Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) can be _misaligned_ with pass@N in that pass@N accuracy _decreases_ with longer CE training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions both with and without Chain-of-Thought reasoning traces; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Discrete diffusion has emerged as a powerful framework for generative modeling in discrete domains, yet efficiently sampling from these models remains challenging. Existing sampling strategies often struggle to balance computation and sample quality when the number of sampling steps is reduced, even when the model has learned the data distribution well. To address these limitations, we propose a predictor-corrector sampling scheme where the corrector is informed by the diffusion model to more reliably counter the accumulating approximation errors. To further enhance the effectiveness of our informed corrector, we introduce complementary architectural modifications based on hollow transformers and a simple tailored training objective that leverages more training signal. We use a synthetic example to illustrate the failure modes of existing samplers and show how informed correctors alleviate these problems. On the Text8 dataset, the informed corrector improves sample quality by generating text with significantly fewer errors than the baselines. On tokenized ImageNet 256x256, this approach consistently produces superior samples with fewer steps, achieving improved FID scores for discrete diffusion models. These results underscore the potential of informed correctors for fast and high-fidelity generation using discrete diffusion.

Lateral and recurrent connections are ubiquitous in biological neural circuits. Yet while the strong computational abilities of feedforward networks have been extensively studied, our understanding of the role and advantages of recurrent computations that might explain their prevalence remains an important open challenge. Foundational studies by Minsky and Roelfsema argued that computations that require propagation of global information for local computation to take place would particularly benefit from the sequential, parallel nature of processing in recurrent networks. Such "tag propagation" algorithms perform repeated, local propagation of information and were originally introduced in the context of detecting connectedness, a task that is challenging for feedforward networks. Here, we advance the understanding of the utility of lateral and recurrent computation by first performing a large-scale empirical study of neural architectures for the computation of connectedness to explore feedforward solutions more fully and establish robustly the importance of recurrent architectures. In addition, we highlight a tradeoff between computation time and performance and construct hybrid feedforward/recurrent models that perform well even in the presence of varying computational time limitations. We then generalize tag propagation architectures to propagating multiple interacting tags and demonstrate that these are efficient computational substrates for more general computations of connectedness by introducing and solving an abstracted biologically inspired decision-making task. Our work thus clarifies and expands the set of computational tasks that can be solved efficiently by recurrent computation, yielding hypotheses for structure in population activity that may be present in such tasks.

Calcium imaging with fluorescent protein sensors is widely used to record activity in neuronal populations. The transform between neural activity and calcium-related fluorescence involves nonlinearities and low-pass filtering, but the effects of the transformation on analyses of neural populations are not well understood. We compared neuronal spikes and fluorescence in matched neural populations in behaving mice. We report multiple discrepancies between analyses performed on the two types of data, including changes in single-neuron selectivity and population decoding. These were only partially resolved by spike inference algorithms applied to fluorescence. To model the relation between spiking and fluorescence we simultaneously recorded spikes and fluorescence from individual neurons. Using these recordings we developed a model transforming spike trains to synthetic-imaging data. The model recapitulated the differences in analyses. Our analysis highlights challenges in relating electrophysiology and imaging data, and suggests forward modeling as an effective way to understand differences between these data.

Early stages of sensory systems face the challenge of compressing information from numerous receptors onto a much smaller number of projection neurons, a so called communication bottleneck. To make more efficient use of limited bandwidth, compression may be achieved using predictive coding, whereby predictable, or redundant, components of the stimulus are removed. In the case of the retina, Srinivasan et al. (1982) suggested that feedforward inhibitory connections subtracting a linear prediction generated from nearby receptors implement such compression, resulting in biphasic center-surround receptive fields. However, feedback inhibitory circuits are common in early sensory circuits and furthermore their dynamics may be nonlinear. Can such circuits implement predictive coding as well? Here, solving the transient dynamics of nonlinear reciprocal feedback circuits through analogy to a signal-processing algorithm called linearized Bregman iteration we show that nonlinear predictive coding can be implemented in an inhibitory feedback circuit. In response to a step stimulus, interneuron activity in time constructs progressively less sparse but more accurate representations of the stimulus, a temporally evolving prediction. This analysis provides a powerful theoretical framework to interpret and understand the dynamics of early sensory processing in a variety of physiological experiments and yields novel predictions regarding the relation between activity and stimulus statistics.

The rich dynamical nature of neurons poses major conceptual and technical challenges for unraveling their nonlinear membrane properties. Traditionally, various current waveforms have been injected at the soma to probe neuron dynamics, but the rationale for selecting specific stimuli has never been rigorously justified. The present experimental and theoretical study proposes a novel framework, inspired by learning theory, for objectively selecting the stimuli that best unravel the neuron's dynamics. The efficacy of stimuli is assessed in terms of their ability to constrain the parameter space of biophysically detailed conductance-based models that faithfully replicate the neuron's dynamics as attested by their ability to generalize well to the neuron's response to novel experimental stimuli. We used this framework to evaluate a variety of stimuli in different types of cortical neurons, ages and animals. Despite their simplicity, a set of stimuli consisting of step and ramp current pulses outperforms synaptic-like noisy stimuli in revealing the dynamics of these neurons. The general framework that we propose paves a new way for defining, evaluating and standardizing effective electrical probing of neurons and will thus lay the foundation for a much deeper understanding of the electrical nature of these highly sophisticated and non-linear devices and of the neuronal networks that they compose.

A striking aspect of cortical neural networks is the divergence of a relatively small number of input channels from the peripheral sensory apparatus into a large number of cortical neurons, an over-complete representation strategy. Cortical neurons are then connected by a sparse network of lateral synapses. Here we propose that such architecture may increase the persistence of the representation of an incoming stimulus, or a percept. We demonstrate that for a family of networks in which the receptive field of each neuron is re-expressed by its outgoing connections, a represented percept can remain constant despite changing activity. We term this choice of connectivity REceptive FIeld REcombination (REFIRE) networks. The sparse REFIRE network may serve as a high-dimensional integrator and a biologically plausible model of the local cortical circuit.