Papers

Differentiable optimization brings the structural guarantees of mathematical optimization to network pipelines, allowing them to be trained end-to-end. However, its application remains challenging for nonconvex constrained problems, as existing differentiable solvers often suffer from limited modeling expressiveness due to their reliance on specialized problem structures, while also incurring substantial computation time and memory overhead in both the forward and backward passes. To address these challenges, we propose lapanda, a matrix-free differentiable solver for nonconvex optimization with general constraints. It reformulates the problem to a sequence of augmented Lagrangian subproblems, each handled by a first-order inner solver through a proximal averaged quasi-Newton algorithm with adaptive linesearch, thus enabling efficient forward optimization. We establish local well-posedness of the solution map and convergence of the outer iterations, and further derive a sensitivity alignment between the original problem and the final subproblem in the backward pass, demonstrating that the subproblem sensitivity, which can be computed efficiently in a matrix-free manner, provides a principled approximation to the exact optimizer sensitivity. We evaluate lapanda on nonconvex constrained Rosenbrock benchmarks, imitation learning with several representative constrained optimal control problems, and embedded robotic obstacle-avoidance tasks. Compared with state-of-the-art differentiable solvers, lapanda delivers substantial reductions in computation time and memory footprint while maintaining reliable constraint satisfaction and learning performance.

Prompt injection is a leading security risk for LLMs and LLM-based applications such as agents. State-of-the-art red-teaming methods for prompt injection leverage reinforcement learning (RL) to train an attacker LLM to generate effective injected prompts. However, when targeting frontier LLMs such as GPT-6-Luna, a major challenge is the cold-start problem: every attack attempt by the attacker LLM fails and thus receives zero reward, providing no signal for learning. In this work, we propose a curriculum learning-based method to address the cold-start problem. In particular, we propose to train the attacker LLM against a sequence of increasingly robust target LLMs, with each stage warm-starting from the attacker LLM obtained in the previous one. However, simply training against a weak target (e.g., GPT-4o-mini) may not sufficiently prepare the attacker LLM to obtain useful learning signals against a frontier LLM (e.g., GPT-5.6-Terra). Instead, we find that the design of the curriculum is critical: after each stage, the attacker LLM needs to partially succeed against the next target LLM such that it can learn from successful attempts to attack the new target. Our extensive evaluation shows that our method can effectively red-team frontier LLMs, achieving an attack success rate (ASR@10) of 93.8% and 45.0% against GPT-5.6-Luna and GPT-5.6-Terra on AgentDyn, whereas state-of-the-art RL methods such as RL-Hammer and PISmith achieve 0% ASR under the same setting. Moreover, we find that the attacker LLM transfers across targets, e.g., an attacker LLM trained to defeat one strong LLM (GPT-5.6-Terra) also succeeds against six other frontier LLMs (e.g., GPT-6-Luna) it was never trained on. Our code is available at https://github.com/albert-y1n/PIForge.

Modern language models are likely to be updated throughout their lifetime rather than trained once and frozen. Each update therefore participates in a recurring cycle: decide which experience to learn from, understand what that update changes, and remain capable of learning from what comes next. We show that these challenges are governed by the same evolving update–behavior interaction. We derive a token- and layer-wise decomposition of how learning from one token changes another prediction. By separating the softmax force, shared readout geometry, and residual connections, it exposes two interaction channels and yields a forward-computable approximation. Following this interaction through time reveals a unified picture of continual adaptation. Positive interaction identifies useful experience; negative interaction produces either concentrated collision or accumulated erosion; over longer horizons, updates reshape the shared geometry mediating future learning signals, reducing their transmission. These predictions lead to effective data selection, mechanism-specific controls for interference, and a readout-based diagnostic of future learnability whose degradation predicts the benefit of restoring the readout. Across models and training regimes, the same local interaction thus explains both what an update changes now and how learning today changes what can be learned tomorrow. This view connects data attribution, forgetting, and plasticity loss as distinct regimes of the same evolving learning dynamics.

In-context learning (ICL) is crucial for boosting the inference performance of large language models (LLMs). However, the effectiveness of ICL in LLMs is greatly influenced by the choice of demonstration sets. Exhaustive searches over these sets are combinatorial, and existing selectors often rely on relevance or likelihood proxies to implicitly assess ICL quality. Making repeated queries to the target LLM with these strategies can incur substantial costs. This work simplifies selection by framing it as a constrained local search problem and presents local demonstration editing (LDE). Starting with an initially retrieved set of demonstrations, LDE employs a single structured edit to explore its surrounding neighborhood while balancing performance gains with search costs. Technically, LDE is reduced to a policy search problem, for which we train a small LLM, referred to as Jev-LDE. This model as the System-1 modifies the retrieved demonstration set by performing actions such as Keep, Delete, or Replace elements, all within a framework of reinforcement learning with verifiable rewards. At test time, Jev-LDE executes a single edit of the retrieved demonstration set, followed by one inference from the target LLM, avoiding the need for iterative context scoring or subset searches. Across standard classification benchmarks, various target LLMs with Jev-LDE as the plug-and-play module consistently improve ICL performance, and Jev-LDE shows transferability to held-out benchmarks and models without retraining. These findings indicate that the LDE approach offers an efficient and adaptable method for harnessing the ICL capabilities of target LLMs.

Pretrained graph-text models align graph representations with textual semantics, enabling recognition of unseen classes and transfer across graph domains. However, as graph data and classes continually arrive, models should learn from new supervision while retaining their zero-shot transfer capabilities and historical task knowledge. Two challenges arise: (i) new classes can overturn historical predictions despite preserved distinctions among historical classes, and (ii) overly strict response preservation can stall learning of new classes. To address these challenges, we propose Hierarchical Response Preservation (HiRP). HiRP represents this competition through a hierarchical response that keeps each historical-class probability and sums new-class probabilities, preserving historical distinctions and aggregate competition while allowing distinctions within the new class group to adapt. It further uses the geometry induced by this response to guide constrained updates, retaining useful adaptation directions while controlling response drift. Across three class-incremental settings, HiRP achieves absolute gains of 1.84-7.95 percentage points in average accuracy over the strongest compared baseline in each setting, while mitigating zero-shot transfer degradation.

Integrated sensing and communication (ISAC) enables joint communication and sensing using a shared waveform, but its signal design is challenging due to the inherent trade-off between the two objectives, particularly in the short blocklength regime. This paper proposes an autoencoder (AE)-based framework for ISAC waveform design in noncoherent settings. We derive a modified Cramér-Rao bound for multi-target delay estimation and analyze the maximum-likelihood decoding rule for noncoherent communication under correlated fading. These results reveal structural connections and trade-offs between communication and sensing objectives in waveform design. Based on this analysis, the AE learns waveform representations that jointly optimize both functionalities, with a tunable parameter controlling the trade-off. Simulation results show that the proposed design outperforms conventional schemes in both communication reliability and sensing accuracy, especially under short blocklength and fading conditions.

Side-channel evaluators routinely inspect leakage tests while acquisition is still running, and extend or stop the campaign based on what they see. Fixed-horizon screening such as the Welch $t$-test with threshold $|t|>4.5$ gives no error guarantee for this monitored decision rule. We study anytime-valid leakage detection based on testing by betting: SKIT-type swap-pair e-processes whose false-alarm probability is controlled uniformly over time under an explicit conditional symmetry null. In matched comparisons that share the frozen witness, rows and payoff, first-crossing detection needed 1.68-2.00$\times$ the traces of a fixed-horizon randomization test at 80% detection on synthetic streams, and 1.68-2.38$\times$ on degraded recordings from an open ML-KEM electromagnetic dataset with the primary Ridge witness at $\alpha=0.05$. With the same primary witness and level, on undegraded reference and pqm4 recordings the monitored procedure stopped early: its median stopping point was 62-72 and 146-316 evaluation traces, i.e. 2-8% of a conservative 4096-trace budget. Under exact designed nulls on the recorded backgrounds, repeated-look $|t|>4.5$ screening over all 13000-20000 samples raised a false alarm in 2.7-12.9% of replicates, against 0.0-4.7% for terminal-only screening and no rejection by a sample-wise e-Bonferroni process, which in a prespecified follow-up detected natural-label associations in 4 of 4 backgrounds after 840-3288 traces. All recordings come from one device, and natural-label results are descriptive; we state the assumptions each claim requires.

Joint-embedding world models enable visual planning by learning action-conditioned dynamics in latent space. Yet they are commonly trained for one-step prediction on encoded states, while planning recursively applies the learned transition to its own predictions. One-step accuracy therefore does not capture how prediction errors propagate under recursive rollout. We decompose multi-step rollout error into the errors introduced at individual steps and their propagation through subsequent transitions. We show that state-affine dynamics are precisely the differentiable transitions with state-independent Jacobians, eliminating the nonlinear propagation residual and making the error propagation operators depend only on the action sequence. Guided by this result, we introduce SALT (State-Affine Latent Transition), an action-conditioned state-affine dynamics model in which the action modulates both the state transformation and the additive update. We train SALT through recursive multi-step rollout supervision, feeding each predicted latent state back into the transition so that training matches how the model is used during planning. Across four visual planning environments, SALT exhibits $1.48$–$2.19\times$ higher one-step prediction error than the matched LeWM baseline, yet improves closed-loop success in every environment by $10.0$ percentage points on average. On OGBench-Cube, the fraction of episodes that fail with a sharp rise in model-predicted cost after execution decreases from $23.3%$ to $2.0%$.

Low-precision Transformer systems increasingly quantize attention matrix multiplications, while softmax often remains at higher precision. During pretraining, an approximate softmax changes the gradients that train the model as well as its forward computation. We study this interaction with K-interval attention, which approximates the exponential using K+1 grid values. We vary per-row grid calibration, interpolation versus hard rounding, and the placement of a straight-through surrogate relative to normalization. We derive the corresponding backward rules, including calibration derivatives, and compare these choices in pretraining experiments matched on model, data, and optimizer. Detaching the row extrema leaves the forward computation unchanged but produces a delayed increase in validation loss. With hard rounding at K=4, min-max calibration and a pre-normalization surrogate incur a large loss gap; changing either choice substantially reduces it. At 124M parameters and 2.5B training tokens, fixed-window calibration with a post-normalization surrogate yields a validation loss gap of +0.019 nats relative to softmax at K=4, and with a pre-normalization surrogate yields +0.004 nats at K=16.

Efficient exploration often remains a central bottleneck in reinforcement learning with verifiable rewards (RLVR). Although temperature control and test-time scaling strategies can increase rollout diversity of large language models (LLMs), they either expand the sample budget at rollout time or leave the benefit of exploration unquantified. To this end, we propose Temperature-Grouped Reinforcement Learning (TGRL), which turns temperature-induced diversity into an explicit training signal. For each prompt, TGRL partitions its rollout group into low- and high-temperature subsets, estimates exploration gain through their reward contrast, and allocates this group-level signal as token-level credit using Jensen–Shannon (JS) divergence between the corresponding temperature-scaled next-token distributions induced by the same logits. Notably, TGRL reaches equivalent accuracy up to 36% faster than strong RLVR baselines without expanding the rollout budget. Across 11 benchmarks from diverse domains, TGRL broadly improves over strong RLVR baselines: it improves the six-benchmark math average by 1.6% at 32B, raises CodeForces rating by 196.7 points and LiveCodeBench Pass@16 by 4.4%, and improves ALFWorld/WebShop success rates by 6.3%/4.9%. Comprehensive ablations and wall-clock analysis confirm the efficacy of all proposed components. Code is available at https://github.com/1229095296/TGRL/tree/main.

On NVIDIA Blackwell B200, tensor-core throughput outpaces special-function exponential throughput by more than two orders of magnitude, exposing exponential evaluation in fused attention kernels. A pretrained Transformer, however, may not need it evaluated accurately at every element. We characterize what a pretrained model does need by approximating softmax at inference in ten frozen decoder-only models (0.5B-72B). The number of positions the softmax map assigns probability to and within-row resolution can be cut substantially, yet uniform weighting of the same positions is damaging. Where a fixed resolution budget is placed matters as much as its size, with resolution near the row maximum consistently favored. Perturbations matched on scalar distortion produce model-dependent responses of opposite sign. These findings motivate Rowmax-PoT, a coarse logarithmic weight representation anchored at each row maximum, and Rowmax-H15, its hardware specialization in FlashAttention-4. On B200, the patched FP8 attention forward is 12.4% faster at causal 8K and 25.8% faster at non-causal 8K in host-side call-latency measurements; board energy per forward falls by 8.4% at causal 16K. Measured separately on the BF16 kernel path at 2K, Rowmax-H15 increases perplexity by 0.091-0.492% across five models from three families.

Learning-augmented algorithms for metrical task systems (MTS) can exploit predictions of canonical dual values, but existing formulations typically require a prediction for every state. We study whether these predictions can be compressed to a small set of representative states while retaining their algorithmic value. We introduce landmark-compressed value predictions, in which the predictor reports predicted dual values only at $m$ landmarks and the remaining values are reconstructed by a Lipschitz extension. Our algorithm achieves additive excess cost $O(T\,r(L) + \sum_t \delta_t)$, where $r(L)$ is the covering radius of the landmarks and $\delta_t$ measures prediction error up to additive shifts; local and value-dependent bounds refine this guarantee. For sparse landmark sets on unit-spaced finite lines, we prove a matching $\Omega(T r_m)$ lower bound for every randomized algorithm using fixed landmarks, even with advance access to their entire exact absolute-value table. The prediction interface also matters: on two states with one landmark, exact absolute values permit horizon-independent excess, whereas exact relative values force worst-case expected excess linear in $T$. We give PAC guarantees for learning compressed prediction tables, with efficient empirical-risk minimization for fixed landmarks. Our results connect metric coverage, prediction interfaces, and learning guarantees for compressed predictions in online MTS.

Group-relative policy optimization (GRPO) makes learner-side activations a major memory-computation bottleneck: gradient checkpointing reduces activation memory through recomputation, but fixed schedules can leave roughly 18 GB unused on a 48-GB GPU despite substantial recomputation overhead. Existing activation-management methods set state fidelity from execution cost, tensor properties, or generic compression sensitivity, without explicitly incorporating GRPO's analytic update structure into state-fidelity allocation. We formalize this dependence as policy-update exposure, linking the current GRPO loss coefficients to state-level approximation sensitivity. These coefficients are available before backward without an additional backward pass. We introduce HiLoRe, which allocates graph-attributed recovery units among high-precision storage, low-precision compression, and deterministic recomputation using measured recovery utility and update-conditioned approximation risk. It combines high-precision storage and deterministic recomputation with low-precision recovery under a calibrated risk budget. Across five model-task settings with 2K responses and memory < 1.10 times GC's per-GPU actor-update peak, HiLoRe's actor-update throughput gains reach 13.5% over GC and 7.9% over the fastest evaluated baseline, with paired mean downstream-score differences below 0.6 percentage points.

Structured quantum-state learning not only depends on an expressive ansatz but also on an operational certificate that stays meaningful with finite measurements and imperfect implementation. We study pure one dimensional states learning by an inverse binary multiscale entanglement renormalization ansatz (MERA). In the learning procedure, the qubits removed during coarse graining are controlled coherently and measured together at the terminal register. We confirm that an ideal sequential and terminal measurement schedule delivers the same complete bit string distribution under matched causal operations, while normalized postselection can amplify perturbations inversely with prefix acceptance. A noise aware theorem introduces an individual calibrated total variation implementation budget to the finite shot certificate. The protocol is estimated on an open boundary transverse field Ising ground state. A frozen 8-qubit schedule using $560$ million simulated training measurements per run achieves fidelity above $0.99$ in all $60$ held-out runs, with a mean fidelity of $0.996886$. 1080 circuit-noise cells and 6480 confidence-coverage rows are covered by fixed-circuit robustness validation without a locked soundness violation. We then address architectural fairness at $n=16$ using three new studies. In a 120-run exact-gradient multistart diagnostic, MERA has higher fidelity in 58/60 paired restarts and lower long-range error in 60/60, although no run met the prespecified stationarity criterion. Finally, a causal cone-complete, parameter matched local circuit achieves $2.62\times$ greater aggregate gate exposure yet loses all 30 paired comparisons in fidelity, long-range error, energy, and entropy.

Time series forecasting requires extrapolating the dynamics of an observed process beyond the last available measurement. Yet recurrent forecasting models typically treat observations as inputs that directly control their latent dynamics. It leads to a regime change when these observations become unavailable at prediction time. Following a state-estimation perspective, we introduce Observer State-Space Models (OSSMs), a class of recurrent models that interprets the observed input time series as measurements of an underlying autonomous dynamical system. OSSMs explicitly separate latent-state propagation from measurement assimilation: a single transition governs the dynamics across both context and forecasting intervals, while available observations correct the estimated state through an observer. This formulation naturally exposes classical control-theoretic properties, including observability and convergence of the state estimation error. We further show that conventional and recent SSMs can be recovered as particular instances of our OSSM framework, thereby providing a unified interpretation of their recurrent dynamics and revealing modeling inconsistencies. We perform experiments across several benchmarks showing that OSSM achieves substantial improvements while maintaining the same parameter count and training setup as the corresponding SSM baseline. These results support a simple principle for recurrent forecasting: observations should correct the estimated latent state, rather than control the dynamics used to propagate it.

World models improve sample efficiency by training policies on imagined trajectories, but their usefulness depends on learning representations that capture the information needed for future control. We study whether self-supervised joint-embedding prediction (JEPA) can provide this learning signal for multi-agent reinforcement learning. We introduce MA-JEPA, a stochastic world model that replaces observation reconstruction with prediction of target representations, enabling model-based multi-agent reinforcement learning with centralized training and decentralized execution. A categorical latent state and a causal Transformer are trained with posterior and action-conditioned dynamics prediction objectives and are then used for actor-critic learning from latent imagination. A training-only joint predictor conditions on all agents' local states and actions to predict each agent's next local observation embedding. These predictions are passed through the same local posterior used during real interaction with a centralized critic that is used only for value learning, with execution remaining decentralized. Our experiments show that this architecture performs strongly on SMAC, matching or exceeding the strongest reported comparator mean win rate on four of eight evaluated maps.

Systematic out-of-distribution (OOD) generation remains a critical bottleneck for continuous-time generative models. While standard joint classifier-free guidance (CFG) routinely fails to synthesize unobserved concept combinations, exact decomposed scoring generalizes robustly at the cost of severe computational overhead. In this work, we reveal that compositional binding is not a uniform process but a highly localized phase transition. We identify the semantic bifurcation window - the precise temporal interval where joint and decomposed vector fields meaningfully diverge. Exploiting this dynamic, we propose surgical guidance, a hybrid sampling strategy that restricts exact multi-pass scoring strictly to this critical window. On an OOD bi-digit MNIST testbed, surgical guidance achieves state-of-the-art compositional fidelity at a fraction of the inference cost, yielding a +5.3% absolute improvement in pairwise accuracy over the joint baseline by intervening during just the first 15% of the diffusion trajectory. Furthermore, our empirical analysis uncovers a fundamental topological divide: diffusion models (SDEs) force conceptual resolution immediately at peak noise, whereas Conditional Flow Matching (ODEs) delays structural binding until intermediate features emerge, establishing a new temporal framework for accelerating large-scale generative decoding.

Multimodal graph predictors combine text, images, and relations to classify connected entities. How much of this input is needed to preserve their predictions? We study budgeted representation selection, which chooses a subset of candidate text and image vectors under a separate capacity for each modality. Predictions from the complete candidate input define the classes to preserve. The challenge is that a representation's contribution depends on the other selected inputs, while graph propagation extends its effects across nodes. Our empirical study shows that candidate rankings change with the selected input, while predicted probabilities remain informative after the class stops changing. Updating scores improves selection, and exchanging inputs can improve a subset whose capacity is already filled. These findings lead to GraphSelect, which starts from individual candidate gains and refines the subset through jointly evaluated exchanges. It screens promising removals and additions, accepts an exchange when it reduces the prediction loss, and updates the scores. Experiments on six graphs show higher mean objective recovery than six attribution and explanation methods adapted to the selection task. Across nine trained architectures on two graphs, retaining 20% of the candidate representations per modality gives a mean accuracy drop of 0.10 percentage points relative to full candidate input, preserving classification performance with substantially fewer text and image representations.

Recipes such as s1 and LIMO teach a model to reason with little data by showing it the same thousand or fewer worked solutions many times over. Judged when that training ends, the repetition looks harmless. But reasoning models are often trained again, and we find that repetition leaves their reasoning fragile to that next stage, even when the stage has nothing to do with reasoning. We fine-tuned Qwen3.5-9B-Base on its own correct solutions to competition math problems, either drilling a few hundred of them about eight times each or showing many more once; with the same amount of training, both solve about 95% of held-out problems. A single pass of ordinary instruction tuning leaves the once-trained model where it was, while the drilled one falls to 86.0%, and harsher later stages take it to 59.3% or below. A third model that visited the drilled problems just as often, with a new solution at every visit, was unharmed, so the damage comes from seeing the same texts again rather than from having few problems. The break recurs with a stronger model's traces, in further training runs and on other models and tasks. It is also cheap to undo: the reasoning is suppressed rather than erased, and five updates of reasoning training bring almost all of it back, as does brief training on the reasoning format with almost no mathematics. Fresh solutions prevented the damage, and so did replaying 6.25% of the original solutions in a gentler later stage, so our claim concerns later training without such replay. Sharpening alone does not explain the break, since a model sharpened three-quarters as much without repetition was unharmed. On a skill the base model could not perform within a token budget, repetition mainly cost learning.

Automatic relevance determination (ARD) is the standard device for input selection in Gaussian process (GP) regression. By giving the covariance kernel a separate lengthscale for every input and learning those lengthscales by maximizing the marginal likelihood, ARD lets the data decide which coordinates matter: irrelevant inputs receive very large lengthscales and are effectively switched off. We trace this mechanism to the Bayesian Occam's razor embodied in the marginal likelihood, derive the gradient through which it prunes inputs, and emphasize that ARD delivers effective rather than exact sparsity. We review the algorithms used in practice and the rules that turn lengthscales into selections, and we survey the asymptotic theory, distinguishing the fixed-domain identifiability obstruction on the lengthscales from the high-dimensional selection-consistency guarantees recently established for hierarchical GP priors, and noting what remains open for plain ARD. We compare ARD with spike-and-slab priors, sparse axis-aligned and global-local shrinkage priors including the Bayesian lasso and horseshoe, penalized likelihood kriging, sensitivity and projection criteria, and additive kernels. We argue that ARD endures because of its seamless integration with kernel learning, universal software support, and low cost, and we close with its limitations and remedies.

Automatic relevance determination (ARD), the default tool for variable selection in Gaussian-process (GP) regression, ranks inputs by inverse lengthscales – which measure how fast a function varies, not how much an input contributes to prediction – and offers no calibrated rule for deciding which inputs to keep. The prediction-centred alternative, the derivative sensitivity $\nu_j = \mathbb{E}[(\partial f/\partial x_j)^2]$, is available in closed form from a fitted GP, but turning it into a selection rule is harder than it looks: at a null input the estimator is a degenerate quadratic form, so Wald and Bernstein-von Mises cutoffs are anti-conservative, and the natural residual bootstrap is mis-scaled. We show that a studentized multiplier bootstrap of the GP derivative process repairs both, prove its validity through an invariance principle for quadratic forms, and obtain asymptotic family-wise and false-discovery-rate control across inputs. Over 100 replications the rule controls FDR wherever inputs are truly null, while uncalibrated derivative rankings breach the target by up to 2x and a Bernstein-von Mises cutoff by 2.2x; at matched FDR it loses no power; it holds under a Matérn kernel and input correlation up to 0.99; on real data with planted and authentic null inputs it admits 5-12x fewer spurious inputs; it costs 5-18% of the GP fit; and a block-averaged variant retains validity at cost linear in $n$.

Fine-tuning anguage models (LLMs) with first-order optimizers requires a memory several times larger than that required for inference. Memory-efficient zeroth-order optimization (MeZO) sidesteps this cost by estimating gradients from forward passes only. However, for BitNet architectures, a family of LLMs with ternary {-1,0,1\} weights and 8-bit activations, fine-tuning requires updating full-precision latent weights, and thus the memory footprint of MeZO no longer matches that of inference. A promising solution is to finetune only a subset of the latent weights, but existing sparse zeroth-order (ZO) methods either ignore the ternary structure or require first-order gradient information to build a sparse mask, which is at odds with the purpose of ZO fine-tuning. We propose TerMeZO, a sparse MeZO scheme that exploits the geometry of the ternary quantizer itself to identify the latent weights that are more likely to change values during fine-tuning, at no additional data or memory cost. Our convergence analysis shows that TerMeZO can converge faster than full-parameter MeZO, owing to its optimized reduction of the fine-tuning effective dimension. We run extensive experiments on BitNet models ranging from 1B to 3B parameters, spanning classification, instruction-following, and mathematical reasoning tasks. TerMeZO matches or exceeds the performance of full-parameter MeZO while substantially reducing the fine-tuning memory footprint.

Coupled rollouts can reduce the noise of counterfactual action comparisons, but two issues prevent standard common-random-number constructions from serving as a general learning primitive in imperfect-information environments. First, an invalid coupling may expose hidden state, synchronize endogenous policy randomness, or misalign chance events after counterfactual histories diverge. Second, in multi-action policy optimization, lower return-contrast variance is not by itself the relevant objective: the optimizer depends on the return covariance matrix after projection through the local policy-gradient geometry. We introduce observation-safe counterfactual coupling (OSCC), a framework that defines an admissible class through marginal preservation, information-state safety, branch-local policy randomness, semantic event alignment, and trace-before-oracle replay. We derive a gradient-aware coupling criterion showing that, for marginal-preserving couplings, policy-gradient noise changes are determined by policy-Jacobian-weighted off-diagonal return covariance. This motivates OSCC-Select, a calibration-only selector that chooses among independent, root-only, continuation-only, and fully coupled rollouts using separate safety and gain certificates. Its gain target combines projected gradient noise with measured physical sampling cost and falls back to independent sampling whenever a simultaneous lower confidence bound does not certify improvement. On 100,000 fixed-root Leduc comparisons, the fully coupled CP-GRPO instantiation reduces return-contrast variance from 41.1158 to 18.1441, a 55.87% reduction, while preserving the declared branch marginals. With three actions, OSCC-Select chooses continuation coupling and attains gradient-noise trace 0.0783 versus 0.0917 for return-variance selection. Increasing calibration from 64 to 2,048 groups raises certification from 0.327 to 0.995.

Large language model (LLM) serving is increasingly constrained by the GPU memory consumed by key-value (KV) caches. Existing compression, eviction, and offloading techniques alleviate this pressure, but serving runtimes typically treat only the configured target KV representation as execution-ready. Under memory pressure, this target-only contract can turn KV shortage into request stalls and preemptions. We present ElasticKV, a mixed-fidelity KV runtime built on the observation that target fidelity need not gate execution. ElasticKV introduces a compact intermediate KV state, making fidelity a runtime-managed execution property. To realize this state in a paged serving runtime, ElasticKV combines (i) a pair-structured layout that turns fidelity reduction into reusable GPU capacity, (ii) a dual-mode attention backend that directly consumes the compact state while preserving the native target-only path, and (iii) pressure-aware fidelity management that adapts KV fidelity to memory pressure. Our extensive evaluation across diverse workloads, model families and scales, and GPU platforms demonstrates the effectiveness and generality of ElasticKV. Under high concurrency, ElasticKV achieves 3.8-4.0$\times$ lower time-to-first-token (TTFT) and 9.1$\times$ lower P90 TTFT than vLLM while preserving generation quality.

Transformers have emerged as powerful architectures for learning solution operators of physical systems. Empirically the prediction error has been observed to decrease when the data size and model size increase, suggesting neural scaling behavior. Yet a theoretical understanding of such scaling laws for transformer-based operator learning remains limited. In this work, we develop a theoretical framework for characterizing the approximation and generalization errors of transformer-based operator learning. Our analysis builds on a local-to-global approximation principle that is naturally aligned with the softmax attention mechanism and yields discretization-invariant output functions. On approximation theory, we derive a universal approximation error of transformer-based operator learning for Hölder-regular operators. On generalization theory, we establish a power scaling law between the prediction error and the training data size. The rate of convergence represented by the scaling exponent explicitly reflects the dimensions of the input and output domains, the regularity of the underlying functions and operators, and crucially, the intrinsic dimension of the input function class. By exploiting this intrinsic low-dimensional structure, our analysis yields a power-law generalization rate for operator learning, in contrast to the logarithmic-type power-law rates appearing in existing analyses of operator learning with feedforward neural networks. Numerical experiments validate the predicted power-law scaling and confirm that the convergence rate varies systematically with the intrinsic dimension of the input function class.

Natural Language Understanding (NLU) plays a crucial role in various applications, yet its performance suffers from weaknesses in handling the complexities of human languages, ranging from lexical ambiguity to high-level reasoning difficulties. Analyzing errors across diverse linguistic phenomena is crucial for NLU improvement, as it will help humans get insights to comprehensively assess models' limitations and capabilities, so optimizing models' generalization. Notably, several benchmarks contain diagnostics datasets designed for investigation and fine-grained error analysis. When highlighting the gaps in the state-of-the-art, we noted that there is no naming convention for macro and micro categories or even a standard set of linguistic phenomena that should be covered. To overcome this gap, we propose an initial hierarchy for Cross-Lingual NLU error analysis. Moreover, we propose a methodology to create an NLI hierarchical framework and applied a case study on Arabic NLU. Moreover, this paper introduces E-CONAN diagnostics dataset, a freely available dataset manually-annotated with coarse-grained and fine-grained categories based on our proposed Arabic hierarchy. E-CONAN dataset helps NLU designers better understand their models by doing error analysis and in-depth investigation. We used E-CONAN to investigate the performance of 9 pretrained language models and 5 LLMs. Results indicate that LLMs outperform pretrained models in world knowledge and commonsense reasoning macro-category, and underperform pretrained models in syntactic macro-category. Moreover, the hardest phenomena for all models is Reasoning, and the easiest phenomena for all pretrained models is Syntactic, and the easiest for LLMs is Lexico-Syntactic.

Parameter space symmetries are important for understanding neural networks' loss landscape, training dynamics, and generalization. However, systematically identifying these symmetries remains a challenge. In this paper, we formalize data-dependent parameter symmetries and characterize loss invariance and the group-action axioms through infinitesimal conditions, which provide objectives for jointly learning group generators and nonlinear action maps. Our framework systematically uncovers parameter symmetries, including previously unknown ones. To study larger networks, we establish conditions under which subnetwork symmetries extend to the full model. The same construction gives an explicit family of finite-batch symmetries, providing both analytical examples and a foundation for discovery through small subnetworks. Using the infinitesimal characterization and subnetwork construction, we implement a framework for automated discovery of parameter symmetries, and successfully uncovered symmetries in various architectures, including pretrained transformer models.

Trust evaluation plays a critical role in cybersecurity by supporting risk mitigation and decision-making. A variety of trust evaluation methods have been proposed, with learning-based approaches offering high accuracy and automation. However, they often require substantial ground truth, suffer from low training efficiency, lack support for basic trust properties, and provide limited explainability. Large Language Models (LLMs) offer a compelling alternative due to their strong zero-/few-shot reasoning abilities and broad knowledge. To this end, we propose LLM4Trust, the first benchmark framework that systematically explores the capabilities of LLMs for trust evaluation. We first construct diverse trust graphs to model five basic trust properties and design corresponding property understanding tasks. We then assess the ability of eight representative LLMs to understand these properties under nine prompt methods. Based on this exploration, we identify the most effective LLM-prompt combinations and apply them to five real-world datasets for validating LLMs' trust evaluation capability. During this process, we propose two strategies to extract key information from large-scale trust graphs, addressing the context window limitations of LLMs. Extensive experiments show that LLMs can effectively understand basic trust properties and have great potential for real-world trust evaluation, particularly under limited supervision. However, they remain vulnerable to attacks targeting trust graphs and demonstration examples used in few-shot prompting, and incur high inference costs. Accordingly, we propose a defense mechanism and batch inference to improve the robustness and efficiency of LLM-based trust evaluation. The source code of LLM4Trust is available at https://github.com/Jieerbobo/LLM4Trust

Many probabilistic predictors must satisfy exact structure in every stochastic realization, yet common hard-constraint approaches form predictions in ambient coordinates and then correct or project them. We introduce SLP-ProbHard, a cross-family, representation-centered framework for probabilistic hard-constrained learning when explicit structural parameterizations are available. Its core object, a Structural Feasible Latent Parameterization (SFLP), combines a structural latent law $Z \sim P^Z_\theta(\cdot\mid x)$ with a feasible map $Y=h_\phi(x,Z)$ that satisfies the constraint for every latent realization. Together these components define the predictive law itself, including its support and boundary probabilities, rather than serving as a final feasibility wrapper. We study how feasible coordinates and maps affect stochastic dimension, dependence, calibration, expressiveness, and computation. Experiments use Gaussian latent laws and fixed geometry-derived maps across affine equalities, ordering and simplex constraints, nonlinear manifolds, and three structural representations of seven-basin hydrological flow-duration-curve (FDC) data. In an official-source affine comparison with ProbHardE2E/DPPL, both methods achieve zero practical constraint violations. SLP-ProbHard uses 8 instead of 11 stochastic coordinates and improves MSE/MAE, while DPPL yields better marginal CRPS and closer-to-nominal coverage; a paired test detects no Energy Score difference across ten seeds. Real-world affine and nonlinear FDC representations reduce 13 to 7 and 14 to 8 ambient versus computational coordinates, respectively. Exact feasibility alone thus does not determine a predictive law, motivating direct structural generation when meaningful feasible coordinates are available.

Deep generative models are used to solve partial differential equations and model distributions of physical system states, but ensuring that the generated samples satisfy the governing laws remains challenging. Projection-based flow-matching methods enforce physics by correcting the flow from an unconstrained noise distribution. These corrections shift the generated samples away from the distribution of target solutions, especially in high noise regions. To address this limitation, we propose Source Anchoring for Physical Consistency (SAPC), a Functional Flow Matching method that encodes the physical constraints into the source noise before generation begins. We evaluate SAPC on five systems governed by partial differential equations, covering six tasks with linear and non-linear dynamics, and compare results against five baselines and the unconstrained backbone. Anchoring the source reduces the need for large corrections that drive samples onto admissible but off-distribution states, and SAPC reproduces the target distributions most accurately on every evaluated task, while matching the constraint precision of the best projection-based baselines. Ablation experiments show that this gain arises from pairing source projection with a matched training objective that regresses toward the projected source. These results identify the source distribution as a key design choice for physically consistent generative modelling.