While Large Language Models (LLMs) demonstrate strong performance across domains, their long-context capabilities are limited by transient neural activations causing information decay and unstructured feed-forward network (FFN) weights leading to semantic fragmentation. Inspired by the brain's working memory and cortical modularity, we propose PaceLLM, featuring two innovations: (1) a Persistent Activity (PA) Mechanism that mimics prefrontal cortex (PFC) neurons' persistent firing by introducing an activation-level memory bank to dynamically retrieve, reuse, and update critical FFN states, addressing contextual decay; and (2) Cortical Expert (CE) Clustering that emulates task-adaptive neural specialization to reorganize FFN weights into semantic modules, establishing cross-token dependencies and mitigating fragmentation.

Accurate network estimation serves as the cornerstone for understanding complex systems across scientific domains, from decoding gene regulatory networks in systems biology to identifying social relationship patterns in computational sociology. Modern applications demand methods that simultaneously address two critical challenges: capturing nonlinear dependencies between variables and reconstructing inherent hierarchical structures where higher-level entities coordinate lower-level components (e.g., functional pathways organizing gene clusters). Traditional Gaussian graphical models fundamentally fail in these aspects due to their restrictive linear assumptions and flat network representations. We propose NNBLNet, a neural network-based learning framework for bi-level network inference. The core innovation lies in hierarchical selection layers that enforce structural consistency between high-level coordinator groups and their constituent low-level connections via adaptive sparsity constraints. This architecture is integrated with a compositional neural network architecture that learn cross-level association patterns through constrained nonlinear transformations, explicitly preserving hierarchical dependencies while overcoming the representational limitations of linear methods. Crucially, we establish formal theoretical guarantees for the consistent recovery of both high-level connections and their internal low-level structures under general statistical regimes. Extensive validation demonstrates NNBLNet's effectiveness across synthetic and real-world scenarios, achieving superior F1 scores compared to competitive methods and particularly beneficial for complex systems analysis through its interpretable bi-level structure discovery.

Invariant object recognition-the ability to identify objects despite changes in appearance-is a hallmark of visual processing in the brain, yet its understanding remains a central challenge in systems neuroscience. Artificial neural networks trained to predict neural responses to visual stimuli ("digital twins") could provide a powerful framework for studying such complex computations in silico. However, while current models accurately capture single-neuron responses within individual visual areas, their ability to reproduce how populations of neurons represent object identity, and how these representations transform across the cortical hierarchy, remains largely unexplored. Here we examine key functional signatures observed experimentally and find that current models account for hierarchical changes in basic single-neuron properties, such as receptive field size, but fail to capture more complex population-level phenomena, particularly invariant object representations. To address this gap, we introduce a biologically inspired hierarchical readout scheme that mirrors cortical anatomy, modeling each visual area as a projection from a distinct depth within a shared core network. This approach significantly improves the prediction of population-level representational transformations, outperforming standard models that use only the final layer, as well as alternatives with modified architecture, regularization, and loss function. Our results suggest that incorporating anatomical information provides a strong inductive bias in digital twin models, enabling them to better capture general principles of brain function.

We study the problem of aligning a generative model's response with a user's preferences. Recent works have proposed several different formulations for personalized alignment; however, they either require a large amount of user preference queries or require that the preference be explicitly specified as a text input. In this paper, we propose a novel inference-time personalized alignment method, USERALIGN, that elicits the user's preferences with a few queries as pairwise response comparisons. In particular, USERALIGN builds on the theoretical framework of best-arm identification in logistic bandits and selects a personalized response from a fixed pool of the model's generated responses. The key idea is to consider the user's feedback consistent and noise-free, and incorporate it into the theoretical framework to identify the best response quickly.

In this paper, we propose a provably convergent and practical framework for multi-objective reinforcement learning with max-min criterion. From a game-theoretic perspective, we reformulate max-min multi-objective reinforcement learning as a two-player zero-sum regularized continuous game and introduce an efficient algorithm based on mirror descent.

This paper presents a comprehensive theoretical analysis of the learnability of neuro-symbolic (NeSy) tasks within hybrid systems. We characterize the learnability of NeSy tasks by their derived constraint satisfaction problems (DCSPs), demonstrating that a task is learnable if and only if its corresponding DCSP admits a unique solution. Under mild assumptions, we establish the sample complexity for learnable tasks and show that, for general tasks, the asymptotic expected concept error is controlled by the degree of disagreement among DCSP solutions. Our findings unify the characterization of learnability and the phenomenon of reasoning shortcuts, providing theoretical guarantees and actionable guidance for the principled design of NeSy systems.

Accelerating large language model (LLM) inference is critical for real-world deployments requiring high throughput and low latency. Contextual sparsity, where each token dynamically activates only a small subset of the model parameters, shows promise but does not scale to large batch sizes due to union of active neurons quickly approaching dense computation. We introduce Polar Sparsity, highlighting a key shift in sparsity importance from MLP to Attention layers as we scale batch size and sequence length. While MLP layers become more compute-efficient under batching, their sparsity vanishes. In contrast, attention becomes increasingly more expensive at scale, while their head sparsity remains stable and batch-invariant. We develop Selective Head Attention with hardware-efficient, sparsity-aware GPU kernels, delivering up to 2.2 end-to-end speedups for models like OPT, LLaMA2 & 3, Qwen, Mistral across various batch sizes and sequence lengths without compromising accuracy. To our knowledge, this is the first work to demonstrate that contextual sparsity can scale effectively to large batch sizes, delivering substantial inference acceleration with minimal changes, making Polar Sparsity practical for large-scale, high-throughput LLM deployment systems.

We study quantum algorithms based on quantum (sub)gradient estimation using noisy function evaluation oracles, and demonstrate the first dimension-independent query complexities (up to poly-logarithmic factors) for zeroth-order convex optimization in both smooth and nonsmooth settings. Interestingly, only using noisy function evaluation oracles, we match the first-order query complexities of classical gradient descent, thereby exhibiting exponential separation between quantum and classical zeroth-order optimization. We then generalize these algorithms to work in non-Euclidean settings by using quantum (sub)gradient estimation to instantiate mirror descent and its variants, including dual averaging and mirror prox. By leveraging a connection between semidefinite programming and eigenvalue optimization, we use our quantum mirror descent method to give a new quantum algorithm for solving semidefinite programs, linear programs, and zero-sum games. We identify a parameter regime in which our zero-sum games algorithm is faster than any existing classical or quantum approach.

Large language models (LLMs) have achieved impressive results on complex reasoning tasks, but their high inference cost remains a major barrier to real-world deployment. A promising solution is to use cascaded inference, where small, cheap models handle easy queries, and only the hardest examples are escalated to more powerful models. However, existing cascade methods typically rely on supervised training with labeled data, offer no theoretical generalization guarantees, and provide limited control over test-time computational cost. We introduce C3PO (Cost Controlled Cascaded Prediction Optimization), a self-supervised framework for optimizing LLM cascades under probabilistic cost constraints. By focusing on minimizing regret with respect to the most powerful model (MPM), C3PO avoids the need for labeled data by constructing a cascade using only unlabeled model outputs. It leverages conformal prediction to bound the probability that inference cost exceeds a user-specified budget. We provide theoretical guarantees on both cost control and generalization error, and show that our optimization procedure is effective even with small calibration sets. Empirically, C3PO achieves stateof-the-art performance across a diverse set of reasoning benchmarks including GSM8K, MATH-500, BigBench-Hard and AIME, outperforming strong LLM cascading baselines in both accuracy and cost-efficiency. Our results demonstrate that principled, label-free cascade optimization can enable scalable LLM deployment.

If you tell a learning model that you prefer an alternative a over another alternative b, then you probably expect the model to be monotone, that is, the valuation of a increases, and that of bdecreases. Yet, perhaps surprisingly, many widely deployed comparison-based preference learning models, including large language models, fail to have this guarantee. Until now, the only comparison-based preference learning algorithms that were proved to be monotone are the Generalized BradleyTerry models [10]. Yet, these models are unable to generalize to uncompared data. In this paper, we advance the understanding of the set of models with generalization ability that are monotone. Namely, we propose a new class of Linear Generalized Bradley-Terry models with Diffusion Priors, and identify sufficient conditions on alternatives' embeddings that guarantee monotonicity. Our experiments show that this monotonicity is far from being a general guarantee, and that our new class of generalizing models improves accuracy, especially when the dataset is limited.