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Michael Deweese

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5 papers

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NeurIPS Conference 2025 Conference Paper

Alternating Gradient Flows: A Theory of Feature Learning in Two-layer Neural Networks

Daniel Kunin
Giovanni Luca Marchetti
Feng Chen
Dhruva Karkada
James Simon
Michael Deweese
Surya Ganguli
Nina Miolane

What features neural networks learn, and how, remains an open question. In this paper, we introduce Alternating Gradient Flows (AGF), an algorithmic framework that describes the dynamics of feature learning in two-layer networks trained from small initialization. Prior works have shown that gradient flow in this regime exhibits a staircase-like loss curve, alternating between plateaus where neurons slowly align to useful directions and sharp drops where neurons rapidly grow in norm. AGF approximates this behavior as an alternating two-step process: maximizing a utility function over dormant neurons and minimizing a cost function over active ones. AGF begins with all neurons dormant, corresponding to an initialization at the origin. At each iteration, a dormant neuron activates, triggering the acquisition of a feature and a drop in the loss. AGF quantifies the order, timing, and magnitude of these drops, matching experiments across several commonly studied architectures. We show that AGF unifies and extends existing saddle-to-saddle analyses in fully connected linear networks and attention-only linear transformers, where the learned features are singular modes and principal components, respectively. In diagonal linear networks, we prove AGF converges to gradient flow in the limit of vanishing initialization. Applying AGF to quadratic networks trained to perform modular addition, we give the first complete characterization of the training dynamics, revealing that networks learn Fourier features in decreasing order of coefficient magnitude. Altogether, AGF offers a promising step towards understanding feature learning in neural networks.

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NeurIPS Conference 2025 Conference Paper

Closed-Form Training Dynamics Reveal Learned Features and Linear Structure in Word2Vec-like Models

Dhruva Karkada
James Simon
Yasaman Bahri
Michael Deweese

Self-supervised word embedding algorithms such as word2vec provide a minimal setting for studying representation learning in language modeling. We examine the quartic Taylor approximation of the word2vec loss around the origin, and we show that both the resulting training dynamics and the final performance on downstream tasks are empirically very similar to those of word2vec. Our main contribution is to analytically solve for both the gradient flow training dynamics and the final word embeddings in terms of only the corpus statistics and training hyperparameters. The solutions reveal that these models learn orthogonal linear subspaces one at a time, each one incrementing the effective rank of the embeddings until model capacity is saturated. Training on Wikipedia, we find that each of the top linear subspaces represents an interpretable topic-level concept. Finally, we apply our theory to describe how linear representations of more abstract semantic concepts emerge during training; these can be used to complete analogies via vector addition.

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NeurIPS Conference 2025 Conference Paper

Quantifying Elicitation of Latent Capabilities in Language Models

Elizabeth Donoway
Hailey Joren
Arushi Somani
Henry Sleight
Julian Michael
Michael Deweese
John Schulman
Ethan Perez

Large language models often possess latent capabilities that lie dormant unless explicitly elicited, or surfaced, through fine-tuning or prompt engineering. Predicting, assessing, and understanding these latent capabilities pose significant challenges in the development of effective, safe AI systems. In this work, we recast elicitation as an information-constrained fine-tuning problem and empirically characterize upper bounds on the minimal number of parameters needed to achieve specific task performances. We find that training as few as 10–100 randomly chosen parameters—several orders of magnitude fewer than state-of-the-art parameter-efficient methods—can recover up to 50\% of the performance gap between pretrained-only and full fine-tuned models, and 1, 000s to 10, 000s of parameters can recover 95\% of this performance gap. We show that a logistic curve fits the relationship between the number of trained parameters and model performance gap recovery. This scaling generalizes across task formats and domains, as well as model sizes and families, extending to reasoning models and remaining robust to increases in inference compute. To help explain this behavior, we consider a simplified picture of elicitation via fine-tuning where each trainable parameter serves as an encoding mechanism for accessing task-specific knowledge. We observe a relationship between the number of trained parameters and how efficiently relevant model capabilities can be accessed and elicited, offering a potential route to distinguish elicitation from teaching.

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NeurIPS Conference 2002 Conference Paper

Binary Coding in Auditory Cortex

Michael Deweese
Anthony Zador

Cortical neurons have been reported to use both rate and temporal codes. Here we describe a novel mode in which each neuron generates exactly 0 or 1 action potentials, but not more, in response to a stimulus. We used cell-attached recording, which ensured single-unit isolation, to record responses in rat auditory cortex to brief tone pips. Surprisingly, the majority of neurons exhibited binary behavior with few multi-spike responses; several dramatic examples consisted of exactly one spike on 100% of trials, with no trial-to-trial variability in spike count. Many neurons were tuned to stimulus frequency. Since individual trials yielded at most one spike for most neurons, the information about stimulus frequency was encoded in the population, and would not have been accessible to later stages of processing that only had access to the activity of a single unit. These binary units allow a more efficient population code than is possible with conventional rate coding units, and are consistent with a model of cortical processing in which synchronous packets of spikes propagate stably from one neuronal population to the next. 1 B i n a r y c o d i n g i n a u d i t o r y c o r t e x We recorded responses of neurons in the auditory cortex of anesthetized rats to pure-tone pips of different frequencies [1, 2]. Each pip was presented repeatedly, allowing us to assess the variability of the neural response to multiple presentations of each stimulus. We first recorded multi-unit activity with conventional tungsten electrodes (Fig. 1a). The number of spikes in response to each pip fluctuated markedly from one trial to the next (Fig. 1e), as though governed by a random mechanism such as that generating the ticks of a Geiger counter. Highly variable responses such as these, which are at least as variable as a Poisson process, are the norm in the cortex [3-7], and have contributed to the widely held view that cortical spike trains are so noisy that only the average firing rate can be used to encode stimuli. Because we were recording the activity of an unknown number of neurons, we could not be sure whether the strong trial-to-trial fluctuations reflected the underlying variability of the single units. We therefore used an alternative technique, cell-

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NeurIPS Conference 1995 Conference Paper

Optimization Principles for the Neural Code

Michael Deweese

Recent experiments show that the neural codes at work in a wide range of creatures share some common features. At first sight, these observations seem unrelated. However, we show that these features arise naturally in a linear filtered threshold crossing (LFTC) model when we set the threshold to maximize the transmitted information. This maximization process requires neural adaptation to not only the DC signal level, as in conventional light and dark adaptation, but also to the statistical structure of the signal and noise distribu(cid: 173) tions. We also present a new approach for calculating the mutual information between a neuron's output spike train and any aspect of its input signal which does not require reconstruction of the in(cid: 173) put signal. This formulation is valid provided the correlations in the spike train are small, and we provide a procedure for checking this assumption. This paper is based on joint work (DeWeese [1], 1995). Preliminary results from the LFTC model appeared in a previous proceedings (DeWeese [2], 1995), and the conclusions we reached at that time have been reaffirmed by further analysis of the model.

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