Mengdi Wang
Publications
DeepLoop: Depth Scaling for Looped Transformers
Looped Transformers scale sequential computation by applying a compact stack of physical blocks for multiple rounds, increasing unrolled depth without increasing stored parameters. This reuse changes the residual-scaling problem: in an untied Transformer, each residual branch receives and applies its own parameter update, whereas in a looped Transformer one shared update aggregates gradients from repeated visits and is read back by those same visits in the next linearized forward pass. We formalize this tied-depth effect through a first-order perturbation bound controlled by a visit-alignment coefficient $κ_R$. The bound recovers the DeepNorm exponent when visits decorrelate, but in the conservative aligned regime it requires the exponent to increase from $1/4$ to $1/2$ as loop count grows at fixed physical depth. The resulting method, \textbf{DeepLoop}, keeps the Post-LN DeepNorm architecture and sets $α=(2N)^{1/2}$ and $β=(8N)^{-1/2}$ for unrolled depth $N$. On GPT-style looped language models at GPT-2 small and GPT-2 medium scale, DeepLoop is neutral when no physical block is revisited and improves validation loss and downstream accuracy once recurrent depth is activated. These results show that stable recurrent depth requires residual scaling rules that account for parameter visits, not only nominal layer count.
Interactive Benchmarks
Standard benchmarks have become increasingly unreliable due to saturation, subjectivity, and poor generalization. We argue that evaluating model's ability to acquire information actively is important to assess model's intelligence. We propose Interactive Benchmarks, a unified evaluation paradigm that assesses model's reasoning ability in an interactive process under budget constraints. We instantiate this framework across two settings: Interactive Proofs, where models interact with a judge to deduce objective truths or answers in logic and mathematics; and Interactive Games, where models reason strategically to maximize long-horizon utilities. Our results show that interactive benchmarks provide a robust and faithful assessment of model intelligence, revealing that there is still substantial room to improve in interactive scenarios. Project page: https://github.com/interactivebench/interactivebench
Deep Delta Learning
The effectiveness of deep residual networks hinges on the identity shortcut connection. While this mechanism alleviates the vanishing-gradient problem, it also has a strictly additive inductive bias on feature transformations, limiting the network's ability to model complex hidden state transitions. In this paper, we introduce \textbf{Deep Delta Learning (DDL)}, which generalizes the shortcut from a fixed identity map to a learnable, state-dependent linear operator. The resulting Delta Operator is a rank-1 perturbation of the identity, $\mathbf{A}(\mathbf{X}) = \mathbf{I}- β(\mathbf{X})\mathbf{k} (\mathbf{X}) \mathbf{k} (\mathbf{X})^\top$, parameterized by a unit direction $\mathbf{k}(\mathbf{X})$ and a scalar gate $β(\mathbf{X})$. We provide a spectral analysis showing that $β(\mathbf{X})$ continuously interpolates the shortcut between identity ($β=0$), orthogonal projection ($β=1$), and Householder reflection ($β=2$). Furthermore, we rewrite the residual update as a synchronized rank-1 delta write: $β$ scales both the removal of the current $\mathbf{k}$-component and the injection of the new $\mathbf{k}$-component. This unification enables explicit control of the shortcut spectrum along a data-dependent direction while retaining stable training behavior. Empirically, replacing Transformer residual additions with DDL improves validation loss and perplexity, as well as downstream evaluation accuracy on language modeling tasks, with larger gains in the expanded-state setting.