arXiv subjects

Micah Adler

Publications and source records attributed to Micah Adler.

8 recordsLinked to original sources

arXiv2026

The Sparsity Whisperer

Pruning reduces the inference cost of large language models, but existing criteria primarily preserve large activations or reconstruct layer outputs. We argue that this overlooks a key computation performed by particularly sparsity-sensitive neurons in the MLP up and gate projections: separating similar inputs into dissimilar outputs. This suggests that effective pruning should preserve not only activations, but also the differences between outputs more broadly. We introduce a family of difference-informed pruning methods built upon this principle. Wisp is a first-order, update-free method that scores weights using input-difference norms, and Wisp+ refines this score neuronwise using the input pairs each neuron separates most strongly. Finally, Whisper is a second-order method that uses a lightly regularized difference Hessian as its reconstruction objective. Across Llama 2 and 3.1 models from 7B to 405B parameters, our second-order variant consistently improves over strong reconstruction-based baselines, while our update-free variants improve over activation-aware baselines, especially in constrained settings. The improvements over Wanda and SparseGPT extend to structured sparsity, downstream evaluations, and other model families. Augmenting stronger techniques such as RIA and ALPS with our difference-informed criteria yields further improvements, shifting the overall accuracy-runtime frontier outward at negligible additional cost. These results suggest that preserving output differences is a broadly useful and composable signal for post-training LLM sparsification.

cs.LG↗

arXiv2026

Understanding Empirical Unlearning with Combinatorial Interpretability

While many recent methods aim to unlearn or remove knowledge from pretrained models, seemingly erased knowledge often persists and can be recovered in various ways. Because large foundation models are far from interpretable, understanding whether and how such knowledge persists remains a significant challenge. To address this, we turn to the recently developed framework of combinatorial interpretability. This framework, designed for two-layer neural networks, enables direct inspection of the knowledge encoded in the model weights. We reproduce baseline unlearning methods within the combinatorial interpretability setting and examine their behavior along two dimensions: (i) whether they truly remove knowledge of a target concept (the concept we wish to remove) or merely inhibit its expression while retaining the underlying information, and (ii) how easily the supposedly erased knowledge can be recovered through various fine-tuning operations. Our results shed light within a fully interpretable setting on how knowledge can persist despite unlearning and when it might resurface.

cs.LG↗

arXiv2025

Expand Neurons, Not Parameters

This work demonstrates how increasing the number of neurons in a network without increasing its total number of non-zero parameters improves performance. We show that this gain corresponds with a decrease in interference between multiple features that would otherwise share the same neurons. On symbolic Boolean tasks, splitting each neuron into sparser sub-neurons with knowledge of the clauses systematically reduces polysemanticity metrics and yields higher task accuracy. Notably, even random splits of neuron weights approximate these gains, indicating that reduced collisions, not precise assignment, are a primary driver. Consistent with the superposition hypothesis, the benefits of this framework grow with increasing interference: when polysemantic load is high, accuracy improvements are the largest. Transferring these insights to more realistic models, including classifiers over CLIP embeddings, convolutional neural networks, and deeper multilayer networks, we find that widening networks while maintaining a constant non-zero parameter count consistently increases accuracy. These results identify an interpretability-grounded mechanism to leverage width against superposition, improving performance without increasing the number of non-zero parameters. Such a direction is well matched to modern accelerators, where memory movement of non-zero parameters, rather than raw compute, is often a dominant bottleneck.

cs.LG↗

arXiv2025

Negative Pre-activations Differentiate Syntax

Modern large language models increasingly use smooth activation functions such as GELU or SiLU, allowing negative pre-activations to carry both signal and gradient. Nevertheless, many neuron-level interpretability analyses have historically focused on large positive activations, often implicitly treating the negative region as less informative, a carryover from the ReLU-era. We challenge this assumption and ask whether and how negative pre-activations are leveraged by models. We address this question by studying a sparse subpopulation of Wasserstein neurons whose output distributions deviate strongly from a Gaussian baseline and that functionally differentiate similar inputs. We show that this negative region plays an active role rather than reflecting a mere gradient optimization side effect. A minimal, sign-specific intervention that zeroes only the negative pre-activations of a small set of Wasserstein neurons substantially increases perplexity and sharply degrades grammatical performance on BLiMP and TSE, whereas both random and perplexity-matched ablations of many more non-Wasserstein neurons in their negative pre-activations leave grammatical performance largely intact. Conversely, on a suite of non-grammatical benchmarks, the perplexity-matched control ablation is more damaging than the Wasserstein neuron ablation, yielding a double dissociation between syntax and other capabilities. Part-of-speech analysis localizes the excess surprisal to syntactic scaffolding tokens, layer-specific interventions show that small local degradations accumulate across depth, and training-dynamics analysis reveals that the same sign-specific ablation becomes more harmful as Wasserstein neurons emerge and stabilize. Together, these results identify negative pre-activations in a sparse subpopulation of Wasserstein neurons as an actively used substrate for syntax in smooth-activation language models.

cs.LG↗

arXiv2025

A Capacity-Based Rationale for Multi-Head Attention

We study the capacity of the self-attention key-query channel: for a fixed budget, how many distinct token-token relations can a single layer reliably encode? We introduce Relational Graph Recognition, where the key-query channel encodes a directed graph and, given a context (a subset of the vertices), must recover the neighbors of each vertex in the context. We measure resources by the total key dimension $D_K = h\,d_k$. In a tractable multi-head model, we prove matching information-theoretic lower bounds and upper bounds via explicit constructions showing that recovering a graph with $m'$ relations in $d_{\text{model}}$-dimensional embeddings requires $D_K$ to grow essentially as $m'/d_{\text{model}}$ up to logarithmic factors, and we obtain corresponding guarantees for scaled-softmax attention. This analysis yields a new, capacity-based rationale for multi-head attention: even in permutation graphs, where all queries attend to a single target, splitting a fixed $D_K$ budget into multiple heads increases capacity by reducing interference from embedding superposition. Controlled experiments mirror the theory, revealing sharp phase transitions at the predicted capacity, and the multi-head advantage persists when adding softmax normalization, value routing, and a full Transformer block trained with frozen GPT-2 embeddings.

cs.LG↗

arXiv2025

The Birth of Knowledge: Emergent Features across Time, Space, and Scale in Large Language Models

This paper studies the emergence of interpretable categorical features within large language models (LLMs), analyzing their behavior across training checkpoints (time), transformer layers (space), and varying model sizes (scale). Using sparse autoencoders for mechanistic interpretability, we identify when and where specific semantic concepts emerge within neural activations. Results indicate clear temporal and scale-specific thresholds for feature emergence across multiple domains. Notably, spatial analysis reveals unexpected semantic reactivation, with early-layer features re-emerging at later layers, challenging standard assumptions about representational dynamics in transformer models.

cs.CL↗

arXiv2025

Towards Combinatorial Interpretability of Neural Computation

We introduce combinatorial interpretability, a methodology for understanding neural computation by analyzing the combinatorial structures in the sign-based categorization of a network's weights and biases. We demonstrate its power through feature channel coding, a theory that explains how neural networks compute Boolean expressions and potentially underlies other categories of neural network computation. According to this theory, features are computed via feature channels: unique cross-neuron encodings shared among the inputs the feature operates on. Because different feature channels share neurons, the neurons are polysemantic and the channels interfere with one another, making the computation appear inscrutable. We show how to decipher these computations by analyzing a network's feature channel coding, offering complete mechanistic interpretations of several small neural networks that were trained with gradient descent. Crucially, this is achieved via static combinatorial analysis of the weight matrices, without examining activations or training new autoencoding networks. Feature channel coding reframes the superposition hypothesis, shifting the focus from neuron activation directionality in high-dimensional space to the combinatorial structure of codes. It also allows us for the first time to exactly quantify and explain the relationship between a network's parameter size and its computational capacity (i.e. the set of features it can compute with low error), a relationship that is implicitly at the core of many modern scaling laws. Though our initial studies of feature channel coding are restricted to Boolean functions, we believe they provide a rich, controlled, and informative research space, and that the path we propose for combinatorial interpretation of neural computation can provide a basis for understanding both artificial and biological neural circuits.

cs.LG↗

arXiv2024

On the Complexity of Neural Computation in Superposition

Superposition, the ability of neural networks to represent more features than neurons, is increasingly seen as key to the efficiency of large models. This paper investigates the theoretical foundations of computing in superposition, establishing complexity bounds for explicit, provably correct algorithms. We present the first lower bounds for a neural network computing in superposition, showing that for a broad class of problems, including permutations and pairwise logical operations, computing $m'$ features in superposition requires at least $\Omega(\sqrt{m' \log m'})$ neurons and $\Omega(m' \log m')$ parameters. This implies an explicit limit on how much one can sparsify or distill a model while preserving its expressibility, and complements empirical scaling laws by implying the first subexponential bound on capacity: a network with $n$ neurons can compute at most $O(n^2 / \log n)$ features. Conversely, we provide a nearly tight constructive upper bound: logical operations like pairwise AND can be computed using $O(\sqrt{m'} \log m')$ neurons and $O(m' \log^2 m')$ parameters. There is thus an exponential gap between the complexity of computing in superposition (the subject of this work) versus merely representing features, which can require as little as $O(\log m')$ neurons based on the Johnson-Lindenstrauss Lemma. Our work analytically establishes that the number of parameters is a good estimator of the number of features a neural network computes.

cs.CC↗