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. Experimental results across several tasks, involving personalized text and image generation, showcase the effectiveness of UserAlign in achieving personalized alignment.

Visual place recognition (VPR) is typically regarded as a specific image retrieval task, whose core lies in representing images as global descriptors. Over the past decade, dominant VPR methods (e.g., NetVLAD) have followed a paradigm that first extracts the patch features/tokens of the input image using a backbone, and then aggregates these patch features into a global descriptor via an aggregator. This backbone-plus-aggregator paradigm has achieved overwhelming dominance in the CNN era and remains widely used in transformer-based models. In this paper, however, we argue that a dedicated aggregator is not necessary in the transformer era, that is, we can obtain robust global descriptors only with the backbone. Specifically, we introduce some learnable aggregation tokens, which are prepended to the patch tokens before a particular transformer block. All these tokens will be jointly processed and interact globally via the intrinsic self-attention mechanism, implicitly aggregating useful information within the patch tokens to the aggregation tokens.

This fact challenges the application of deep neural network fingerprints as the cost of queries is becoming a bottleneck. This paper studies the performance of deep neural network fingerprints from an information theoretical perspective.

We study the problem of entropy calibration, which asks whether a language model's entropy over generations matches its log loss on human text. Past work found that models are miscalibrated, with entropy per step increasing as generations grow longer, due to error accumulation. To calibrate the model and improve text quality, it has become standard practice to truncate the distribution, but this approach reduces output diversity, which we would like to avoid. Therefore, in this paper, we ask: does miscalibration improve automatically with scale, and if not, is it theoretically possible to calibrate without tradeoffs? To build intuition, we first study a simplified theoretical setting to characterize the scaling behavior of miscalibration with respect to dataset size. We find that the rate of scaling depends on the power law exponent of the data distribution --- in particular, for a power law exponent close to 1, the scaling exponent is close to 0, meaning that miscalibration improves very slowly with scale.

We establish a comprehensive finite-sample and asymptotic theory for stochastic gradient descent (SGD) with constant learning rates. First, we propose a novel linear approximation technique to provide a quenched central limit theorem (CLT) for SGD iterates with refined tail properties, showing that regardless of the chosen initialization, the fluctuations of the algorithm around its target point converge to a multivariate normal distribution. Our conditions are substantially milder than those required in the classical CLTs for SGD, yet offering a stronger convergence result. Furthermore, we derive the first Berry-Esseen bound -- the Gaussian approximation error -- for the constant learning-rate SGD, which is sharp compared to the decaying learning-rate schemes in the literature. Beyond the moment convergence, we also provide the Nagaev-type inequality for the SGD tail probabilities by adopting the autoregressive approximation techniques, which entails non-asymptotic large-deviation guarantees. These results are verified via numerical simulations, paving the way for theoretically grounded uncertainty quantification, especially with non-asymptotic validity.

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.

We propose an algorithm with improved query-complexity for the problem of hypothesis selection under local differential privacy constraints. Given a set of $k$ probability distributions $Q$, we describe an algorithm that satisfies local differential privacy, performs $\tilde{O}(k^{3/2})$ non-adaptive queries to individuals who each have samples from a probability distribution $p$, and outputs a probability distribution from the set $Q$ which is nearly the closest to $p$. Previous algorithms required either $\Omega(k^2)$ queries or many rounds of interactive queries. Technically, we introduce a new object we dub the Scheff\'e graph, which captures structure of the differences between distributions in $Q$, and may be of more broad interest for hypothesis selection tasks.

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\times) end-to-end speedups for models like OPT, LLaMA-2 & 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.