Daily Papers

Vision-Language-Action (VLA) models enable instruction-following embodied control, but their large compute and memory footprints hinder deployment on resource-constrained robots and edge platforms. While reducing weights to 1-bit precision through binarization can greatly improve efficiency, existing methods fail to narrow the distribution gap between binarized and full-precision weights, causing quantization errors to accumulate under long-horizon closed-loop execution and severely degrade actions. To fill this gap, we propose HBVLA, a VLA-tailored binarization framework. First, we use a policy-aware enhanced Hessian to identify weights that are truly critical for action generation. Then, we employ a sparse orthogonal transform for non-salient weights to induce a low-entropy intermediate state. Finally, we quantize both salient and non-salient weights in the Harr domain with group-wise 1-bit quantization. We have evaluated our approach on different VLAs: on LIBERO, quantized OpenVLA-OFT retains 92.2% of full-precision performance; on SimplerEnv, quantized CogAct retains 93.6%, significantly outperforming state-of-the-art binarization methods. We further validate our method on real-world evaluation suite and the results show that HBVLA incurs only marginal success-rate degradation compared to the full-precision model, demonstrating robust deployability under tight hardware constraints. Our work provides a practical foundation for ultra-low-bit quantization of VLAs, enabling more reliable deployment on hardware-limited robotic platforms.

Large Language Models (LLMs) with multimodal capabilities have revolutionized vision-language tasks, but their deployment often requires huge memory and computational resources. While post-training quantization (PTQ) has successfully compressed language models to as low as 1-bit precision without significant performance loss, its effectiveness for multimodal LLMs (MLLMs) remains relatively unexplored. In this paper, we present the first study on ultra-low bit (<4-bit) quantization for multimodal LLMs. Our analysis reveals that multimodal tokens and intermediate layer activations produced by them exhibit significantly higher statistical variance and entropy compared to text tokens, making them less tolerant to ultra-low bit quantization. However, the activation distributions of multimodal tokens varies significantly over different layers, with some layers having lower entropy activation distributions. We empirically show that such layers in these models can better tolerate ultra-low bit quantization. Building on these insights, we propose a novel strategy for MLLM quantization, LUQ: Layerwise Ultra-Low Bit Quantization, which selectively applies ultra-low bit quantization to layers that are more resilient to it. Additionally, we also show that using a mix of multimodal tokens (image and text) for PTQ boosts VQA performance in the ultra-low bit regime. We evaluate our method on LLaVA-1.5 and Qwen-2.5-VL across 9 popular VQA benchmarks. The resulting LUQ models use 40% and 31% less memory than their 4-bit counterparts, respectively, while exhibiting a performance degradation of less than 10% on the MME benchmark.

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time via Hamiltonian dynamics. Its entropy, at any time t, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time t. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells Δ_α. The initial and final macrostates of the system are equilibrium states in volumes V and 2V, with the same energy E and particle number N. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the Δ_α. The intermediate (non-equilibrium) entropy does however depend on the size of the cells Δ_α. Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining Δv: it produces entropy at a rate proportional to Δv. This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of Δv and is given by the Boltzmann equation for the limit Δvrightarrow 0. We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes.

This paper studies generative flow networks (GFlowNets) to sample objects from the Boltzmann energy distribution via a sequence of actions. In particular, we focus on improving GFlowNet with partial inference: training flow functions with the evaluation of the intermediate states or transitions. To this end, the recently developed forward-looking GFlowNet reparameterizes the flow functions based on evaluating the energy of intermediate states. However, such an evaluation of intermediate energies may (i) be too expensive or impossible to evaluate and (ii) even provide misleading training signals under large energy fluctuations along the sequence of actions. To resolve this issue, we propose learning energy decompositions for GFlowNets (LED-GFN). Our main idea is to (i) decompose the energy of an object into learnable potential functions defined on state transitions and (ii) reparameterize the flow functions using the potential functions. In particular, to produce informative local credits, we propose to regularize the potential to change smoothly over the sequence of actions. It is also noteworthy that training GFlowNet with our learned potential can preserve the optimal policy. We empirically verify the superiority of LED-GFN in five problems including the generation of unstructured and maximum independent sets, molecular graphs, and RNA sequences.

In this paper I apply newly-proposed information-theoretic principles to thermodynamic work extraction. I show that if it is possible to extract work deterministically from a physical system prepared in any one of a set of states, then those states must be distinguishable from one another. This result is formulated independently of scale and of particular dynamical laws; it also provides a novel connection between thermodynamics and information theory, established via the law of conservation of energy (rather than the second law of thermodynamics). Albeit compatible with these conclusions, existing thermodynamics approaches cannot provide a result of such generality, because they are scale-dependent (relying on ensembles or coarse-graining) or tied to particular dynamical laws. This paper thus provides a broader foundation for thermodynamics, with implications for the theory of von Neumann's universal constructor

In this paper, we examine the thermodynamic behavior of a quantum harmonic oscillator with a position-dependent mass (PDM), where spatial inhomogeneity is modeled through a deformation parameter α. Based on the exact energy spectrum, we explore the resulting thermodynamic quantities and superstatistics. Our findings reveal that increasing α leads to a decrease in entropy and specific heat, reflecting a confinement-induced reduction in the number of accessible states. The partition function and free energy exhibit smooth behavior across all parameter regimes, indicating the absence of critical phase transitions. This study underscores the influence of mass deformation on quantum thermal responses and demonstrates that, while the overall thermodynamic trends are consistent with those reported in the literature, certain distinctive features emerge due to the specific form of the deformation.

The final state interactions (FSI) model in which soft rescattering of low mass intermediate states dominates is suggested. It explains why the strong interaction phases are large in the B_dtopipi channel and are considerably smaller in the B_dtorhorho one. Direct CP asymmetries of B_dtopipi decays which are determined by FSI phases are considered as well.

Large Reasoning Models (LRMs) have recently achieved strong mathematical and code reasoning performance through Reinforcement Learning (RL) post-training. However, we show that modern reasoning post-training induces an unintended exploration collapse: temperature-based sampling no longer increases pass@n accuracy. Empirically, the final-layer posterior of post-trained LRMs exhibit sharply reduced entropy, while the entropy of intermediate layers remains relatively high. Motivated by this entropy asymmetry, we propose Latent Exploration Decoding (LED), a depth-conditioned decoding strategy. LED aggregates intermediate posteriors via cumulative sum and selects depth configurations with maximal entropy as exploration candidates. Without additional training or parameters, LED consistently improves pass@1 and pass@16 accuracy by 0.61 and 1.03 percentage points across multiple reasoning benchmarks and models. Project page: https://GitHub.com/Xiaomi-Research/LED.

We present a comprehensive numerical study of a six-state clock model with a long-range dipolar type interaction. This model is motivated by the ferroelectric orders in the multiferroic hexagonal manganites. At low temperatures, trimerization of local atomic structures leads to six distinct but energetically degenerate structural distortion, which can be modeled by a six-state clock model. Moreover, the atomic displacements in the trimerized state further produce a local electric polarization whose sign depends on whether the clock variable is even or odd. These induced electric dipoles, which can be modeled by emergent Ising degrees of freedom, interact with each other via long-range dipolar interactions. Extensive Monte Carlo simulations are carried out to investigate low temperature phases resulting from the competing interactions. Upon lowering temperature, the system undergoes two Berezinskii-Kosterlitz-Thouless (BKT) transitions, characteristic of the standard six-state clock model in two dimensions. The dipolar interaction between emergent Ising spins induces a first-order transition into a ground state characterized by a three-fold degenerate stripe order. The intermediate phase between the discontinuous and the second BKT transition corresponds to a maze-like hexagonal liquid with short-range stripe ordering. Moreover, this intermediate phase also exhibits an unusual ferromagnetic order with two adjacent clock variables occupying the two types of stripes of the labyrinthine pattern.

This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.

Latent Chain-of-Thought (Latent-CoT) aims to enable step-by-step computation without emitting long rationales, yet its mechanisms remain unclear. We study CODI, a continuous-thought teacher-student distillation model, on strictly sequential polynomial-iteration tasks. Using logit-lens decoding, linear probes, attention analysis, and activation patching, we localize intermediate-state representations and trace their routing to the final readout. On two- and three-hop tasks, CODI forms the full set of bridge states that become decodable across latent-thought positions, while the final input follows a separate near-direct route; predictions arise via late fusion at the end-of-thought boundary. For longer hop lengths, CODI does not reliably execute a full latent rollout, instead exhibiting a partial latent reasoning path that concentrates on late intermediates and fuses them with the last input at the answer readout position. Ablations show that this partial pathway can collapse under regime shifts, including harder optimization. Overall, we delineate when CODI-style latent-CoT yields faithful iterative computation versus compressed or shortcut strategies, and highlight challenges in designing robust latent-CoT objectives for sequential reasoning.

Large language models (LLMs) can be adapted to new tasks using parameter-efficient fine-tuning (PEFT) methods that modify only a small number of trainable parameters, often through low-rank updates. In this work, we adopt a quantum-information-inspired perspective to understand their effectiveness. From this perspective, low-rank parameterizations naturally correspond to low-dimensional Matrix Product States (MPS) representations, which enable entanglement-based characterizations of parameter structure. Thereby, we term and measure "Artificial Entanglement", defined as the entanglement entropy of the parameters in artificial neural networks (in particular the LLMs). We first study the representative low-rank adaptation (LoRA) PEFT method, alongside full fine-tuning (FFT), using LLaMA models at the 1B and 8B scales trained on the Tulu3 and OpenThoughts3 datasets, and uncover: (i) Internal artificial entanglement in the updates of query and value projection matrices in LoRA follows a volume law with a central suppression (termed as the "Entanglement Valley"), which is sensitive to hyper-parameters and is distinct from that in FFT; (ii) External artificial entanglement in attention matrices, corresponding to token-token correlations in representation space, follows an area law with logarithmic corrections and remains robust to LoRA hyper-parameters and training steps. Drawing a parallel to the No-Hair Theorem in black hole physics, we propose that although LoRA and FFT induce distinct internal entanglement signatures, such differences do not manifest in the attention outputs, suggesting a "no-hair" property that results in the effectiveness of low rank updates. We further provide theoretical support based on random matrix theory, and extend our analysis to an MPS Adaptation PEFT method, which exhibits qualitatively similar behaviors.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids ("coffee" and "cream"). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton's state, which we dub the "apparent complexity." We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the "coffee cup's" horizontal dimension. We raise the problem of proving this behavior analytically.

Existing reinforcement learning (RL) approaches treat large language models (LLMs) as a single unified policy, overlooking their internal mechanisms. Understanding how policy evolves across layers and modules is therefore crucial for enabling more targeted optimization and raveling out complex reasoning mechanisms. In this paper, we decompose the language model policy by leveraging the intrinsic split of the Transformer residual stream and the equivalence between the composition of hidden states with the unembedding matrix and the resulting samplable policy. This decomposition reveals Internal Layer Policies, corresponding to contributions from individual layers, and Internal Modular Policies, which align with the self-attention and feed-forward network (FFN) components within each layer. By analyzing the entropy of internal policy, we find that: (a) Early layers keep high entropy for exploration, top layers converge to near-zero entropy for refinement, with convergence patterns varying across model series. (b) LLama's prediction space rapidly converges in the final layer, whereas Qwen-series models, especially Qwen3, exhibit a more human-like, progressively structured reasoning pattern. Motivated by these findings, we propose Bottom-up Policy Optimization (BuPO), a novel RL paradigm that directly optimizes the internal layer policy during early training. By aligning training objective at lower layer, BuPO reconstructs foundational reasoning capabilities and achieves superior performance. Extensive experiments on complex reasoning benchmarks demonstrates the effectiveness of our method. Our code is available at https://github.com/Trae1ounG/BuPO.

We introduce a modern Hopfield network with continuous states and a corresponding update rule. The new Hopfield network can store exponentially (with the dimension of the associative space) many patterns, retrieves the pattern with one update, and has exponentially small retrieval errors. It has three types of energy minima (fixed points of the update): (1) global fixed point averaging over all patterns, (2) metastable states averaging over a subset of patterns, and (3) fixed points which store a single pattern. The new update rule is equivalent to the attention mechanism used in transformers. This equivalence enables a characterization of the heads of transformer models. These heads perform in the first layers preferably global averaging and in higher layers partial averaging via metastable states. The new modern Hopfield network can be integrated into deep learning architectures as layers to allow the storage of and access to raw input data, intermediate results, or learned prototypes. These Hopfield layers enable new ways of deep learning, beyond fully-connected, convolutional, or recurrent networks, and provide pooling, memory, association, and attention mechanisms. We demonstrate the broad applicability of the Hopfield layers across various domains. Hopfield layers improved state-of-the-art on three out of four considered multiple instance learning problems as well as on immune repertoire classification with several hundreds of thousands of instances. On the UCI benchmark collections of small classification tasks, where deep learning methods typically struggle, Hopfield layers yielded a new state-of-the-art when compared to different machine learning methods. Finally, Hopfield layers achieved state-of-the-art on two drug design datasets. The implementation is available at: https://github.com/ml-jku/hopfield-layers

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) for Large Language Model (LLM) reasoning have been hindered by a persistent challenge: exploration collapse. The semantic homogeneity of random rollouts often traps models in narrow, over-optimized behaviors. While existing methods leverage policy entropy to encourage exploration, they face inherent limitations. Global entropy regularization is susceptible to reward hacking, which can induce meaningless verbosity, whereas local token-selective updates struggle with the strong inductive bias of pre-trained models. To address this, we propose Latent Policy Optimization via Iterative Information Bottleneck (IIB-LPO), a novel approach that shifts exploration from statistical perturbation of token distributions to topological branching of reasoning trajectories. IIB-LPO triggers latent branching at high-entropy states to diversify reasoning paths and employs the Information Bottleneck principle both as a trajectory filter and a self-reward mechanism, ensuring concise and informative exploration. Empirical results across four mathematical reasoning benchmarks demonstrate that IIB-LPO achieves state-of-the-art performance, surpassing prior methods by margins of up to 5.3% in accuracy and 7.4% in diversity metrics.

Long short-term memory (LSTM) is a kind of recurrent neural networks (RNN) for sequence and temporal dependency data modeling and its effectiveness has been extensively established. In this work, we propose a hybrid quantum-classical model of LSTM, which we dub QLSTM. We demonstrate that the proposed model successfully learns several kinds of temporal data. In particular, we show that for certain testing cases, this quantum version of LSTM converges faster, or equivalently, reaches a better accuracy, than its classical counterpart. Due to the variational nature of our approach, the requirements on qubit counts and circuit depth are eased, and our work thus paves the way toward implementing machine learning algorithms for sequence modeling on noisy intermediate-scale quantum (NISQ) devices.

The Sachdev-Ye-Kitaev (SYK) model, known for its strong quantum correlations and chaotic behavior, serves as a key platform for quantum gravity studies. However, variationally preparing thermal states on near-term quantum processors for large systems (N>12, where N is the number of Majorana fermions) presents a significant challenge due to the rapid growth in the complexity of parameterized quantum circuits. This paper addresses this challenge by integrating reinforcement learning (RL) with convolutional neural networks, employing an iterative approach to optimize the quantum circuit and its parameters. The refinement process is guided by a composite reward signal derived from entropy and the expectation values of the SYK Hamiltonian. This approach reduces the number of CNOT gates by two orders of magnitude for systems Ngeq12 compared to traditional methods like first-order Trotterization. We demonstrate the effectiveness of the RL framework in both noiseless and noisy quantum hardware environments, maintaining high accuracy in thermal state preparation. This work advances a scalable, RL-based framework with applications for quantum gravity studies and out-of-time-ordered thermal correlators computation in quantum many-body systems on near-term quantum hardware. The code is available at https://github.com/Aqasch/solving_SYK_model_with_RL.

We prove theoretically that generalization improves not only through data scaling but also by compressing internal representations. To operationalize this insight, we introduce the Information Bottleneck Language Modeling (IBLM) objective, which reframes language modeling as a constrained optimization problem: minimizing representation entropy subject to optimal prediction performance. Empirically, we observe an emergent memorization-compression cycle during LLM pretraining, evidenced by oscillation positive/negative gradient alignment between cross-entropy and Matrix-Based Entropy (MBE), a measure of representation entropy. This pattern closely mirrors the predictive-compressive trade-off prescribed by IBLM and also parallels the biological alternation between awake learning and sleep consolidation. Motivated by this observation, we propose Gated Phase Transition (GAPT), a training algorithm that adaptively switches between memorization and compression phases. When applied to GPT-2 pretraining on FineWeb dataset, GAPT reduces MBE by 50% and improves cross-entropy by 4.8%. GAPT improves OOD generalizatino by 35% in a pretraining task on arithmetic multiplication. In a setting designed to simulate catastrophic forgetting, GAPT reduces interference by compressing and separating representations, achieving a 97% improvement in separation - paralleling the functional role of sleep consolidation.

We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.

Generative Flow Networks or GFlowNets are related to Monte-Carlo Markov chain methods (as they sample from a distribution specified by an energy function), reinforcement learning (as they learn a policy to sample composed objects through a sequence of steps), generative models (as they learn to represent and sample from a distribution) and amortized variational methods (as they can be used to learn to approximate and sample from an otherwise intractable posterior, given a prior and a likelihood). They are trained to generate an object x through a sequence of steps with probability proportional to some reward function R(x) (or exp(-E(x)) with E(x) denoting the energy function), given at the end of the generative trajectory. Like for other RL settings where the reward is only given at the end, the efficiency of training and credit assignment may suffer when those trajectories are longer. With previous GFlowNet work, no learning was possible from incomplete trajectories (lacking a terminal state and the computation of the associated reward). In this paper, we consider the case where the energy function can be applied not just to terminal states but also to intermediate states. This is for example achieved when the energy function is additive, with terms available along the trajectory. We show how to reparameterize the GFlowNet state flow function to take advantage of the partial reward already accrued at each state. This enables a training objective that can be applied to update parameters even with incomplete trajectories. Even when complete trajectories are available, being able to obtain more localized credit and gradients is found to speed up training convergence, as demonstrated across many simulations.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

Training LLM agents in multi-turn environments with sparse rewards, where completing a single task requires 30+ turns of interaction within an episode, presents a fundamental challenge for reinforcement learning. We identify a critical failure mode unique to this setting: the exploration-exploitation cascade failure. This cascade begins with early-stage policy premature convergence, where sparse feedback causes agents to commit to flawed, low-entropy strategies. Subsequently, agents enter late-stage policy collapse, where conventional entropy regularization becomes counterproductive, promoting chaotic exploration that destabilizes training. We propose Entropy-regularized Policy Optimization (EPO), a general framework that breaks this failure cycle through three synergistic mechanisms: (1) adopting entropy regularization in multi-turn settings to enhance exploration, (2) an entropy smoothing regularizer that bounds policy entropy within historical averages to prevent abrupt fluctuations, and (3) adaptive phase-based weighting that balances exploration and exploitation across training. Our analysis justifies that EPO guarantees monotonically decreasing entropy variance while maintaining convergence. EPO achieves up to 152% performance improvement on ScienceWorld and up to 19.8% on ALFWorld. Our work demonstrates that multi-turn sparse-reward settings require fundamentally different entropy control than traditional RL, with broad implications for LLM agent training.

Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid premature convergence to sub-optimal solutions. However, existing reinforcement learning methods struggle to maintain an appropriate level of entropy, as the training process involves a mix of positive and negative samples, each affecting entropy in different ways across steps. To address this, we propose Entropy stablilization via Proportional-Integral Control (EntroPIC), a novel method that adaptively adjusts the influence of positive and negative samples by dynamically tuning their loss coefficients. This approach stabilizes entropy throughout training, ensuring efficient exploration and steady progress. We provide a comprehensive theoretical analysis for both on-policy and off-policy learning settings, demonstrating that EntroPIC is effective at controlling entropy in large-scale LLM training. Experimental results show that our method successfully maintains desired entropy levels, enabling stable and optimal RL training for LLMs.

We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

This paper aims to overcome a major obstacle in scaling RL for reasoning with LLMs, namely the collapse of policy entropy. Such phenomenon is consistently observed across vast RL runs without entropy intervention, where the policy entropy dropped sharply at the early training stage, this diminished exploratory ability is always accompanied with the saturation of policy performance. In practice, we establish a transformation equation R=-a*e^H+b between entropy H and downstream performance R. This empirical law strongly indicates that, the policy performance is traded from policy entropy, thus bottlenecked by its exhaustion, and the ceiling is fully predictable H=0, R=-a+b. Our finding necessitates entropy management for continuous exploration toward scaling compute for RL. To this end, we investigate entropy dynamics both theoretically and empirically. Our derivation highlights that, the change in policy entropy is driven by the covariance between action probability and the change in logits, which is proportional to its advantage when using Policy Gradient-like algorithms. Empirical study shows that, the values of covariance term and entropy differences matched exactly, supporting the theoretical conclusion. Moreover, the covariance term stays mostly positive throughout training, further explaining why policy entropy would decrease monotonically. Through understanding the mechanism behind entropy dynamics, we motivate to control entropy by restricting the update of high-covariance tokens. Specifically, we propose two simple yet effective techniques, namely Clip-Cov and KL-Cov, which clip and apply KL penalty to tokens with high covariances respectively. Experiments show that these methods encourage exploration, thus helping policy escape entropy collapse and achieve better downstream performance.

Low-mass X-ray binaries with a neutron star as the primary object show a complex array of phenomenology during outbursts. The observed variability in X-ray emission primarily arises from changes in the innermost regions of the accretion disk, neutron star surface, and corona. In this work, we present the results of a comprehensive X-ray spectral and timing analysis of the neutron star transient MAXI J1807+132 during its 2023 outburst using data from the NICER observatory. The outburst is marked by a very rapid rise in the count rate by about a factor of 20 in a day. The source undergoes full state transitions and displays hysteresis effect in the hardness and rms intensity diagrams. Spectral analysis with a three-component model is consistent with disk truncation during the hard states and reaching the last stable orbit during the intermediate and soft states. We discuss the different values of the last stable radius in the context of possible distance of the source and magnetic field strength. The characteristic frequencies throughout the hard and intermediate states are found to be strongly correlated with the inner radius of the disk. Together with the spectral and fast variability properties, we attempt to trace the evolution of the size of the corona along the outburst. Following the main outburst, the source undergoes a high amplitude reflare wherein it shows a complex behavior with relatively high variability (10 %), but low hardness.

State-of-the-art language generation models can degenerate when applied to open-ended generation problems such as text completion, story generation, or dialog modeling. This degeneration usually shows up in the form of incoherence, lack of vocabulary diversity, and self-repetition or copying from the context. In this paper, we postulate that ``human-like'' generations usually lie in a narrow and nearly flat entropy band, and violation of these entropy bounds correlates with degenerate behavior. Our experiments show that this stable narrow entropy zone exists across models, tasks, and domains and confirm the hypothesis that violations of this zone correlate with degeneration. We then use this insight to propose an entropy-aware decoding algorithm that respects these entropy bounds resulting in less degenerate, more contextual, and "human-like" language generation in open-ended text generation settings.

From the dynamics of a broad class of classical mean-field glass models one may obtain a quantum model with finite zero-temperature entropy, a quantum transition at zero temperature, and a time-reparametrization (quasi-)invariance in the dynamical equations for correlations. The low eigenvalue spectrum of the resulting quantum model is directly related to the structure and exploration of metastable states in the landscape of the original classical glass model. This mapping reveals deep connections between classical glasses and the properties of SYK-like models.

Large language models (LLMs) are increasingly considered as tutoring aids in science education. Yet their readiness for unsupervised use in undergraduate instruction remains uncertain, as reliable teaching requires more than fluent recall: it demands consistent, principle-grounded reasoning. Thermodynamics, with its compact laws and subtle distinctions between state and path functions, reversibility, and entropy, provides an ideal testbed for evaluating such capabilities. Here we present UTQA, a 50-item undergraduate thermodynamics question answering benchmark, covering ideal-gas processes, reversibility, and diagram interpretation. No leading 2025-era model exceeded our 95\% competence threshold: the best LLMs achieved 82\% accuracy, with text-only items performing better than image reasoning tasks, which often fell to chance levels. Prompt phrasing and syntactic complexity showed modest to little correlation with performance. The gap concentrates in finite-rate/irreversible scenarios and in binding visual features to thermodynamic meaning, indicating that current LLMs are not yet suitable for unsupervised tutoring in this domain.

This paper explores the relationship between the condition number of a neural network's weight tensor and the extent of information encoded by the associated processing unit, viewed through the lens of information theory. It argues that a high condition number, though not sufficient for effective knowledge encoding, may indicate that the unit has learned to selectively amplify and compress information. This intuition is formalized for linear units with Gaussian inputs, linking the condition number and the transformation's log-volume scaling factor to the characteristics of the output entropy and the geometric properties of the learned transformation. The analysis demonstrates that for a fixed weight norm, a concentrated distribution of singular values (high condition number) corresponds to reduced overall information transfer, indicating a specialized and efficient encoding strategy. Furthermore, the linear stage entropy bound provides an upper limit on post-activation information for contractive, element-wise nonlinearities, supporting the condition number as a scale-invariant proxy for encoding capacity in practical neural networks. An empirical case study applies these principles to guide selective fine-tuning of Large Language Models for both a new task and a new input modality. The experiments show that the proposed method, named KappaTune, effectively mitigates catastrophic forgetting. Unlike many existing catastrophic forgetting mitigation methods that rely on access to pre-training statistics, which are often unavailable, this selective fine-tuning approach offers a way to bypass this common requirement.

The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we interpret the resulting training dynamics and the phase transitions that characterize different trajectories? To understand the effect of randomness on the dynamics and outcomes of neural network training, we train models multiple times with different random seeds and compute a variety of metrics throughout training, such as the L_2 norm, mean, and variance of the neural network's weights. We then fit a hidden Markov model (HMM) over the resulting sequences of metrics. The HMM represents training as a stochastic process of transitions between latent states, providing an intuitive overview of significant changes during training. Using our method, we produce a low-dimensional, discrete representation of training dynamics on grokking tasks, image classification, and masked language modeling. We use the HMM representation to study phase transitions and identify latent "detour" states that slow down convergence.

It has been well-known that Chain-of-Thought can remarkably enhance LLMs' performance on complex tasks. However, because it also introduces slower inference speeds and higher computational costs, many researches have attempted to use implicit CoT, which does not need LLMs to explicitly generate the intermediate steps. But there is still gap between their efficacy and typical explicit CoT methods. This leaves us a doubt that, does implicit CoT really equal to explicit CoT? Therefore, in this study, we address this question through experiments. We probe the information of intermediate steps from the model's hidden states when it is performing implicit CoT. The results surprisingly indicate that LLMs hardly think about intermediate steps, suggesting they may just rely on experience rather than strict step-by-step reasoning. Moreover, we find LLMs' implicit reasoning capabilities are susceptible and unstable, reaffirming the necessity of explicit CoT to effectively support complex tasks.

Integrating and processing information from various sources or modalities are critical for obtaining a comprehensive and accurate perception of the real world in autonomous systems and cyber-physical systems. Drawing inspiration from neuroscience, we develop the Information-Theoretic Hierarchical Perception (ITHP) model, which utilizes the concept of information bottleneck. Different from most traditional fusion models that incorporate all modalities identically in neural networks, our model designates a prime modality and regards the remaining modalities as detectors in the information pathway, serving to distill the flow of information. Our proposed perception model focuses on constructing an effective and compact information flow by achieving a balance between the minimization of mutual information between the latent state and the input modal state, and the maximization of mutual information between the latent states and the remaining modal states. This approach leads to compact latent state representations that retain relevant information while minimizing redundancy, thereby substantially enhancing the performance of multimodal representation learning. Experimental evaluations on the MUStARD, CMU-MOSI, and CMU-MOSEI datasets demonstrate that our model consistently distills crucial information in multimodal learning scenarios, outperforming state-of-the-art benchmarks. Remarkably, on the CMU-MOSI dataset, ITHP surpasses human-level performance in the multimodal sentiment binary classification task across all evaluation metrics (i.e., Binary Accuracy, F1 Score, Mean Absolute Error, and Pearson Correlation).

Visual-Interleaved Chain-of-Thought (VI-CoT) enables MLLMs to continually update their understanding and decisions based on step-wise intermediate visual states (IVS), much like a human would, which demonstrates impressive success in various tasks, thereby leading to emerged advancements in related benchmarks. Despite promising progress, current benchmarks provide models with relatively fixed IVS, rather than free-style IVS, whch might forcibly distort the original thinking trajectories, failing to evaluate their intrinsic reasoning capabilities. More importantly, existing benchmarks neglect to systematically explore the impact factors that IVS would impart to untamed reasoning performance. To tackle above gaps, we introduce a specialized benchmark termed ViC-Bench, consisting of four representive tasks: maze navigation, jigsaw puzzle, embodied long-horizon planning, and complex counting, where each task has dedicated free-style IVS generation pipeline supporting function calls. To systematically examine VI-CoT capability, we propose a thorough evaluation suite incorporating a progressive three-stage strategy with targeted new metrics. Besides, we establish Incremental Prompting Information Injection (IPII) strategy to ablatively explore the prompting factors for VI-CoT. We extensively conduct evaluations for 18 advanced MLLMs, revealing key insights into their VI-CoT capability. Our proposed benchmark is publicly open at Huggingface.

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the Generalized Gibbs Ensemble description for this infinite dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve towards the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a Generalized Gibbs Ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states which would potentially not be described by the Gibbs Generalized Ensemble description.

We introduce Psi-Turing Machines (Psi-TM): classical Turing machines equipped with a constant-depth introspection interface iota and an explicit per-step information budget B(d,n)=c,dlog_2 n . With the interface frozen, we develop an information-theoretic lower-bound toolkit: Budget counting, Psi -Fooling, and Psi -Fano, with worked examples L_k and L_k^{phase} . We prove an oracle-relative separation P^{Psi} neq NP^{Psi} and a strict depth hierarchy, reinforced by an Anti-Simulation Hook that rules out polynomial emulation of iota_k using many calls to iota_{k-1} under the budget regime. We also present two independent platforms (Psi-decision trees and interface-constrained circuits IC-AC^{0}/IC-NC^{1}) and bridges that transfer bounds among machine, tree, and circuit with explicit poly/log losses. The model preserves classical computational power outside iota yet enables precise oracle-aware statements about barriers (relativization; partial/conditional progress on natural proofs and proof complexity). The aim is a standardized minimal introspection interface with clearly accounted information budgets.

Multipartite entanglement, characterized by the quantum Fisher information (QFI), plays a central role in quantum-enhanced metrology and understanding quantum many-body physics. With a dynamical generalization of the Mazur-Suzuki relations, we provide a rigorous lower bound on the QFI for the thermal Gibbs states in terms of dynamical symmetries, i.e., operators with periodic time dependence. We demonstrate that this bound can be saturated when considering a complete set of dynamical symmetries. Moreover, this lower bound with dynamical symmetries can be generalized to the QFI matrix and to the QFI for the thermal pure states, predicted by the eigenstate thermalization hypothesis. Our results reveal a new perspective to detect multipartite entanglement and other generalized variances in an equilibrium system, from its nonstationary dynamical properties, and is promising for studying emergent nonequilibrium many-body physics.

We discovered the underlying physics in Next-token Prediction (NTP). We identified the law of information conservation within NTP and proposed the First Law of Information Capacity (IC-1), demonstrating that the essence of intelligence emergence in auto-regressive models is fundamentally a process of information transfer. We also introduced Landauer's Principle into NTP, formulating the Second Law of Information Capacity (IC-2), which establishes the relationship between auto-regressive model training and energy consumption. Additionally, we presented several corollaries, which hold practical significance for production practices. Finally, we validated the compatibility and complementarity of our findings with existing theories.

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Linear sequence modeling methods, such as linear attention, state space modeling, and linear RNNs, offer significant efficiency improvements by reducing the complexity of training and inference. However, these methods typically compress the entire input sequence into a single fixed-size memory state, which leads to suboptimal performance on recall-intensive downstream tasks. Drawing inspiration from neuroscience, particularly the brain's ability to maintain robust long-term memory while mitigating "memory interference", we introduce a novel architecture called Mixture-of-Memories (MoM). MoM utilizes multiple independent memory states, with a router network directing input tokens to specific memory states. This approach greatly enhances the overall memory capacity while minimizing memory interference. As a result, MoM performs exceptionally well on recall-intensive tasks, surpassing existing linear sequence modeling techniques. Despite incorporating multiple memory states, the computation of each memory state remains linear in complexity, allowing MoM to retain the linear-complexity advantage during training, while constant-complexity during inference. Our experimental results show that MoM significantly outperforms current linear sequence models on downstream language tasks, particularly recall-intensive tasks, and even achieves performance comparable to Transformer models. The code is released at https://github.com/OpenSparseLLMs/MoM and is also released as a part of https://github.com/OpenSparseLLMs/Linear-MoE.

A critical approach for efficiently deploying computationally demanding large language models (LLMs) is Key-Value (KV) caching. The KV cache stores key-value states of previously generated tokens, significantly reducing the need for repetitive computations and thereby lowering latency in autoregressive generation. However, the size of the KV cache grows linearly with sequence length, posing challenges for applications requiring long context input and extensive sequence generation. In this paper, we present a simple yet effective approach, called MiniCache, to compress the KV cache across layers from a novel depth perspective, significantly reducing the memory footprint for LLM inference. Our approach is based on the observation that KV cache states exhibit high similarity between the adjacent layers in the middle-to-deep portion of LLMs. To facilitate merging, we propose disentangling the states into the magnitude and direction components, interpolating the directions of the state vectors while preserving their lengths unchanged. Furthermore, we introduce a token retention strategy to keep highly distinct state pairs unmerged, thus preserving the information with minimal additional storage overhead. Our MiniCache is training-free and general, complementing existing KV cache compression strategies, such as quantization and sparsity. We conduct a comprehensive evaluation of MiniCache utilizing various models including LLaMA-2, LLaMA-3, Phi-3, Mistral, and Mixtral across multiple benchmarks, demonstrating its exceptional performance in achieving superior compression ratios and high throughput. On the ShareGPT dataset, LLaMA-2-7B with 4-bit MiniCache achieves a remarkable compression ratio of up to 5.02x, enhances inference throughput by approximately 5x, and reduces the memory footprint by 41% compared to the FP16 full cache baseline, all while maintaining near-lossless performance.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central approach for improving the reasoning ability of large language models. Recent work studies RLVR through token entropy, arguing that high-entropy tokens drive exploration and should receive stronger updates. However, they overlook the fact that most of a reasoning trajectory consists of low-entropy segments that encode stable and reusable structural patterns. Through qualitative and quantitative analyses, we find that the overlap of low-entropy segments across correct responses strongly correlates with model accuracy, while overlaps involving incorrect responses exhibit stable but unproductive patterns. Motivated by these findings, we propose LESS, a correctness-aware reinforcement framework that performs fine-grained advantage modulation over low-entropy segments. LESS amplifies segments unique to correct responses, suppresses those unique to incorrect ones, and neutralizes segments shared by both, while preserving high-entropy exploration in the underlying RL algorithm. Instantiated on top of the popular GRPO, LESS consistently improves accuracy over strong RL baselines across three backbones and six math benchmarks, achieves stronger robustness of the performance floor.

Machine learning interatomic potentials (MLIPs) have become increasingly effective at approximating quantum mechanical calculations at a fraction of the computational cost. However, lower errors on held out test sets do not always translate to improved results on downstream physical property prediction tasks. In this paper, we propose testing MLIPs on their practical ability to conserve energy during molecular dynamic simulations. If passed, improved correlations are found between test errors and their performance on physical property prediction tasks. We identify choices which may lead to models failing this test, and use these observations to improve upon highly-expressive models. The resulting model, eSEN, provides state-of-the-art results on a range of physical property prediction tasks, including materials stability prediction, thermal conductivity prediction, and phonon calculations.

Training large language models (LLMs) typically relies on adaptive optimizers such as Adam, which require significant memory to maintain first- and second-moment matrices, known as optimizer states. While recent works such as GaLore, Fira, and APOLLO have proposed state-compressed variants to reduce memory consumption, a fundamental question remains: What is the minimal amount of optimizer state that is truly necessary to retain state-of-the-art performance in LLM pretraining? In this work, we systematically investigate this question using a bottom-up approach. We find that two memory- and compute-efficient optimization techniques are particularly effective: (1) column-wise gradient normalization significantly boosts the performance of plain SGD without requiring momentum; and (2) adding first-order momentum only to the output layer - where gradient variance is highest - yields performance competitive with fully adaptive methods such as Muon. Based on these insights, we propose SCALE (Stochastic Column-normalized Last-layer Momentum), a new optimizer that combines column-normalized SGD with last-layer momentum, where column normalization refers to normalizing the gradient along the output dimension. Across multiple LLaMA models (60M-1B), SCALE matches or exceeds the performance of Adam while using only 35-45% of the total memory. It also consistently outperforms memory-efficient optimizers such as GaLore, Fira, and APOLLO, making it a strong candidate for large-scale pretraining under memory constraints. For the LLaMA 7B model, SCALE outperforms the state-of-the-art method APOLLO in terms of both perplexity and memory consumption. In addition, our method serves as a minimalist baseline for more sophisticated optimizer design.

Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct connection between symmetry properties of a many-body model and measures of quantum asymmetry, showing that asymmetry monotones provide a robust and physically transparent indicator of dynamical quantum criticality. Focusing on the quenched Lipkin-Meshkov-Glick model, we demonstrate that asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries. Remarkably, the time-averaged asymmetry exhibits clear signatures of the dynamical critical point, in close correspondence with both the dynamical order parameter and the behavior of entropy production. We further uncover a quantitative link between asymmetry generation and thermodynamic irreversibility, showing that peaks in asymmetry coincide with maximal entropy production across the transition. Our results position asymmetry as a unifying concept bridging symmetry, information-theoretic quantifiers, and nonequilibrium thermodynamics in dynamical quantum phase transitions, providing a powerful framework for understanding critical dynamics beyond traditional order parameters.

We study a K-armed bandit with delayed feedback and intermediate observations. We consider a model where intermediate observations have a form of a finite state, which is observed immediately after taking an action, whereas the loss is observed after an adversarially chosen delay. We show that the regime of the mapping of states to losses determines the complexity of the problem, irrespective of whether the mapping of actions to states is stochastic or adversarial. If the mapping of states to losses is adversarial, then the regret rate is of order (K+d)T (within log factors), where T is the time horizon and d is a fixed delay. This matches the regret rate of a K-armed bandit with delayed feedback and without intermediate observations, implying that intermediate observations are not helpful. However, if the mapping of states to losses is stochastic, we show that the regret grows at a rate of big(K+min{|mathcal{S|,d}big)T} (within log factors), implying that if the number |S| of states is smaller than the delay, then intermediate observations help. We also provide refined high-probability regret upper bounds for non-uniform delays, together with experimental validation of our algorithms.

Model editing techniques modify a minor proportion of knowledge in Large Language Models (LLMs) at a relatively low cost, which have demonstrated notable success. Existing methods assume Transformer Layer (TL) hidden states are values of key-value memories of the Feed-Forward Network (FFN). They usually optimize the TL hidden states to memorize target knowledge and use it to update the weights of the FFN in LLMs. However, the information flow of TL hidden states comes from three parts: Multi-Head Self-Attention (MHSA), FFN, and residual connections. Existing methods neglect the fact that the TL hidden states contains information not specifically required for FFN. Consequently, the performance of model editing decreases. To achieve more precise model editing, we analyze hidden states of MHSA and FFN, finding that MHSA encodes certain general knowledge extraction patterns. This implies that MHSA weights do not require updating when new knowledge is introduced. Based on above findings, we introduce PMET, which simultaneously optimizes Transformer Component (TC, namely MHSA and FFN) hidden states, while only using the optimized TC hidden states of FFN to precisely update FFN weights. Our experiments demonstrate that PMET exhibits state-of-the-art performance on both the COUNTERFACT and zsRE datasets. Our ablation experiments substantiate the effectiveness of our enhancements, further reinforcing the finding that the MHSA encodes certain general knowledge extraction patterns and indicating its storage of a small amount of factual knowledge. Our code is available at https://github.com/xpq-tech/PMET.

This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenvalues. We leverage upon this observation to construct a local-entropy-based objective function that favors well-generalizable solutions lying in large flat regions of the energy landscape, while avoiding poorly-generalizable solutions located in the sharp valleys. Conceptually, our algorithm resembles two nested loops of SGD where we use Langevin dynamics in the inner loop to compute the gradient of the local entropy before each update of the weights. We show that the new objective has a smoother energy landscape and show improved generalization over SGD using uniform stability, under certain assumptions. Our experiments on convolutional and recurrent networks demonstrate that Entropy-SGD compares favorably to state-of-the-art techniques in terms of generalization error and training time.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

While Reinforcement Learning with Verifiable Rewards (RLVR) can enhance LLM reasoning, its training process poses a critical risk: entropy collapse. This phenomenon is a rapid loss of policy diversity, stemming from the exploration-exploitation imbalance and leading to a lack of generalization. Recent entropy-intervention methods aim to prevent entropy collapse, yet their underlying mechanisms remain unclear. In this paper, we conduct a quantitative analysis to reveal token-level entropy changes and how existing entropy intervention methods help avoid entropy collapse. Our findings point out a fundamental limitation of existing methods: they attempt to control entropy dynamics indirectly. By only affecting related factors, such as the advantage signal and generation probability, their effectiveness is inherently limited and could potentially fail. To address this limitation, we introduce an entropy-change-aware reweighting scheme, namely Stabilizing Token-level Entropy-changE via Reweighting (STEER), that adaptively stabilizes entropy dynamics through fine-grained token-level adjustments. Our approach mitigates over-exploitation while fostering robust exploration. Extensive experiments demonstrate that STEER significantly mitigates entropy collapse, stabilizes entropy dynamics, and achieves stronger downstream performance across various mathematical reasoning benchmarks \footnote{Our code is available at https://github.com/zz-haooo/STEER.

Whether AI models can introspect is an increasingly important practical question. But there is no consensus on how introspection is to be defined. Beginning from a recently proposed ''lightweight'' definition, we argue instead for a thicker one. According to our proposal, introspection in AI is any process which yields information about internal states through a process more reliable than one with equal or lower computational cost available to a third party. Using experiments where LLMs reason about their internal temperature parameters, we show they can appear to have lightweight introspection while failing to meaningfully introspect per our proposed definition.

Large language model (LLM)-driven agents are emerging as a powerful new paradigm for solving complex problems. Despite the empirical success of these practices, a theoretical framework to understand and unify their macroscopic dynamics remains lacking. This Letter proposes a method based on the least action principle to estimate the underlying generative directionality of LLMs embedded within agents. By experimentally measuring the transition probabilities between LLM-generated states, we statistically discover a detailed balance in LLM-generated transitions, indicating that LLM generation may not be achieved by generally learning rule sets and strategies, but rather by implicitly learning a class of underlying potential functions that may transcend different LLM architectures and prompt templates. To our knowledge, this is the first discovery of a macroscopic physical law in LLM generative dynamics that does not depend on specific model details. This work is an attempt to establish a macroscopic dynamics theory of complex AI systems, aiming to elevate the study of AI agents from a collection of engineering practices to a science built on effective measurements that are predictable and quantifiable.

Optimizer states are a major source of memory consumption for training neural networks, limiting the maximum trainable model within given memory budget. Compressing the optimizer states from 32-bit floating points to lower bitwidth is promising to reduce the training memory footprint, while the current lowest achievable bitwidth is 8-bit. In this work, we push optimizer states bitwidth down to 4-bit through a detailed empirical analysis of first and second moments. Specifically, we find that moments have complicated outlier patterns, that current block-wise quantization cannot accurately approximate. We use a smaller block size and propose to utilize both row-wise and column-wise information for better quantization. We further identify a zero point problem of quantizing the second moment, and solve this problem with a linear quantizer that excludes the zero point. Our 4-bit optimizers are evaluated on a wide variety of benchmarks including natural language understanding, machine translation, image classification, and instruction tuning. On all the tasks our optimizers can achieve comparable accuracy with their full-precision counterparts, while enjoying better memory efficiency.

The equivalence of 1 bit of information to entropy was given by Landauer in 1961 as kln2, k the Boltzmann constant. Erasing information implies heat dissipation and the energy of 1 bit would then be (the Landauers limit) kT ln 2, T being the ambient temperature. From a quantum-cosmological point of view the minimum quantum of energy in the universe corresponds today to a temperature of 10^(-29) degrees K, probably forming a cosmic background of a Bose condensate [1]. Then, the bit with minimum energy today in the Universe is a quantum of energy 10^(-45)ergs, with an equivalent mass of 10^(-66)g. Low temperature implies low energy per bit and, of course, this is the way for faster and less energy dissipating computing devices. Our conjecture is this: the possibility of a future access to the CBBC (a coupling/channeling?) would mean a huge jump in the performance of these devices.

We propose the Automatic-differentiated Physics-Informed Echo State Network (API-ESN). The network is constrained by the physical equations through the reservoir's exact time-derivative, which is computed by automatic differentiation. As compared to the original Physics-Informed Echo State Network, the accuracy of the time-derivative is increased by up to seven orders of magnitude. This increased accuracy is key in chaotic dynamical systems, where errors grows exponentially in time. The network is showcased in the reconstruction of unmeasured (hidden) states of a chaotic system. The API-ESN eliminates a source of error, which is present in existing physics-informed echo state networks, in the computation of the time-derivative. This opens up new possibilities for an accurate reconstruction of chaotic dynamical states.

Chain-of-Thought (CoT) has unlocked advanced reasoning abilities of Large Language Models (LLMs) with intermediate steps, yet incurs prohibitive computational costs due to generation of extra tokens. Recent studies empirically show that compressing reasoning steps into latent states, or implicit CoT compression, offers a token-efficient alternative. However, the mechanism behind CoT compression remains unclear. In this paper, we provide the first theoretical analysis of the difficulty of learning to internalize intermediate reasoning steps. By introducing Order-r Interaction, we prove that the learning signal for high-order logical dependencies exponentially decays to solve irreducible problem, where skipping intermediate steps inevitably leads to high-order interaction barriers. To empirically validate this, we introduce NatBool-DAG, a challenging benchmark designed to enforce irreducible logical reasoning and eliminate semantic shortcuts. Guided by our theoretical findings, we propose ALiCoT (Aligned Implicit CoT), a novel framework that overcomes the signal decay by aligning latent token distributions with intermediate reasoning states. Experimental results demonstrate that ALiCoT successfully unlocks efficient reasoning: it achieves a 54.4x speedup while maintaining performance comparable to explicit CoT.

Standing as one of the most significant barriers to reaching quantum advantage, state-preparation fidelities on noisy intermediate-scale quantum processors suffer from quantum-gate errors, which accumulate over time. A potential remedy is pulse-based state preparation. We numerically investigate the minimal evolution times (METs) attainable by optimizing (microwave and exchange) pulses on silicon hardware. We investigate two state preparation tasks. First, we consider the preparation of molecular ground states and find the METs for H_2, HeH^+, and LiH to be 2.4 ns, 4.4 ns, and 27.2 ns, respectively. Second, we consider transitions between arbitrary states and find the METs for transitions between arbitrary four-qubit states to be below 50 ns. For comparison, connecting arbitrary two-qubit states via one- and two-qubit gates on the same silicon processor requires approximately 200 ns. This comparison indicates that pulse-based state preparation is likely to utilize the coherence times of silicon hardware more efficiently than gate-based state preparation. Finally, we quantify the effect of silicon device parameters on the MET. We show that increasing the maximal exchange amplitude from 10 MHz to 1 GHz accelerates the METs, e.g., for H_2 from 84.3 ns to 2.4 ns. This demonstrates the importance of fast exchange. We also show that increasing the maximal amplitude of the microwave drive from 884 kHz to 56.6 MHz shortens state transitions, e.g., for two-qubit states from 1000 ns to 25 ns. Our results bound both the state-preparation times for general quantum algorithms and the execution times of variational quantum algorithms with silicon spin qubits.

Large Language Models (LLMs) using Chain-of-Thought (CoT) prompting excel at complex reasoning but generate verbose thought processes with considerable redundancy, leading to increased inference costs and reduced efficiency. We introduce a novel CoT compression framework based on step entropy, a metric that quantifies the informational contribution of individual reasoning steps to identify redundancy. Through theoretical analysis and extensive empirical validation on mathematical reasoning benchmarks, we demonstrate that steps with low entropy are indeed highly redundant. Our experiments reveal that an astonishing 80\% of low-entropy intermediate steps can be pruned with minor degradation in the final answer accuracy across DeepSeek-R1-7B, 14B and Qwen3-8B. This finding sharply contrasts with random or high-entropy pruning, which severely impairs reasoning performance. Building on this, we propose a novel two-stage training strategy combining Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO) reinforcement learning. This approach enables LLMs to autonomously learn to generate compressed COTs during inference by strategically incorporating [SKIP] tokens. Our method significantly enhances LLM inference efficiency while rigorously preserving accuracy, offering profound implications for practical LLM deployment and a deeper understanding of reasoning structures.

Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.

Generalist robot policies trained on large-scale, visually homogeneous datasets can be susceptible to shortcut learning, which impairs their out-of-distribution (OOD) generalization. While generative data augmentation is a common approach to introduce diversity, it presents a subtle challenge: data composition. Naively mixing real and synthetic data can corrupt the learning signal, as this process often prioritizes visual diversity at the expense of information fidelity. This paper suggests that robust generalization depends on principled, fidelity-aware data composition. We introduce Coherent Information Fidelity Tuning (CIFT), a framework that treats data composition as an optimization problem. CIFT uses a practical proxy for Information Fidelity based on the feature-space geometry of a dataset. This enables the identification of a phase transition, termed the Decoherence Point, where training stability degrades. The framework includes a generative engine, Multi-View Video Augmentation (MVAug), to synthesize a causally disentangled data spectrum for this tuning process. Applying CIFT to policy architectures such as pi_0 and Diffusion Policy improves OOD success rates by over 54\%. These results indicate that fidelity-aware composition, beyond data synthesis alone, is an important component for developing robust, general-purpose robots.

All current formulations of thermodynamics invoke some form of coarse-graining or ensembles as the supposed link between their own laws and the microscopic laws of motion. They deal only with ensemble-averages, expectation values, macroscopic limits, infinite heat baths, etc., not with the details of physical variables of individual microscopic systems. They are consistent with the laws of motion for finite systems only in certain approximations, which improve with increasing scale, given various assumptions about initial conditions which are neither specified precisely nor even thought to hold exactly in nature. Here I propose a new formulation of the zeroth, first and second laws, improving upon the axiomatic approach to thermodynamics (Carath\'eodory, 1909; Lieb & Yngvason, 1999), via the principles of the recently proposed constructor theory. Specifically, I provide a non-approximative, scale-independent formulation of 'adiabatic accessibility'; this in turn provides a non-approximative, scale-independent distinction between work and heat and reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second). It also achieves the long-sought unification of the axiomatic approach with Kelvin's.

Precise determination of thermodynamic parameters in ultracold Bose gases remains challenging due to the destructive nature of conventional measurement techniques and inherent experimental uncertainties. We demonstrate an artificial intelligence approach for rapid, non-destructive estimation of the chemical potential and temperature from single-shot, in situ imaged density profiles of finite-temperature Bose gases. Our convolutional neural network is trained exclusively on quasi-2D `pancake' condensates in harmonic trap configurations. It achieves parameter extraction within fractions of a second. The model also demonstrates zero-shot generalisation across both trap geometry and thermalisation dynamics, successfully estimating thermodynamic parameters for toroidally trapped condensates with errors of only a few nanokelvin despite no prior exposure to such geometries during training, and maintaining predictive accuracy during dynamic thermalisation processes after a relatively brief evolution without explicit training on non-equilibrium states. These results suggest that supervised learning can overcome traditional limitations in ultracold atom thermometry, with extension to broader geometric configurations, temperature ranges, and additional parameters potentially enabling comprehensive real-time analysis of quantum gas experiments. Such capabilities could significantly streamline experimental workflows whilst improving measurement precision across a range of quantum fluid systems.

Understanding the training dynamics of deep neural networks remains a major open problem, with physics-inspired approaches offering promising insights. Building on this perspective, we develop a thermodynamic framework to describe the stationary distributions of stochastic gradient descent (SGD) with weight decay for scale-invariant neural networks, a setting that both reflects practical architectures with normalization layers and permits theoretical analysis. We establish analogies between training hyperparameters (e.g., learning rate, weight decay) and thermodynamic variables such as temperature, pressure, and volume. Starting with a simplified isotropic noise model, we uncover a close correspondence between SGD dynamics and ideal gas behavior, validated through theory and simulation. Extending to training of neural networks, we show that key predictions of the framework, including the behavior of stationary entropy, align closely with experimental observations. This framework provides a principled foundation for interpreting training dynamics and may guide future work on hyperparameter tuning and the design of learning rate schedulers.

Stateful optimizers maintain gradient statistics over time, e.g., the exponentially smoothed sum (SGD with momentum) or squared sum (Adam) of past gradient values. This state can be used to accelerate optimization compared to plain stochastic gradient descent but uses memory that might otherwise be allocated to model parameters, thereby limiting the maximum size of models trained in practice. In this paper, we develop the first optimizers that use 8-bit statistics while maintaining the performance levels of using 32-bit optimizer states. To overcome the resulting computational, quantization, and stability challenges, we develop block-wise dynamic quantization. Block-wise quantization divides input tensors into smaller blocks that are independently quantized. Each block is processed in parallel across cores, yielding faster optimization and high precision quantization. To maintain stability and performance, we combine block-wise quantization with two additional changes: (1) dynamic quantization, a form of non-linear optimization that is precise for both large and small magnitude values, and (2) a stable embedding layer to reduce gradient variance that comes from the highly non-uniform distribution of input tokens in language models. As a result, our 8-bit optimizers maintain 32-bit performance with a small fraction of the memory footprint on a range of tasks, including 1.5B parameter language modeling, GLUE finetuning, ImageNet classification, WMT'14 machine translation, MoCo v2 contrastive ImageNet pretraining+finetuning, and RoBERTa pretraining, without changes to the original optimizer hyperparameters. We open-source our 8-bit optimizers as a drop-in replacement that only requires a two-line code change.

We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for supporting empirical evidence and formal statements concerning mathematical generality. We recall how the quantum model for natural language that we employ canonically combines linguistic meanings with rich linguistic structure, most notably grammar. In particular, the fact that it takes a quantum-like model to combine meaning and structure, establishes QNLP as quantum-native, on par with simulation of quantum systems. Moreover, the now leading Noisy Intermediate-Scale Quantum (NISQ) paradigm for encoding classical data on quantum hardware, variational quantum circuits, makes NISQ exceptionally QNLP-friendly: linguistic structure can be encoded as a free lunch, in contrast to the apparently exponentially expensive classical encoding of grammar. Quantum speed-up for QNLP tasks has already been established in previous work with Will Zeng. Here we provide a broader range of tasks which all enjoy the same advantage. Diagrammatic reasoning is at the heart of QNLP. Firstly, the quantum model interprets language as quantum processes via the diagrammatic formalism of categorical quantum mechanics. Secondly, these diagrams are via ZX-calculus translated into quantum circuits. Parameterisations of meanings then become the circuit variables to be learned. Our encoding of linguistic structure within quantum circuits also embodies a novel approach for establishing word-meanings that goes beyond the current standards in mainstream AI, by placing linguistic structure at the heart of Wittgenstein's meaning-is-context.

Recently, reinforcement learning with verifiable rewards (RLVR) has been widely used for enhancing the reasoning abilities of large language models (LLMs). A core challenge in RLVR involves managing the exchange between entropy and performance of policies. Despite the importance of this exchange, a fine-grained understanding of when and how this exchange operates most effectively remains limited. To bridge this gap, we conduct a systematic empirical analysis of the entropy-performance exchange mechanism of RLVR across different levels of granularity. Specifically, we first divide the training process into two distinct stages based on entropy dynamics, i.e., rising stage and plateau stage, and then systematically investigate how this mechanism varies across stage-level, instance-level, and token-level granularitiess. Our analysis reveals that, in the rising stage, entropy reduction in negative samples facilitates the learning of effective reasoning patterns, which in turn drives rapid performance gains. Moreover, in the plateau stage, learning efficiency strongly correlates with high-entropy tokens present in low-perplexity samples and those located at the end of sequences. Motivated by these findings, we propose two methods that dynamically adjust the reward signal using perplexity and positional information to focus RL updates on tokens that exhibit high learning potential, achieving improvements compared to the baseline methods on various LLMs.

The role of hidden units in recurrent neural networks is typically seen as modeling memory, with research focusing on enhancing information retention through gating mechanisms. A less explored perspective views hidden units as active participants in the computation performed by the network, rather than passive memory stores. In this work, we revisit bi-linear operations, which involve multiplicative interactions between hidden units and input embeddings. We demonstrate theoretically and empirically that they constitute a natural inductive bias for representing the evolution of hidden states in state tracking tasks. These are the simplest type of task that require hidden units to actively contribute to the behavior of the network. We also show that bi-linear state updates form a natural hierarchy corresponding to state tracking tasks of increasing complexity, with popular linear recurrent networks such as Mamba residing at the lowest-complexity center of that hierarchy.

We formulate nonequilibrium thermodynamics in which intensive variables acquire operational meaning through measurement protocols consistent with local reciprocity. Using physical equilibrium as a reference, conjugate observables are constructed by continuously adjusting devices along the local tangent space of the statistical manifold. In this relativity of observation, Onsager reciprocity holds locally, allowing inference-based Lagrange multipliers to be directly measured. This provides a systematic method to extend operational definitions of intensive variables to nonequilibrium states, highlighting their context-dependent nature and offering a concrete experimental strategy.

Deep Reinforcement Learning is emerging as a promising approach for the continuous control task of robotic arm movement. However, the challenges of learning robust and versatile control capabilities are still far from being resolved for real-world applications, mainly because of two common issues of this learning paradigm: the exploration strategy and the slow learning speed, sometimes known as "the curse of dimensionality". This work aims at exploring and assessing the advantages of the application of Quantum Computing to one of the state-of-art Reinforcement Learning techniques for continuous control - namely Soft Actor-Critic. Specifically, the performance of a Variational Quantum Soft Actor-Critic on the movement of a virtual robotic arm has been investigated by means of digital simulations of quantum circuits. A quantum advantage over the classical algorithm has been found in terms of a significant decrease in the amount of required parameters for satisfactory model training, paving the way for further promising developments.

The liquid state machine (LSM) combines low training complexity and biological plausibility, which has made it an attractive machine learning framework for edge and neuromorphic computing paradigms. Originally proposed as a model of brain computation, the LSM tunes its internal weights without backpropagation of gradients, which results in lower performance compared to multi-layer neural networks. Recent findings in neuroscience suggest that astrocytes, a long-neglected non-neuronal brain cell, modulate synaptic plasticity and brain dynamics, tuning brain networks to the vicinity of the computationally optimal critical phase transition between order and chaos. Inspired by this disruptive understanding of how brain networks self-tune, we propose the neuron-astrocyte liquid state machine (NALSM) that addresses under-performance through self-organized near-critical dynamics. Similar to its biological counterpart, the astrocyte model integrates neuronal activity and provides global feedback to spike-timing-dependent plasticity (STDP), which self-organizes NALSM dynamics around a critical branching factor that is associated with the edge-of-chaos. We demonstrate that NALSM achieves state-of-the-art accuracy versus comparable LSM methods, without the need for data-specific hand-tuning. With a top accuracy of 97.61% on MNIST, 97.51% on N-MNIST, and 85.84% on Fashion-MNIST, NALSM achieved comparable performance to current fully-connected multi-layer spiking neural networks trained via backpropagation. Our findings suggest that the further development of brain-inspired machine learning methods has the potential to reach the performance of deep learning, with the added benefits of supporting robust and energy-efficient neuromorphic computing on the edge.

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which can be challenging for large, strongly-correlated systems. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping eigenvalues into positive and negative subspaces separated by a large gap. This automatically ensures that all states within each subspace conserve energy with respect to the transformed Hamiltonian. Subsequent time-evolution with a perturbed Hamiltonian induces transitions to lower-energy states while preventing unwanted jumps to higher energy states. The approach does not rely on a priori knowledge of energy gaps and requires no additional qubits to model a bath. Furthermore, it makes mathcal{O}(d^{,3/2}/epsilon) queries to the time-evolution operator of the system and mathcal{O}(d^{,3/2}) queries to a block-encoding of the perturbation, for d cooling steps and an epsilon-accurate energy resolution. Our results provide a framework for combining quantum signal processing and Hamiltonian simulation to design heuristic quantum algorithms for ground-state preparation.

In Retrieval-Augmented Generation (RAG) and agent-based frameworks, the "Chain of Models" approach is widely used, where multiple specialized models work sequentially on distinct sub-tasks. This approach is effective but increases resource demands as each model must be deployed separately. Recent advancements attempt to address this by applying prompt tuning, which allows a shared base model to adapt to multiple tasks with minimal parameter changes. However, a key challenge remains: intermediate outputs, passed between models as plain text, require recomputation of hidden states (i.e., Key and Value (KV) states in Transformers) during inference. In this paper, we introduce FTHSS, a novel prompt-tuning method that enables models to share KV hidden states, eliminating redundant forward passes and reducing KV cache storage. By modifying input and attention masks during training, FTHSS allows models to effectively utilize KV hidden states from prior models in both single- and multi-round scenarios. Empirical results on four tasks show that FTHSS matches the performance of traditional model chains while improving inference efficiency.

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D J_1-J_2 Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for scientific simulations of quantum many-body physics and quantum technology.

The pervasiveness of proprietary language models has raised critical privacy concerns, necessitating advancements in private inference (PI), where computations are performed directly on encrypted data without revealing users' sensitive information. While PI offers a promising solution, its practical deployment is hindered by substantial communication and latency overheads, primarily stemming from nonlinear operations. To address this, we introduce an information-theoretic framework to characterize the role of nonlinearities in decoder-only language models, laying a principled foundation for optimizing transformer-architectures tailored to the demands of PI. By leveraging Shannon's entropy as a quantitative measure, we uncover the previously unexplored dual significance of nonlinearities: beyond ensuring training stability, they are crucial for maintaining attention head diversity. Specifically, we find that their removal triggers two critical failure modes: {\em entropy collapse} in deeper layers that destabilizes training, and {\em entropic overload} in earlier layers that leads to under-utilization of Multi-Head Attention's (MHA) representational capacity. We propose an entropy-guided attention mechanism paired with a novel entropy regularization technique to mitigate entropic overload. Additionally, we explore PI-friendly alternatives to layer normalization for preventing entropy collapse and stabilizing the training of LLMs with reduced-nonlinearities. Our study bridges the gap between information theory and architectural design, establishing entropy dynamics as a principled guide for developing efficient PI architectures. The code and implementation are available at https://github.com/Nandan91/entropy-guided-attention-llm{entropy-guided-llm}.

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This conflict between generation steps and output quality arises from restrictive training objectives that focus exclusively on either infinitesimal dynamics (PF-ODEs) or direct endpoint prediction. We address this challenge by introducing an exact, continuous-time dynamics equation that analytically defines state transitions across any finite time interval. This leads to a novel generative paradigm, Transition Models (TiM), which adapt to arbitrary-step transitions, seamlessly traversing the generative trajectory from single leaps to fine-grained refinement with more steps. Despite having only 865M parameters, TiM achieves state-of-the-art performance, surpassing leading models such as SD3.5 (8B parameters) and FLUX.1 (12B parameters) across all evaluated step counts. Importantly, unlike previous few-step generators, TiM demonstrates monotonic quality improvement as the sampling budget increases. Additionally, when employing our native-resolution strategy, TiM delivers exceptional fidelity at resolutions up to 4096x4096.

The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps of the MED, principally solving a minimization problem with a preconditioned Newton's algorithm, as well as how to extract global susceptibilities and thermal responses. We demonstrate the power of the method with the spin-1/2 XXZ model on the 2D square lattice, including the extraction of critical points and details of each phase. Although the method shares some qualitative similarities with exact-diagonalization, we show the MED is both more accurate and significantly more flexible.

Predicting the dynamics of interacting objects is essential for both humans and intelligent systems. However, existing approaches are limited to simplified, toy settings and lack generalizability to complex, real-world environments. Recent advances in generative models have enabled the prediction of state transitions based on interventions, but focus on generating a single future state which neglects the continuous dynamics resulting from the interaction. To address this gap, we propose InterDyn, a novel framework that generates videos of interactive dynamics given an initial frame and a control signal encoding the motion of a driving object or actor. Our key insight is that large video generation models can act as both neural renderers and implicit physics ``simulators'', having learned interactive dynamics from large-scale video data. To effectively harness this capability, we introduce an interactive control mechanism that conditions the video generation process on the motion of the driving entity. Qualitative results demonstrate that InterDyn generates plausible, temporally consistent videos of complex object interactions while generalizing to unseen objects. Quantitative evaluations show that InterDyn outperforms baselines that focus on static state transitions. This work highlights the potential of leveraging video generative models as implicit physics engines. Project page: https://interdyn.is.tue.mpg.de/

Quantum many-body scars (QMBS) are exotic many-body states that exhibit anomalous non-thermal behavior in an otherwise ergodic system. In this work, we demonstrate a simple, scalable and intuitive construction of QMBS in a kinetically constrained quantum model exhibiting weak Hilbert space fragmentation. We show that exact QMBS can be constructed by injecting a quasiparticle that partially activates the frozen regions in the lattice. Meanwhile, the inelastic collision between multiple quasiparticles allows for the construction of approximate scars, whose damping is governed by an emergent two-body loss. Our findings establish direct connections between quantum many-body scarring and Hilbert space fragmentation, paving the way for systematically constructing exact and approximate QMBS with nontrivial spatial connectivity. The proposed model can be readily implemented in neutral-atom quantum simulators aided by strong Rydberg interactions.

Recently, recurrent models such as state space models and linear attention have become popular due to their linear complexity in the sequence length. Thanks to their recurrent nature, in principle they can process arbitrarily long sequences, but their performance sometimes drops considerably beyond their training context lengths-i.e. they fail to length generalize. In this work, we provide comprehensive empirical and theoretical analysis to support the unexplored states hypothesis, which posits that models fail to length generalize when during training they are only exposed to a limited subset of the distribution of all attainable states (i.e. states that would be attained if the recurrence was applied to long sequences). Furthermore, we investigate simple training interventions that aim to increase the coverage of the states that the model is trained on, e.g. by initializing the state with Gaussian noise or with the final state of a different input sequence. With only 500 post-training steps (sim 0.1% of the pre-training budget), these interventions enable length generalization for sequences that are orders of magnitude longer than the training context (e.g. 2klongrightarrow 128k) and show improved performance in long context tasks, thus presenting a simple and efficient way to enable robust length generalization in general recurrent models.

Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling gates scales quadratically with the dimension of the dataset and the number of qubits. In this work, we introduce a quantum feature map designed to handle high-dimensional data with a significantly reduced number of qubits and entangling operations. Our approach preserves essential data characteristics while promoting computational efficiency, as evidenced by extensive experiments on benchmark datasets that demonstrate a marked improvement in both accuracy and resource utilization when using our feature map as a kernel for characterization, as compared to state-of-the-art quantum feature maps. Our noisy simulation results, combined with lower resource requirements, highlight our map's ability to function within the constraints of noisy intermediate-scale quantum devices. Through numerical simulations and small-scale implementation on a superconducting circuit quantum computing platform, we demonstrate that our scheme performs on par or better than a set of classical algorithms for classification. While quantum kernels are typically stymied by exponential concentration, our approach is affected with a slower rate with respect to both the number of qubits and features, which allows practical applications to remain within reach. Our findings herald a promising avenue for the practical implementation of quantum machine learning algorithms on near future quantum computing platforms.

Training stability is of great importance to Transformers. In this work, we investigate the training dynamics of Transformers by examining the evolution of the attention layers. In particular, we track the attention entropy for each attention head during the course of training, which is a proxy for model sharpness. We identify a common pattern across different architectures and tasks, where low attention entropy is accompanied by high training instability, which can take the form of oscillating loss or divergence. We denote the pathologically low attention entropy, corresponding to highly concentrated attention scores, as entropy collapse. As a remedy, we propose sigmaReparam, a simple and efficient solution where we reparametrize all linear layers with spectral normalization and an additional learned scalar. We demonstrate that the proposed reparameterization successfully prevents entropy collapse in the attention layers, promoting more stable training. Additionally, we prove a tight lower bound of the attention entropy, which decreases exponentially fast with the spectral norm of the attention logits, providing additional motivation for our approach. We conduct experiments with sigmaReparam on image classification, image self-supervised learning, machine translation, automatic speech recognition, and language modeling tasks, across Transformer architectures. We show that sigmaReparam provides stability and robustness with respect to the choice of hyperparameters, going so far as enabling training (a) a Vision Transformer to competitive performance without warmup, weight decay, layer normalization or adaptive optimizers; (b) deep architectures in machine translation and (c) speech recognition to competitive performance without warmup and adaptive optimizers.

Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an atomistic model for glass-forming liquids. This is a notoriously difficult task, as it amounts to ergodically exploring the complex free energy landscape of a disordered and frustrated many-body system. We optimize a normalizing flow model to successfully transform high-temperature configurations of a dense liquid into low-temperature ones, near the glass transition. We perform a detailed comparative analysis with established enhanced sampling techniques developed in the physics literature to assess and rank the performance of normalizing flows against state-of-the-art algorithms. We demonstrate that machine learning methods are very promising, showing a large speedup over conventional molecular dynamics. Normalizing flows show performances comparable to parallel tempering and population annealing, while still falling far behind the swap Monte Carlo algorithm. Our study highlights the potential of generative machine learning models in scientific computing for complex systems, but also points to some of its current limitations and the need for further improvement.

A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is inspired by cognitive neuroscience theories of consciousness, seen as a bottleneck through which just a few elements, after having been selected by attention from a broader pool, are then broadcast and condition further processing, both in perception and decision-making. The set of recently selected elements one becomes aware of is seen as forming a low-dimensional conscious state. This conscious state is combining the few concepts constituting a conscious thought, i.e., what one is immediately conscious of at a particular moment. We claim that this architectural and information-processing constraint corresponds to assumptions about the joint distribution between high-level concepts. To the extent that these assumptions are generally true (and the form of natural language seems consistent with them), they can form a useful prior for representation learning. A low-dimensional thought or conscious state is analogous to a sentence: it involves only a few variables and yet can make a statement with very high probability of being true. This is consistent with a joint distribution (over high-level concepts) which has the form of a sparse factor graph, i.e., where the dependencies captured by each factor of the factor graph involve only very few variables while creating a strong dip in the overall energy function. The consciousness prior also makes it natural to map conscious states to natural language utterances or to express classical AI knowledge in a form similar to facts and rules, albeit capturing uncertainty as well as efficient search mechanisms implemented by attention mechanisms.

Scaling has been critical in improving model performance and generalization in machine learning. It involves how a model's performance changes with increases in model size or input data, as well as how efficiently computational resources are utilized to support this growth. Despite successes in other areas, the study of scaling in Neural Network Interatomic Potentials (NNIPs) remains limited. NNIPs act as surrogate models for ab initio quantum mechanical calculations. The dominant paradigm here is to incorporate many physical domain constraints into the model, such as rotational equivariance. We contend that these complex constraints inhibit the scaling ability of NNIPs, and are likely to lead to performance plateaus in the long run. In this work, we take an alternative approach and start by systematically studying NNIP scaling strategies. Our findings indicate that scaling the model through attention mechanisms is efficient and improves model expressivity. These insights motivate us to develop an NNIP architecture designed for scalability: the Efficiently Scaled Attention Interatomic Potential (EScAIP). EScAIP leverages a multi-head self-attention formulation within graph neural networks, applying attention at the neighbor-level representations. Implemented with highly-optimized attention GPU kernels, EScAIP achieves substantial gains in efficiency--at least 10x faster inference, 5x less memory usage--compared to existing NNIPs. EScAIP also achieves state-of-the-art performance on a wide range of datasets including catalysts (OC20 and OC22), molecules (SPICE), and materials (MPTrj). We emphasize that our approach should be thought of as a philosophy rather than a specific model, representing a proof-of-concept for developing general-purpose NNIPs that achieve better expressivity through scaling, and continue to scale efficiently with increased computational resources and training data.

Understanding what defines a good representation in large language models (LLMs) is fundamental to both theoretical understanding and practical applications. In this paper, we investigate the quality of intermediate representations in various LLM architectures, including Transformers and State Space Models (SSMs). We find that intermediate layers often yield more informative representations for downstream tasks than the final layers. To measure the representation quality, we adapt and apply a suite of metrics - such as prompt entropy, curvature, and augmentation-invariance - originally proposed in other contexts. Our empirical study reveals significant architectural differences, how representations evolve throughout training, and how factors like input randomness and prompt length affect each layer. Notably, we observe a bimodal pattern in the entropy of some intermediate layers and consider potential explanations tied to training data. Overall, our results illuminate the internal mechanics of LLMs and guide strategies for architectural optimization and training.

Collective motion in fish schools exemplifies emergent self-organization in active matter systems, yet computational tools for simulating and analyzing these dynamics remain fragmented across research groups. We present dewi-kadita, an open-source Python library implementing the three-dimensional Couzin zone-based model with comprehensive entropy diagnostics tailored for marine collective behavior research. The library introduces seven information-theoretic metrics -- school cohesion entropy, polarization entropy, depth stratification entropy, angular momentum entropy, nearest-neighbor entropy, velocity correlation entropy, and school shape entropy -- that characterize distinct organizational features inaccessible to classical order parameters. These metrics combine into an Oceanic Schooling Index (OSI) providing a single scalar measure of collective disorder. Validation across four canonical configurations (swarm, torus, dynamic parallel, highly parallel) confirms correct reproduction of known phase behaviors: the swarm maintains disorder with polarization P < 0.1 and OSI approx 0.71, while the highly parallel state achieves P = 0.998 with OSI = 0.24 and velocity correlation entropy vanishing to zero. The entropy framework successfully discriminates the torus and dynamic parallel configurations that exhibit comparable order parameter magnitudes through different organizational mechanisms. Numba just-in-time (JIT) compilation accelerates pairwise interaction calculations by 10--100times, enabling simulations of 150--250 agents over 1000--2000 time steps within five minutes on standard workstation hardware. NetCDF4 output ensures interoperability with oceanographic analysis tools. The library addresses the need for standardized, reproducible infrastructure in collective behavior modeling analogous to established molecular dynamics codes.

Recent advances in Reinforcement Learning with Verified Reward (RLVR) have driven the emergence of more sophisticated cognitive behaviors in large language models (LLMs), thereby enhancing their reasoning capabilities. However, in prior RLVR pipelines, the repeated use of static initial-state sampling drawn exactly from the dataset distribution during each sampling phase produced overly deterministic, low diversity model behavior, which manifested as rapid entropy collapse and hindered sustained performance gains during prolonged training. To address this issue, we introduce CURE (Critical-token-gUided Re concatenation for Entropy-collapse prevention), a two-stage framework that balances exploration and exploitation. Specifically, in the first stage, to deliberately steer the model toward novel yet coherent contexts, we re-generate at high-entropy critical tokens and jointly optimize the original and the branched trajectories. The further comparison with vanilla DAPO shows that the regeneration process achieves a better performance on math reasoning tasks while sustaining a high-level entropy degree for exploration. In the second stage, we continue training with static initial-state sampling by DAPO, intentionally placing the model in a familiar state to gradually strengthen exploitation. Extensive experiments on Qwen-2.5-Math-7B show that, compared to other RLVR methods, CURE achieves a 5% performance gain across six math benchmarks, establishing state-of-the-art performance in both entropy and accuracy. A series of experiments further validate the effectiveness of our approach. Code is available at https://github.com/bytedance/CURE.

While recent breakthroughs have proven the ability of noisy intermediate-scale quantum (NISQ) devices to achieve quantum advantage in classically-intractable sampling tasks, the use of these devices for solving more practically relevant computational problems remains a challenge. Proposals for attaining practical quantum advantage typically involve parametrized quantum circuits (PQCs), whose parameters can be optimized to find solutions to diverse problems throughout quantum simulation and machine learning. However, training PQCs for real-world problems remains a significant practical challenge, largely due to the phenomenon of barren plateaus in the optimization landscapes of randomly-initialized quantum circuits. In this work, we introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for PQCs, which we show significantly improves the trainability and performance of PQCs on a variety of problems. Given a specific optimization task, this method first utilizes tensor network (TN) simulations to identify a promising quantum state, which is then converted into gate parameters of a PQC by means of a high-performance decomposition procedure. We show that this learned initialization avoids barren plateaus, and effectively translates increases in classical resources to enhanced performance and speed in training quantum circuits. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing, and opens up new avenues to harness the power of modern quantum hardware for realizing practical quantum advantage.

For RL algorithms, appropriate entropy control is crucial to their effectiveness. To control the policy entropy, a commonly used method is entropy regularization, which is adopted in various popular RL algorithms including PPO, SAC and A3C. Although entropy regularization proves effective in robotic and games RL conventionally, studies found that it gives weak to no gains in LLM-RL training. In this work, we study the issues of entropy bonus in LLM-RL setting. Specifically, we first argue that the conventional entropy regularization suffers from the LLM's extremely large response space and the sparsity of the optimal outputs. As a remedy, we propose AEnt, an entropy control method that utilizes a new clamped entropy bonus with an automatically adjusted coefficient. The clamped entropy is evaluated with the re-normalized policy defined on certain smaller token space, which encourages exploration within a more compact response set. In addition, the algorithm automatically adjusts entropy coefficient according to the clamped entropy value, effectively controlling the entropy-induced bias while leveraging the entropy's benefits. AEnt is tested in math-reasoning tasks under different base models and datasets, and it is observed that AEnt outperforms the baselines consistently across multiple benchmarks.

Entropy minimization (EM) trains the model to concentrate even more probability mass on its most confident outputs. We show that this simple objective alone, without any labeled data, can substantially improve large language models' (LLMs) performance on challenging math, physics, and coding tasks. We explore three approaches: (1) EM-FT minimizes token-level entropy similarly to instruction finetuning, but on unlabeled outputs drawn from the model; (2) EM-RL: reinforcement learning with negative entropy as the only reward to maximize; (3) EM-INF: inference-time logit adjustment to reduce entropy without any training data or parameter updates. On Qwen-7B, EM-RL, without any labeled data, achieves comparable or better performance than strong RL baselines such as GRPO and RLOO that are trained on 60K labeled examples. Furthermore, EM-INF enables Qwen-32B to match or exceed the performance of proprietary models like GPT-4o, Claude 3 Opus, and Gemini 1.5 Pro on the challenging SciCode benchmark, while being 3x more efficient than self-consistency and sequential refinement. Our findings reveal that many pretrained LLMs possess previously underappreciated reasoning capabilities that can be effectively elicited through entropy minimization alone, without any labeled data or even any parameter updates.

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo (MCMC) or Langevin Dynamics (LD) can suffer from slow mixing times there is a growing interest in using normalizing flows in order to learn the transformation of a simple prior distribution to the given target distribution. Here we propose a generalized and combined approach to sample target densities: Stochastic Normalizing Flows (SNF) -- an arbitrary sequence of deterministic invertible functions and stochastic sampling blocks. We show that stochasticity overcomes expressivity limitations of normalizing flows resulting from the invertibility constraint, whereas trainable transformations between sampling steps improve efficiency of pure MCMC/LD along the flow. By invoking ideas from non-equilibrium statistical mechanics we derive an efficient training procedure by which both the sampler's and the flow's parameters can be optimized end-to-end, and by which we can compute exact importance weights without having to marginalize out the randomness of the stochastic blocks. We illustrate the representational power, sampling efficiency and asymptotic correctness of SNFs on several benchmarks including applications to sampling molecular systems in equilibrium.

In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a one-particle problem in very high dimension to which we apply different theoretical methods tailored for high-dimensional lattices: the Forward-Scattering Approximation, a mapping to the Rosenzweig-Porter model, and the cavity method. Our results indicate the existence of two transition lines and three distinct dynamical phases: a completely many-body localized phase at low energy, a fully ergodic phase at high energy, and a multifractal "bad metal" phase at intermediate energy. In the latter, eigenfunctions occupy a diverging volume, yet an exponentially vanishing fraction of the total Hilbert space. We discuss the limitations of our approximations and the relationship with previous studies.

Chain-of-thoughts (CoT) requires large language models (LLMs) to generate intermediate steps before reaching the final answer, and has been proven effective to help LLMs solve complex reasoning tasks. However, the inner mechanism of CoT still remains largely unclear. In this paper, we empirically study the role of CoT tokens in LLMs on two compositional tasks: multi-digit multiplication and dynamic programming. While CoT is essential for solving these problems, we find that preserving only tokens that store intermediate results would achieve comparable performance. Furthermore, we observe that storing intermediate results in an alternative latent form will not affect model performance. We also randomly intervene some values in CoT, and notice that subsequent CoT tokens and the final answer would change correspondingly. These findings suggest that CoT tokens may function like variables in computer programs but with potential drawbacks like unintended shortcuts and computational complexity limits between tokens. The code and data are available at https://github.com/solitaryzero/CoTs_are_Variables.

We propose a formal reconstruction of quantum mechanics grounded not in external mathematical abstractions, but in the structured dynamics of subjective experience. The Qualia Abstraction Language (QAL) models physical systems as evolving streams of introspective units, structured sequences of modality, shape, and functional effect, rather than as state vectors in Hilbert space. This approach reimagines core quantum concepts: superposition becomes a form of structured ambiguity; collapse is reframed as an introspective contraction; and entanglement is modeled as semantic resonance across streams of qualia. Drawing on insights from nominalist philosophy and oversight theoretic limits in AI, we argue that the observer paradox in quantum mechanics reflects not an ontological lacuna, but a linguistic one: the absence of a formal vocabulary for modeling first person structure. QAL introduces such a vocabulary, providing a morphodynamic framework that embeds the observer within the system and replaces abstract projection with endogenous transformation. We analyze the alignment of QAL with endophysical approaches, contrast it with standard interpretations of quantum theory, and explore its implications for a post Platonist, introspectively grounded physics.

We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of epsilon-optimal policies reaching a set S_L^{rightarrow} of incrementally L-controllable states. We introduce a novel layered decomposition of the set of incrementally L-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of mathcal{O}(LS^{rightarrow}_{L(1+epsilon)}Gamma_{L(1+epsilon)} A ln^{12}(S^{rightarrow}_{L(1+epsilon)})/epsilon^2), where S^{rightarrow}_{L(1+epsilon)} is the number of states that are incrementally L(1+epsilon)-controllable, A is the number of actions, and Gamma_{L(1+epsilon)} is the branching factor of the transitions over such states. LAE improves over the algorithm of Tarbouriech et al. (2020a) by a factor of L^2 and it is the first algorithm for AX that works in a countably-infinite state space. Moreover, we show that, under a certain identifiability assumption, LAE achieves minimax-optimal sample complexity of mathcal{O}(LS^{rightarrow}_{L}Aln^{12}(S^{rightarrow}_{L})/epsilon^2), outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

The prediction of material degradation is an important problem to solve in many industries. Environmental conditions, such as humidity and temperature, are important drivers of degradation processes, with corrosion being one of the most prominent ones. Quantum machine learning is a promising research field but suffers from well known deficits such as barren plateaus and measurement overheads. To address this problem, recent research has examined quantum reservoir computing to address time-series prediction tasks. Although a promising idea, developing circuits that are expressive enough while respecting the limited depths available on current devices is challenging. In classical reservoir computing, the onion echo state network model (ESN) [https://doi.org/10.1007/978-3-031-72359-9_9] was introduced to increase the interpretability of the representation structure of the embeddings. This onion ESN model utilizes a concatenation of smaller reservoirs that describe different time scales by covering different regions of the eigenvalue spectrum. Here, we use the same idea in the realm of quantum reservoir computing by simultaneously evolving smaller quantum reservoirs to better capture all the relevant time-scales while keeping the circuit depth small. We do this by modifying the rotation angles which we show alters the eigenvalues of the quantum evolution, but also note that modifying the number of mid-circuit measurements accomplishes the same goals of changing the long-term or short-term memory. This onion QRC outperforms a simple model and a single classical reservoir for predicting the degradation of aluminum alloys in different environmental conditions. By combining the onion QRC with an additional classical reservoir layer, the prediction accuracy is further improved.

Quantum Zeno Effect (QZE) has been one of the most interesting phenomena in quantum mechanics ever since its discovery in 1977 by Misra and Sudarshan [J. Math. Phys. 18, 756 (1977)]. There have been many attempts for experimental realization of the same. Here, we present the first ever simulation of QZE on IBM quantum experience platform. We simulate a two-level system for Rabi-driven oscillation and then disturb the time evolution by intermediate repetitive measurements using quantum gates to increase the survival probability of the qubit in the initial state. The circuits are designed along with the added intermediate measurements and executed on IBM quantum simulator, and the outcomes are shown to be consistent with the predictions. The increasing survival probability with the number of intermediate measurements demonstrates QZE. Furthermore, some alternative explanations for the obtained results are provided which leads to some ambiguity in giving the exact reasoning for the observed outcomes.

Object Hallucination (OH) has been acknowledged as one of the major trustworthy challenges in Large Vision-Language Models (LVLMs). Recent advancements in Large Language Models (LLMs) indicate that internal states, such as hidden states, encode the "overall truthfulness" of generated responses. However, it remains under-explored how internal states in LVLMs function and whether they could serve as "per-token" hallucination indicators, which is essential for mitigating OH. In this paper, we first conduct an in-depth exploration of LVLM internal states in relation to OH issues and discover that (1) LVLM internal states are high-specificity per-token indicators of hallucination behaviors. Moreover, (2) different LVLMs encode universal patterns of hallucinations in common latent subspaces, indicating that there exist "generic truthful directions" shared by various LVLMs. Based on these discoveries, we propose Truthful-Guided Pre-Intervention (TruthPrInt) that first learns the truthful direction of LVLM decoding and then applies truthful-guided inference-time intervention during LVLM decoding. We further propose ComnHallu to enhance both cross-LVLM and cross-data hallucination detection transferability by constructing and aligning hallucination latent subspaces. We evaluate TruthPrInt in extensive experimental settings, including in-domain and out-of-domain scenarios, over popular LVLMs and OH benchmarks. Experimental results indicate that TruthPrInt significantly outperforms state-of-the-art methods. Codes will be available at https://github.com/jinhaoduan/TruthPrInt.

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of 2-outcome POVMs. However, these shadow tomography procedures yield poor bounds if there are more than 2 outcomes per measurement. In this paper, we consider a general problem of learning properties from unknown quantum states: given an unknown d-dimensional quantum state rho and M unknown quantum measurements M_1,...,M_M with Kgeq 2 outcomes, estimating the probability distribution for applying M_i on rho to within total variation distance epsilon. Compared to the special case when K=2, we need to learn unknown distributions instead of values. We develop an online shadow tomography procedure that solves this problem with high success probability requiring O(Klog^2Mlog d/epsilon^4) copies of rho. We further prove an information-theoretic lower bound that at least Omega(min{d^2,K+log M}/epsilon^2) copies of rho are required to solve this problem with high success probability. Our shadow tomography procedure requires sample complexity with only logarithmic dependence on M and d and is sample-optimal for the dependence on K.

Entropy serves as a critical metric for measuring the diversity of outputs generated by large language models (LLMs), providing valuable insights into their exploration capabilities. While recent studies increasingly focus on monitoring and adjusting entropy to better balance exploration and exploitation in reinforcement fine-tuning (RFT), a principled understanding of entropy dynamics during this process is yet to be thoroughly investigated. In this paper, we establish a theoretical framework for analyzing the entropy dynamics during the RFT process, which begins with a discriminant expression that quantifies entropy change under a single logit update. This foundation enables the derivation of a first-order expression for entropy change, which can be further extended to the update formula of Group Relative Policy Optimization (GRPO). The corollaries and insights drawn from the theoretical analysis inspire the design of entropy control methods, and also offer a unified lens for interpreting various entropy-based methods in existing studies. We provide empirical evidence to support the main conclusions of our analysis and demonstrate the effectiveness of the derived entropy-discriminator clipping methods. This study yields novel insights into RFT training dynamics, providing theoretical support and practical strategies for optimizing the exploration-exploitation balance during LLM fine-tuning.

Iterative generative policies, such as diffusion models and flow matching, offer superior expressivity for continuous control but complicate Maximum Entropy Reinforcement Learning because their action log-densities are not directly accessible. To address this, we propose Field Least-Energy Actor-Critic (FLAC), a likelihood-free framework that regulates policy stochasticity by penalizing the kinetic energy of the velocity field. Our key insight is to formulate policy optimization as a Generalized Schrödinger Bridge (GSB) problem relative to a high-entropy reference process (e.g., uniform). Under this view, the maximum-entropy principle emerges naturally as staying close to a high-entropy reference while optimizing return, without requiring explicit action densities. In this framework, kinetic energy serves as a physically grounded proxy for divergence from the reference: minimizing path-space energy bounds the deviation of the induced terminal action distribution. Building on this view, we derive an energy-regularized policy iteration scheme and a practical off-policy algorithm that automatically tunes the kinetic energy via a Lagrangian dual mechanism. Empirically, FLAC achieves superior or comparable performance on high-dimensional benchmarks relative to strong baselines, while avoiding explicit density estimation.

We introduce a differentiable estimator of range-partition entropy, a recent concept from computational geometry that enables algorithms to adapt to the "sortedness" of their input. While range-partition entropy provides strong guarantees in algorithm design, it has not yet been made accessible to deep learning. In this work, we (i) propose the first differentiable approximation of range-partition entropy, enabling its use as a trainable loss or regularizer; (ii) design EntropyNet, a neural module that restructures data into low-entropy forms to accelerate downstream instance-optimal algorithms; and (iii) extend this principle beyond geometry by applying entropy regularization directly to Transformer attention. Across tasks, we demonstrate that differentiable entropy improves efficiency without degrading correctness: in geometry, our method achieves up to 4.1times runtime speedups with negligible error (<0.2%); in deep learning, it induces structured attention patterns that yield 6% higher accuracy at 80% sparsity compared to L1 baselines. Our theoretical analysis provides approximation bounds for the estimator, and extensive ablations validate design choices. These results suggest that entropy-bounded computation is not only theoretically elegant but also a practical mechanism for adaptive learning, efficiency, and structured representation.

Despite their strong performance on reasoning tasks, large reasoning models (LRMs) often suffer from overthinking, producing unnecessarily long outputs and incurring high end-to-end latency, a significant limitation to their real-world deployment. To address overthinking, early-exit mechanisms have been proposed to terminate reasoning before typical completion, showing that this approach can effectively shorten generation length with minimal impact on accuracy. However, their reliance on probing mechanisms introduces a detection overhead that limits their end-to-end latency gains and compromises their generalizability across diverse problems. Inspired by the use of hidden states in speculative decoding, we propose SpecExit, a novel framework that predicts both future tokens and an early-exit signal directly from a lightweight draft model without probing overhead. Our method offers significant improvements, reducing average generation length by 66\% and achieving a 2.5x speedup in end-to-end latency compared to the speculative decoding baseline, without compromising accuracy. Our method leverages the inherent signals from hidden states to provide effective early-exit signals, suggesting broader use of hidden states for efficient reasoning. Our code is available at https://github.com/Tencent/AngelSlim.

The varying significance of distinct primitive behaviors during the policy learning process has been overlooked by prior model-free RL algorithms. Leveraging this insight, we explore the causal relationship between different action dimensions and rewards to evaluate the significance of various primitive behaviors during training. We introduce a causality-aware entropy term that effectively identifies and prioritizes actions with high potential impacts for efficient exploration. Furthermore, to prevent excessive focus on specific primitive behaviors, we analyze the gradient dormancy phenomenon and introduce a dormancy-guided reset mechanism to further enhance the efficacy of our method. Our proposed algorithm, ACE: Off-policy Actor-critic with Causality-aware Entropy regularization, demonstrates a substantial performance advantage across 29 diverse continuous control tasks spanning 7 domains compared to model-free RL baselines, which underscores the effectiveness, versatility, and efficient sample efficiency of our approach. Benchmark results and videos are available at https://ace-rl.github.io/.

We consider the problem of online preemptive scheduling on a single machine to minimize the total flow time. In clairvoyant scheduling, where job processing times are revealed upon arrival, the Shortest Remaining Processing Time (SRPT) algorithm is optimal. In practice, however, exact processing times are often unknown. At the opposite extreme, non-clairvoyant scheduling, in which processing times are revealed only upon completion, suffers from strong lower bounds on the competitive ratio. This motivates the study of intermediate information models. We introduce a new model in which processing times are revealed gradually during execution. Each job consists of a sequence of operations, and the processing time of an operation becomes known only after the preceding one completes. This models many scheduling scenarios that arise in computing systems. Our main result is a deterministic O(m^2)-competitive algorithm, where m is the maximum number of operations per job. More specifically, we prove a refined competitive ratio in O(m_1 cdot m_2), where m_1 and m_2 are instance-dependent parameters describing the operation size structure. Our algorithm and analysis build on recent advancements in robust flow time minimization (SODA '26), where jobs arrive with estimated sizes. However, in our setting we have no bounded estimate on a job's processing time. Thus, we design a highly adaptive algorithm that gradually explores a job's operations while working on them, and groups them into virtual chunks whose size can be well-estimated. This is a crucial ingredient of our result and requires a much more careful analysis compared to the robust setting. We also provide lower bounds showing that our bounds are essentially best possible. For the special case of scheduling with uniform obligatory tests, we show that SRPT at the operation level is 2-competitive, which is best possible.

Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order log M measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.

Every act of language generation compresses a rich internal state into a single token sequence. We call this process intention collapse: a many-to-one projection from a high dimensional intention space I into an external language space L. We formalize intention collapse for contemporary language models, define three simple, model agnostic intention metrics (intention entropy Hint, effective dimensionality dimeff, and latent knowledge recoverability Recov), and propose an empirical agenda for studying how inference time computation shapes internal intentions before they are verbalized. We also report a first small scale experiment. Using a 4 bit Mistral 7B model on 200 GSM8K problems, we compare a direct answer baseline, a chain of thought (CoT) regime, and a babble control. CoT raises accuracy from 5.5 percent to 53 percent, sharply reduces pre collapse intention entropy (from 1.42 to 0.37 bits), and shows higher global effective dimensionality than the other regimes despite producing fewer tokens than babble. At the same time, Hint has little item level predictive power, and a linear probe on I achieves AUROC 0.65 in the CoT regime but only about chance in the baseline regime, where it collapses to the majority class. These preliminary results indicate that intention level metrics can distinguish inference regimes and expose latent information that is partly lost during collapse, while also revealing important limitations of our current proxies

Understanding the loss landscape is an important problem in machine learning. One key feature of the loss function, common to many neural network architectures, is the presence of exponentially many low lying local minima. Physical systems with similar energy landscapes may provide useful insights. In this work, we point out that black holes naturally give rise to such landscapes, owing to the existence of black hole entropy. For definiteness, we consider 1/8 BPS black holes in N = 8 string theory. These provide an infinite family of potential landscapes arising in the microscopic descriptions of corresponding black holes. The counting of minima amounts to black hole microstate counting. Moreover, the exact numbers of the minima for these landscapes are a priori known from dualities in string theory. Some of the minima are connected by paths of low loss values, resembling mode connectivity. We estimate the number of runs needed to find all the solutions. Initial explorations suggest that Stochastic Gradient Descent can find a significant fraction of the minima.

Large language models (LLMs) are typically developed through large-scale pre-training followed by task-specific fine-tuning. Recent advances highlight the importance of an intermediate mid-training stage, where models undergo multiple annealing-style phases that refine data quality, adapt optimization schedules, and extend context length. This stage mitigates diminishing returns from noisy tokens, stabilizes convergence, and expands model capability in late training. Its effectiveness can be explained through gradient noise scale, the information bottleneck, and curriculum learning, which together promote generalization and abstraction. Despite widespread use in state-of-the-art systems, there has been no prior survey of mid-training as a unified paradigm. We introduce the first taxonomy of LLM mid-training spanning data distribution, learning-rate scheduling, and long-context extension. We distill practical insights, compile evaluation benchmarks, and report gains to enable structured comparisons across models. We also identify open challenges and propose avenues for future research and practice.

Coupling together distinct correlated and topologically non-trivial electronic phases of matter can potentially induce novel electronic orders and phase transitions among them. Transition metal dichalcogenide compounds serve as a bedrock for exploration of such hybrid systems. They host a variety of exotic electronic phases and their Van der Waals nature enables to admix them, either by exfoliation and stacking or by stoichiometric growth, and thereby induce novel correlated complexes. Here we investigate the compound 4Hb-TaS_2 that interleaves the Mott-insulating state of 1T-TaS_2 and the putative spin liquid it hosts together with the metallic state of 2H-TaS_2 and the low temperature superconducting phase it harbors. We reveal a thermodynamic phase diagram that hosts a first order quantum phase transition between a correlated Kondo cluster state and a flat band state in which the Kondo cluster becomes depleted. We demonstrate that this intrinsic transition can be induced by an electric field and temperature as well as by manipulation of the interlayer coupling with the probe tip, hence allowing to reversibly toggle between the Kondo cluster and the flat band states. The phase transition is manifested by a discontinuous change of the complete electronic spectrum accompanied by hysteresis and low frequency noise. We find that the shape of the transition line in the phase diagram is determined by the local compressibility and the entropy of the two electronic states. Our findings set such heterogeneous structures as an exciting platform for systematic investigation and manipulation of Mott-metal transitions and strongly correlated phases and quantum phase transitions therein.

Artificial Intelligence (AI), with its multiplier effect and wide applications in multiple areas, could potentially be an important application of quantum computing. Since modern AI systems are often built on neural networks, the design of quantum neural networks becomes a key challenge in integrating quantum computing into AI. To provide a more fine-grained characterisation of the impact of quantum components on the performance of neural networks, we propose a framework where classical neural network layers are gradually replaced by quantum layers that have the same type of input and output while keeping the flow of information between layers unchanged, different from most current research in quantum neural network, which favours an end-to-end quantum model. We start with a simple three-layer classical neural network without any normalisation layers or activation functions, and gradually change the classical layers to the corresponding quantum versions. We conduct numerical experiments on image classification datasets such as the MNIST, FashionMNIST and CIFAR-10 datasets to demonstrate the change of performance brought by the systematic introduction of quantum components. Through this framework, our research sheds new light on the design of future quantum neural network models where it could be more favourable to search for methods and frameworks that harness the advantages from both the classical and quantum worlds.

Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on a quantum device. To guide the selection of measurement methods designed for this observable estimation problem, we propose a benchmark called CSHOREBench (Common States and Hamiltonians for ObseRvable Estimation Benchmark) that assesses the performance of these methods against a set of common molecular Hamiltonians and common states encountered during the runtime of hybrid quantum-classical algorithms. In CSHOREBench, we account for resource utilization of a quantum computer through measurements of a prepared state, and a classical computer through computational runtime spent in proposing measurements and classical post-processing of acquired measurement outcomes. We apply CSHOREBench considering a variety of measurement methods on Hamiltonians of size up to 16 qubits. Our discussion is aided by using the framework of decision diagrams which provides an efficient data structure for various randomized methods and illustrate how to derandomize distributions on decision diagrams. In numerical simulations, we find that the methods of decision diagrams and derandomization are the most preferable. In experiments on IBM quantum devices against small molecules, we observe that decision diagrams reduces the number of measurements made by classical shadows by more than 80%, that made by locally biased classical shadows by around 57%, and consistently require fewer quantum measurements along with lower classical computational runtime than derandomization. Furthermore, CSHOREBench is empirically efficient to run when considering states of random quantum ansatz with fixed depth.

LLMs have seen rapid adoption in all domains. They need to be trained on high-end high-performance computing (HPC) infrastructures and ingest massive amounts of input data. Unsurprisingly, at such a large scale, unexpected events (e.g., failures of components, instability of the software, undesirable learning patterns, etc.), are frequent and typically impact the training in a negative fashion. Thus, LLMs need to be checkpointed frequently so that they can be rolled back to a stable state and subsequently fine-tuned. However, given the large sizes of LLMs, a straightforward checkpointing solution that directly writes the model parameters and optimizer state to persistent storage (e.g., a parallel file system), incurs significant I/O overheads. To address this challenge, in this paper we study how to reduce the I/O overheads for enabling fast and scalable checkpointing for LLMs that can be applied at high frequency (up to the granularity of individual iterations) without significant impact on the training process. Specifically, we introduce a lazy asynchronous multi-level approach that takes advantage of the fact that the tensors making up the model and optimizer state shards remain immutable for extended periods of time, which makes it possible to copy their content in the background with minimal interference during the training process. We evaluate our approach at scales of up to 180 GPUs using different model sizes, parallelism settings, and checkpointing frequencies. The results show up to 48times faster checkpointing and 2.2times faster end-to-end training runtime compared with the state-of-art checkpointing approaches.

The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this paper, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure (POVM), we compactly represent quantum states with autoregressive transformer neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of String States to partially restore the symmetry of the autoregressive transformer neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo to sample restricted Boltzmann machines. Our work provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

We develop a deep variational free energy framework to compute the equation of state of hydrogen in the warm dense matter region. This method parameterizes the variational density matrix of hydrogen nuclei and electrons at finite temperature using three deep generative models: a normalizing flow model that represents the Boltzmann distribution of the classical nuclei, an autoregressive transformer that models the distribution of electrons in excited states, and a permutational equivariant flow model that constructs backflow coordinates for electrons in Hartree-Fock orbitals. By jointly optimizing the three neural networks to minimize the variational free energy, we obtain the equation of state and related thermodynamic properties of dense hydrogen. We compare our results with other theoretical and experimental results on the deuterium Hugoniot curve, aiming to resolve existing discrepancies. The calculated results provide a valuable benchmark for deuterium in the warm dense matter region.

From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the Kuramoto model. A new way of thinking is to interpret the deterministic time evolution of a macroscopic variable as an external operation to a thermodynamic system. We then find that the irreversible work determines the equation for the collective dynamics. When analyzing the Kuramoto model, we employ a generalized concept of irreversible work which originates from a non-equilibrium identity associated with steady state thermodynamics.