Taylor Berg-Kirkpatrick

Traditional fixed-depth architectures scale quality by increasing training FLOPs, typically through increased parameterization, at the expense of higher memory footprints, or data. A potential alternative is ooped architectures, which instead increase FLOPs by sending activations through a block of layers in a loop. While promising, existing recipes for training looped architectures can be unstable, suffering from residual explosion and loss spikes. We address these challenges by recasting looping as a nonlinear time-variant dynamical system over the residual stream. Via a linear approximation to this system, we find that instability occurs in existing looped architectures as a result of large spectral norms in their injection parameters. To address these instability issues, we propose Parcae, a novel stable, looped architecture that constrains the spectral norm of the injection parameters via discretization of a negative diagonal parameterization. As a result, Parcae achieves up to 6.3% lower validation perplexity over prior large-scale looped models. Using our stable looped architecture, we investigate the scaling properties of looping as a medium to improve quality by increasing FLOPs in training and test-time. For training, we derive predictable power laws to scale FLOPs while keeping parameter count fixed. Our initial scaling laws suggest that looping and data should be increased in tandem, given a fixed FLOP budget. At test-time, we find that Parcae can use looping to scale compute, following a predictable, saturating exponential decay. When scaled up to 1.3B parameters, we find that Parcae improves CORE and Core-Extended quality by 2.99 and 1.18 points when compared to strong Transformer baselines under a fixed parameter and data budget, achieving a relative quality of up to 87.5% a Transformer twice the size.

DeepSeek-OCR shows that rendered text can be reconstructed from a small number of vision tokens, sparking excitement about using vision as a compression medium for long textual contexts. But this pipeline requires rendering token embeddings to pixels and compressing from there—discarding learned representations in favor of an image the vision encoder must then recover from. We ask whether this detour helps. Comparing DeepSeek-OCR's vision encoder against near-zero-parameter mean pooling and a learned hierarchical encoder, we find it does not. For reconstruction, simple direct methods match or surpass vision at every compression ratio. For language modeling, vision performs comparably to truncation—a baseline that simply discards context—and loses to the hierarchical encoder at every compression ratio. As expected, all compression methods outperform truncation for factual recall, but vision never surpasses the best direct baseline. The excitement around optical context compression outpaces the evidence. Code and checkpoints are available at https://github.com/ivnle/bad-autoencoding.

Asking a large language model to respond in JSON should be a formatting choice, not a capability tax. Yet we find that structured output requirements—JSON, XML, LaTeX, Markdown—substantially degrade reasoning and writing performance across open-weight models. The research response has focused on constrained decoding, but sampling bias accounts for only a fraction of the degradation. The dominant cost enters at the prompt: format-requesting instructions alone cause most of the accuracy loss, before any decoder constraint is applied. This diagnosis points to a simple principle: decouple reasoning from formatting. Across six open-weight models, four API models, four formats, and tasks spanning math, science, logic, and writing, generating freeform first and reformatting in a second pass recovers most lost accuracy; enabling extended thinking within a single generation recovers more on reasoning tasks but can cost writing quality. Notably, most recent closed-weight models show little to no format tax, suggesting the problem is not inherent to structured generation but a gap that current open-weight models have yet to close. Code is available at https://github.com/ivnle/the-format-tax.

We investigate whether hidden states from Structured State Space Models (SSMs) can be merged post hoc to support downstream reasoning. Inspired by model souping, we study document souping, a strategy where documents are encoded independently, and their representations are pooled, via simple operations like averaging, into a single context state. This approach enables modular encoding and reuse without reprocessing the full input for each query. We demonstrate that finetuned Mamba2 models with souped representations achieve competitive or superior performance across multi-hop QA, sparse retrieval, and long-document reasoning tasks compared to the standard monolithic encoding approach. For example, on the RACE and QuALITY benchmarks for long document question answering, this method substantially outperforms a traditional concatenation approach. Crucially, this modular design scales to hundreds of segments (we test up to 256), while delivering substantial savings in inference cost, unlocking new possibilities for large-scale corpus reasoning.