupling between Gumbel noise and one-hot token sequences induced by an autoregressive model yields non-intersecting linear paths connecting the noise to the sequence representations. To further enhance high-quality few-step path sampling, we use a flow map semigroup objective where the tangent (velocity) condition is guided directly by the AR teacher. Across various benchmarks, including pretraining and downstream tasks, GSF can outperform current few-step language generation baselines.

Mixture-of-LoRA-experts methods raise the capacity of low-rank adaptation by routing each token to a few low-rank experts. Nearly all of them tie one input-side factor to one output-side factor per expert, and nearly all of them route by scoring the token: the router picks experts without seeing what any of them would write. We argue that the router should score the update. To first order, adding an expert's update to a layer output lowers the loss by the inner product between that update and the negative loss gradient at the output. This usefulness is quadratic in the token, so a router that is linear in the token sees only the part of it that runs through the token mean, and routers that rank experts by the norm of their own activations never see the output factor. If each expert is split into a reader (down-projection) and a writer (up-projection), the usefulness of every reader–writer pair becomes an inner product in the shared rank-$r$ space, and all $N_AN_B$ pairs can be scored from $N_A+N_B$ vectors. We build VANE on this identity. A low-rank compass predicts the descent direction of each token. VANE scores every pair by the alignment between its update and the compass without forming any update, activates the top-$k$ pairs with additive gates, and gives every pair its exact first-order router gradient. On single-domain commonsense reasoning and a four-domain multi-task mixture with Llama-3.2-3B and Llama-3.1-8B, VANE attains the best average among twelve PEFT and MoE-LoRA baselines, by 0.9–1.1 and 1.3–1.5 points respectively, with less than half the trainable parameters of an 8-expert MoE-LoRA. Its router scores also track the measured usefulness of experts far more closely than token routers do.

Autonomously constructing physically realizable 3D structures remains a significant challenge due to combinatorial action spaces, interchangeable components, equifinal assembly sequences, and strict stability requirements during construction. State-of-the-art methods fine-tune large language models for text-based generative construction. However, these approaches do not allow for Multimodal (text, image, sketch) conditioning, overlook the practical role of scaffolding for stabilizing intermediate structures, and suffer from slow inference speeds. Therefore, we formulate construction as a probabilistic next-block generation task with multiple potential assembly actions and multiple potential task conditioning modalities. Concurrently, we explicitly consider the utility of scaffolding by introducing an auxiliary scaffold block token. We present Scaffold Multimodal Monte Carlo (ScaffoldM3C), a multimodal, lightweight, auto-regressive model for stable block-based construction, that proposes a set of next-step candidate blocks. Leveraging these candidates, we utilize Sequential Monte Carlo (SMC) to maintain a population of possible assembly sequences, allowing us to consider multiple, potentially different, assembly directions simultaneously. We train our multimodal architecture by extending the StableText2Brick dataset to contain image conditioning prompts and scaffold-stabilized build sequences. ScaffoldM3C is 4x smaller than competing baselines, yielding a 5x to 20x speedup during inference, while achieving comparable construction quality to state-of-the-art methods and higher overall stability. We demonstrate the effectiveness of our approach through simulations and real-world robot assembly demonstrations.

Next-generation large language models (LLMs) are expanding from the cloud to ubiquitous edge devices. However, edge devices typically either lack the memory to store increasingly large LLM weights or, even with enough memory, spend unaffordable energy on loading the weights. This raises our question: can an edge device run an LLM without storing or loading its weights, but receive them over the air and consume them on the fly? Inspired by wireless broadcasting, we present AIR-LLM, an LLM inference architecture for edge devices, which is composed of: (i) a central radio (e.g., 5G base stations) that broadcasts the LLM weights into the air, and (ii) the edge user that receives the weights and completes the general matrix-vector multiplication (GEMV) of LLM inference directly in the radio frequency (RF) domain using RF mixers. To further shorten the airtime, AIR-LLM exploits MIMO spatial multiplexing and proposes an energy-efficient precoder-postcoder pair on the edge to calibrate its own wireless channel. Since the central radio stays user-unaware, AIR-LLM is user-scalable so that one broadcast serves unlimited users within its coverage. We implement AIR-LLM on the NVIDIA Sionna ray-traced channels of two real-world urban scenes and the profiling of a real RF mixer. With a WikiText-2 perplexity degradation of 4.0% on LLaMA-3.1-8B, AIR-LLM saves the energy by 157.7x/40.4x against the FP16 and weight-only quantization baselines; with 20 users, its airtime is 104.1x/26.0x shorter, respectively.

Human motion, environmental contacts, and interaction forces are governed by common physical laws, yet existing approaches typically separate visual pose reconstruction from contact and force estimation. This separation limits joint reasoning and can propagate errors between stages. We introduce PACT, an end-to-end model that jointly learns to estimate human pose, contacts and contact forces from monocular video. Our approach augments a human reconstruction foundation model with learnable contact-force tokens and a temporal transformer that integrates visual features with world-space motion. Joint prediction heads refine human poses and estimate contacts and forces, while physics-based supervision encourages consistency between the reconstructed motion and interaction forces. To address the scarcity of force annotations, we develop a data annotation pipeline that combines contact labeling with physics-based motion and force optimization, producing training supervision from synthetic and real-world videos. We also introduce a real-world climbing benchmark ForceWall with climbing videos and corresponding ground-truth contact forces obtained from the force sensors. Experiments demonstrate state-of-the-art contact and force estimation, outperforming staged reconstruction approaches and generalizing to interactions beyond the training distribution. These results support end-to-end joint learning as an effective approach to recovering human motion and physical interactions from video.

As an alternative to the standard geometric analyses, we give an exact, information-theoretic analysis of stochastic gradient descent (SGD) and its variants. We show that a preconditioned SGD step is the posterior-mean update of a Gaussian Bayes model, and that its one-step regret splits into an intrinsic-time cost and a change in comparator information. The split extends to an identity for the objective itself. Convex convergence, strict-saddle-point escape, the link between flatness and generalization, the standard learning-rate schedules, adaptive optimizers, and the noisy, momentum, heavy-tailed, and gradient-free variants of SGD each correspond to a term or a special case of this identity. We measure its terms on synthetic and real training runs. On real networks it attributes the slack of classical convergence bounds to the terms their derivations drop and separates optimizers that reach the same training loss. That separation follows the number and consistency of their steps. Its relation to which of them generalizes better differs between networks. For gradient-free SGD the identity determines how a curvature preconditioner should enter the update. The sharpness-based generalization certificate it yields, with a data-independent isotropic prior, is vacuous at network scale unless the curvature spectrum is nearly flat across all parameters.

Pairwise guide–transcript scores do not enforce conservation of a finite guide-loaded RISC pool when they are interpreted independently as occupancies. We formulate a differentiable scalar equilibrium layer: one conservation equation with a unique positive root and exact implicit gradients. It yields a redistribution theorem, a qualified high-resource limit, an analysis of the retrieval approximation, and a conditional rank-invariance result: within one construct at one dose, rankings by fractional occupancy cannot distinguish equilibrium from independent scoring. We therefore audit the two experiments that proposition leaves open, dose and cross-context, on archival off-target data. Corrected thermodynamic affinities associate weakly with measured repression in the direction a working predictor requires, but a paired permutation test and a construct-cluster bootstrap do not establish added predictive value from the coupling: what survives their differing permutation-null baselines is \GapNet{}, a descriptive \GapNetOverSE{} of the equilibrium association's cluster standard error. The dose fits are heterogeneous and frequently violate the model-implied exponent constraint, which is superlinear rather than sublinear, so these data do not identify the competition parameter. A saturable compression of the competitor set holds both accuracy targets on held-out guide families but is not faster at the size measured. The contribution is a reusable conservation operator and the experimental information needed to test it. The code for this study is available at https://github.com/shadi97kh/One-Pool-Many-Targets.

Online batch selection fine-tunes a language model on the most useful part of each candidate batch. Selectors that match the gradient of the candidate batch are attractive because they need no held-out data, yet they rarely beat training on the whole batch. We show why. In-sample gradient matching uses every example as part of its own target, so its objective credits each example with its own gradient noise. This is the covariance penalty that makes training error optimistic, now sitting on the diagonal of the gradient Gram matrix: it steers selection toward the noisiest examples and makes the full batch the best solution the objective can reach. The fix costs nothing. For each example, the other candidates form an independent sample of the data distribution, so removing the diagonal turns the matching objective into an unbiased estimate of the update's error with respect to the population gradient. The minimizer of this leave-one-out objective weights examples by their gradient signal-to-noise ratio (SNR), and whenever per-example SNR is heterogeneous enough, half of a batch yields a lower-error update than the whole batch; we give the exact condition. We build \method{} on this principle. It computes the Gram matrix in the metric of the Adam preconditioner during the ordinary backward pass, selects a weighted subset greedily with a $(1-e^{-\gamma})$ guarantee, and uses no held-out data. Across four fine-tuning tasks and seven backbones from 1.5B to 8B parameters, LOOM improves on full-batch training by 2.3 and 2.4 points on Llama-3.1-8B and Qwen2.5-7B, exceeds every in-sample gradient matcher by 2.4 points and the validation-guided GREATS and OPUS by 1.6–2.0, and selects injected label noise at under a fifth of its base rate.

Trellis-coded quantization enables high-dimensional compression of large language model (LLM) weights at ultra-low bit widths without the exponentially large codebooks required by conventional vector quantization. Practical deployment, however, presents two challenges: reconstructing compressed weights at sufficient parallel throughput to avoid making dequantization an inference bottleneck, and maintaining quantization accuracy without costly incoherence transformations. We address these challenges with two complementary techniques. First, we introduce an ultra-low-complexity trellis dequantizer that uses a structured, hardware-efficient state-to-value mapping while preserving diverse reconstruction choices for trellis search. Second, we reformulate discrete trellis path optimization with a curvature-aware objective that reflects model sensitivity directly in the original coordinate space. Together, these techniques enable high-quality ultra-low-bit trellis quantization with inexpensive, highly parallel runtime reconstruction and without relying on Hadamard-based incoherence processing.

Continual parameter-efficient fine-tuning for large language models (LLMs) must balance retention of previously acquired knowledge, adaptation to new tasks, and strict parameter budgets. We present ChainLoRA, a replay-free continual merging framework built on chain-updated task-vector geometry. From a parameter-merging perspective, we formulate a geometric view of forgetting through a measurable interaction between task updates, separating directional overlap from coefficient coupling. Building on this view, ChainLoRA combines chain-updated training with post-stream adaptive SVD merging. During training, initialization and a one-sided orthogonality proxy use only the last carrier, keeping their historical-state footprint and regularization overhead constant as the task stream grows. At merging time, Adaptive SVD extracts a shared carrier and aligns it to the latest task through Procrustes adaptation. Our theoretical analysis shows that Procrustes adaptation facilitates geometric approximate separation of shared and task-specific components. The one-sided proxy further bounds inter-task interference. An effective-rank penalty additionally promotes efficient utilization of the task subspace during continual learning. Experiments show that ChainLoRA achieves state-of-the-art performance among the evaluated replay-free methods on the Large and SuperNI benchmarks, while remaining competitive on Standard CL and attaining almost the closest average scores to the evaluated replay-based method across all three benchmarks.

We introduce IrekoGPT, a post-hoc method for converting pretrained LLMs into slimmable models whose width can be adjusted at inference time. Building on SliceGPT, we retain its projection matrices without pruning them, allowing a single model to expose nested subnetworks at different widths. We improve robustness by calibrating each layer across multiple compression ratios, and correct downstream linear layers through gradient-free ridge regression. Across Llama and Qwen models, preliminary results show improvements over naive PCA-based slimming, with the largest gains at high compression. Code is available at https://github.com/aimagelab/IrekoGPT

Knowing how much a causal predictor could improve need not reveal the gain of the repair actually learned. We quantify this gap in a scalar Gaussian causal experiment with known intervention geometry: auxiliary data identify effect magnitude up to bounded contamination, while diagnostics identify direction. The target is the squared-loss gain of the realized trained repair relative to a fitted reference. Jointly optimizing the learner and assessor under uniform learning MSE $\eta$ avoids the trivial solution of making no repair. At the usual $1/k$ learning scale, every feasible learner incurs a $k^{-2}$ assessment floor, even when oracle potential is estimable at a faster rate. In the magnitude-rich regime, we characterize a sharp leading-log frontier: the assessment exponent is $\min{\ell_k,2k\eta_k/U}$ to first relative order, where $\ell_k=\log(1/(k^2E_k))$ and $E_k$ is auxiliary precision. A diagnostic-abstention rule attains this exponent with unknown nuisance parameters. We also bound the critical allowance window and transfer the frontier to adaptive sampling by exact Gaussian simulation. Finite-grid experiments distinguish sign-tail suppression from total MSE and expose conservative finite-budget behavior. The result isolates how the assessment target changes information requirements in this experiment; it is not a general causal identifiability claim.