Second Mathematician Presses OpenAI Over Possible Use of Nonpublic Research

01Second mathematician asks OpenAI to prove it did not use nonpublic research, widening training-data transparency dispute

A second mathematician has asked OpenAI to prove that nonpublic research did not help its models produce a celebrated mathematical result, widening a dispute over how the company uses data supplied through its products. Andreas Thom raised the concern after OpenAI announced work on non-sofic groups—infinite mathematical structures that, roughly speaking, cannot be approximated by finite ones.

Thom’s challenge follows questions from New York University mathematics professor Tristan Buckmaster about whether OpenAI’s models benefited from unpublished work he processed with Codex. OpenAI’s non-sofic-groups result built heavily on previous work by Thom and mathematician Gábor Kun, according to the company’s own acknowledgment.

Thom said his suspicions arose partly from OpenAI’s “detailed command” of techniques developed by him and his colleagues. He said those methods were neither the most obvious nor the most promising routes to a solution at the time. OpenAI had also faced criticism from mathematicians for initially failing to acknowledge recent contributions from Thom and Kun, then quietly amended its account of the result.

Thom emailed OpenAI researchers Sébastien Bubeck and Mark Sellke to ask whether his ChatGPT interactions had become part of the training data or were accessible during the model’s reasoning process. According to Thom, the response addressed only whether particular conversations could be accessed directly. It did not explain whether de-identified material from those exchanges might have entered broader datasets used to improve the models.

That distinction mirrors OpenAI’s public explanation in the separate Navier–Stokes controversy involving Buckmaster. The company said neither its researchers nor its agents had accessed any specific user data to solve that problem. But it also said that, while unlikely, it could not rule out the possibility that de-identified data derived from researchers’ use of its products had helped improve its models.

For Thom, removing identifying information would not eliminate the intellectual content of a mathematical idea. He accused OpenAI of giving an unjustifiably broad and misleading denial, but neither his allegations nor Buckmaster’s establish that unpublished research actually entered the company’s training data or affected a result.

Thom said researchers cannot reconstruct OpenAI’s training pipeline themselves because only the company holds the relevant records. He called on OpenAI to disclose the necessary datasets and clarify the settings and terms governing data use. OpenAI did not immediately respond to The Verge’s request for comment, leaving the relevant datasets, user settings and training records undisclosed.

02GE-Act 2.0 Expands Robot Training Data to 30,000 Hours, Lifting Zero-Shot Manipulation Success as High as 44.1%

GE-Act 2.0 is a world-action model designed to guide robots by predicting a future state and then determining the actions needed to reach it. Unlike systems that inherit pretrained video generators, all of its trainable generation and action components were initialized from scratch on robot-manipulation data. Its developers have now reported how its zero-shot performance changed as joint-training data grew from 300 to 30,000 hours.

The model divides planning and action generation among three components. A control-oriented autoencoder aggressively compresses observations while retaining information relevant to instructions and actions. A single-step visual planner produces a complete future state in one differentiable pass, while an inverse dynamics model translates the predicted state change into robot actions.

This separation lets the visual planner and inverse dynamics model be pretrained on complementary datasets, including video without action labels and interactions with recorded actions. They are then jointly trained using “knowledge-aligned selective optimization,” which limits mismatched supervision by selecting only predicted futures judged behaviorally compatible with the recorded action.

The researchers evaluated pretrained checkpoints directly, without fine-tuning for individual tasks. Testing covered 100 tasks across 20 manipulation-skill groups, including held-out scenes, backgrounds, lighting conditions and object instances.

When co-training data increased from 300 to 30,000 hours, the success rate on the G1-OP test setting rose from 17.1% to 44.1%, a gain of 27 percentage points. On G2-90D, it increased from 13.4% to 31.1%, or 17.7 points. The source does not specify the precise hardware differences between those two platforms.

The improvements extended across 19 of 20 skill groups on one setting and 18 of 20 on the other, supporting transfer across tasks rather than gains confined to a small subset. Skill-specific data coverage also correlated strongly with zero-shot, out-of-distribution success, with a Pearson correlation of 0.80 and a Spearman correlation of 0.85.

G2-90D represented less than 2% of the joint-training data but still gained 17.7 percentage points. The team interprets that result as evidence suggesting transfer across robot embodiments, though it does not establish universal cross-robot transfer. The source provides no independent replication, long-term deployment results, full breakdown of the 30,000 training hours, or training-cost figures.

03BeaconKV Uses “Beacon Queries” to Compress Long-Reasoning Caches, With Team Reporting Up to 5.8× Lower Memory Use

Large reasoning models can produce extended chains of thought to solve complex tasks, but every additional token expands the model’s key-value, or KV, cache. This cache stores information used to calculate attention during generation, grows linearly with sequence length, and can exceed a GPU’s capacity during long reasoning traces.

Existing compression methods try to control that growth by using recent queries—the representations of what the model is currently seeking—to estimate which earlier tokens will matter later. The researchers behind BeaconKV say this assumption breaks down in long-horizon reasoning because models sometimes return to distant material, such as a task-solving plan formulated near the beginning. A policy guided mainly by recent activity may discard that material before the model needs it again.

The team found that queries associated with these returns to distant context, which it calls Thought Revisiting Tokens, form a small number of similarity clusters in embedding space. BeaconKV keeps a compact representative, or “beacon query,” for each global query cluster. Those representatives are used to predict which historical key-value pairs are likely to be accessed again.

BeaconKV combines these beacon queries with recent queries when deciding what to retain. The approach is designed to preserve both information relevant to the model’s immediate reasoning and older content that matches recurring long-range attention patterns. It does not require storing the complete history of queries and needs no additional training.

Tests covered four open-source large reasoning models and a range of reasoning benchmarks. The researchers report that BeaconKV generally outperformed existing cache-compression methods while nearly preserving the accuracy obtained with a full KV cache. They also report memory-use reductions of up to 5.8 times and throughput improvements of more than 4.3 times.

Those figures are maximum reported results within the team’s test scope, not guaranteed gains across every model or production workload. The source does not provide model-by-model or benchmark-by-benchmark results, quantify the accuracy loss implied by “nearly preserving” full-cache performance, or say whether the peak memory and throughput gains came from the same configuration.