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Nov 11

MC-GRPO: Median-Centered Group Relative Policy Optimization for Small-Rollout Reinforcement Learning

Group-relative policy optimization methods train language models by generating multiple rollouts per prompt and normalizing rewards with a shared mean reward baseline. In resource-constrained settings where the rollout budget is small, accuracy often degrades. We find that noise in the shared baseline induces advantage sign flips, where some rollouts receive an incorrect advantage sign, and the update direction is reversed. To address this, we propose Median-Centered Group Relative Policy Optimization (MC-GRPO), a simple and effective solution for small-rollout training. Our main idea is to replace the mean baseline with a median baseline: the median is far less sensitive to outlier rewards than the mean, mitigating the sign flips under small rollout size (G). We generate one additional rollout for median reference (G+1), and compute advantages by using the group median. With an odd-sized group, exactly one completion is the median and receives zero advantage, we exclude this pivot rollout from backpropagation so the number of gradient-contributing samples per prompt remains G, preserving the core update cost of standard G-rollout training. Across various GRPO-family methods and a wide range of models and scales, this median-centered training consistently improves stability and final accuracy in the low-rollout regime, reducing the gap between G=2 and G=8 to within 1%. Code is available at https://github.com/lotusroot-kim/MC-GRPO

  • 1 authors
·
Jan 30

Can Large Reasoning Models Improve Accuracy on Mathematical Tasks Using Flawed Thinking?

Chain-of-thought (CoT) prompting has become central to mathematical reasoning in large language models, yet models remain brittle to early errors: a single arithmetic slip or unjustified inference typically propagates uncorrected to an incorrect final answer. We investigate whether training on intentionally flawed reasoning traces can teach models to detect and recover from such errors without degrading standard problem-solving ability. Using competition-level problems from MATH-lighteval, we generate CoT prefixes containing exactly one controlled error, either a calculation error (sign flips, dropped terms) or a reasoning error (misapplied rules, unjustified logical steps), and fine-tune Qwen3-4B with GRPO using a binary final-answer reward. Our Mixed-CoT-RL model matches standard RL on clean problems (41% vs 41%) while substantially outperforming it on problems prefilled with flawed reasoning (24% vs 19%). Notably, clean-only RL fine-tuning degrades robustness below the untuned baseline 19% vs. 20%), indicating that conventional training increases susceptibility to misleading prefills. Among error types, training on reasoning errors yields greater robustness gains than calculation errors alone, with mixed training performing best. These findings demonstrate that exposure to flawed traces during training can improve error-recovery behavior without sacrificing accuracy, suggesting a path toward more robust mathematical reasoning in LLMs.

  • 4 authors
·
Dec 18, 2025

Tree-Ising: Repairing Language Models with Bit-Level Ising Edits

Weight-space programming, introduced in recent MIT work by Takehi et al., enables a frontier LLM agent to read a network's weights and write a repair. Their GPT-6 Astra agent corrected the reasoning loops of Qwen3.5-0.8B without gradients, using 158 agent turns, 89.7 million tokens, and 50 forward-pass requests. Our method, Tree-Ising, casts this repair as a sparse discrete optimization problem over the model's own BF16 weights. Forward statistics define an objective that weakens a loop direction, strengthens a concluding direction, and preserves the layer's output on productive tokens. Within a state-tree representation, where lossless BF16 storage acts as a special case, the admissible edits are sign flips and exponent shifts that preserve all shared group exponents and mantissas. We decompose this objective exactly into independent QUBO (Ising) problems, one per output row, which we solve on a GPU using simulated annealing or quantum-inspired simulated bifurcation. On the agent's two layers, Tree-Ising achieves 54.6% on MATH-500, outperforming the agent's edit (51.7%) under the same evaluation protocol, while the base model scores 7.9% as reported. The simulated bifurcation solver yields a statistically indistinguishable repair at 55.1%. Both solvers outperform the agent edit across all five math benchmarks, with statistically significant improvements on MATH-500 and GSM8K after correcting for multiple comparisons. Our approach modifies 13% to 17% fewer weights and reduces BF16 bit flips by a factor of 2.2 to 2.3. It requires only four forward-pass requests and zero LLM tokens, with the annealing recipe costing about $0.90 in GPU time. On Qwen3.5-2B, with layers and dose selected using only the base model, the same recipe increases greedy GSM8K accuracy from 21.6% to 69.4%. As a proof of concept, we execute an eight-variable repair subproblem using QAOA on an IBM Heron processor.

  • 2 authors
·
Nov 9 1

The Signs Were Always There: Training-Free Detection and Control in Raw Transformer Dimensions

Because of polysemanticity and superposition, it has been challenging to attribute token understanding and generation to specific neurons or dimensions. Yet the information in the hidden states is so rich that the signs of the residual stream can surface semantic content in early layers and control what the model generates. We call this sign-pattern-driven interpretation approach Bag of Dims (BoD). Using BoD, we read each dimension of the residual stream individually. Since dimensions carry almost no shared information, a concept is simply the set of dimensions that agree in sign. This lets us discover tens to hundreds of thousands of concepts per model without training or labels. A concept is detectable as early as the first few layers, at AUC above 0.9 across the model families we tested, well before the answer it resolves to becomes legible. BoD can therefore screen harmful prompts at prefill, without a trained guard model. The prediction capability of the signs is strong: setting all magnitudes to unity preserves 56-94% top-5 next-token accuracy through the language model head. Flipping a concept's sign pattern during the forward pass suppresses its logits, and a separate training-free intervention steers a chosen concept into generated text. The BoD method depends on the transformers' per-dimension sign pattern, present across the residual stream, attention, and MLP subspaces, rather than on any particular architecture, making it applicable to a wide range of models.

  • 3 authors
·
Oct 18 2

Long-Short History of Gradients is All You Need: Detecting Malicious and Unreliable Clients in Federated Learning

Federated learning offers a framework of training a machine learning model in a distributed fashion while preserving privacy of the participants. As the server cannot govern the clients' actions, nefarious clients may attack the global model by sending malicious local gradients. In the meantime, there could also be unreliable clients who are benign but each has a portion of low-quality training data (e.g., blur or low-resolution images), thus may appearing similar as malicious clients. Therefore, a defense mechanism will need to perform a three-fold differentiation which is much more challenging than the conventional (two-fold) case. This paper introduces MUD-HoG, a novel defense algorithm that addresses this challenge in federated learning using long-short history of gradients, and treats the detected malicious and unreliable clients differently. Not only this, but we can also distinguish between targeted and untargeted attacks among malicious clients, unlike most prior works which only consider one type of the attacks. Specifically, we take into account sign-flipping, additive-noise, label-flipping, and multi-label-flipping attacks, under a non-IID setting. We evaluate MUD-HoG with six state-of-the-art methods on two datasets. The results show that MUD-HoG outperforms all of them in terms of accuracy as well as precision and recall, in the presence of a mixture of multiple (four) types of attackers as well as unreliable clients. Moreover, unlike most prior works which can only tolerate a low population of harmful users, MUD-HoG can work with and successfully detect a wide range of malicious and unreliable clients - up to 47.5% and 10%, respectively, of the total population. Our code is open-sourced at https://github.com/LabSAINT/MUD-HoG_Federated_Learning.

  • 4 authors
·
Aug 14, 2022

Verifying Text-to-SQL Queries under Changing Business Semantics

In text-to-SQL and AI-agent analytics, successful SQL execution does not establish semantic correctness under changing business definitions. We study revalidation of fixed queries after changes to refund attribution, tax treatment, eligible populations and exchange-rate dates. An executable verification profile binds the requested revision and knowledge cutoff to legal counterexample data and exact monetary comparison. A preregistered confirmation on 32 newly authored revision families and two local producer bundles retains 192 query-definition cells: 144 nonconforming, 36 finite-suite agreeing and 12 unresolved. Of the nonconforming cells, 63 agree on the current snapshot. At an eight-ledger budget, obligation-guided checking detects 137 discrepancies versus 127 for generic ordering, a paired difference of 6.9 percentage points (family bootstrap 95% interval [2.1, 13.6]; exact family sign-flip p=0.0156). Every ledger arm rejects zero of the 36 agreeing cells. Current-obligation and equal-weight scoring match the guided result, identifying coverage rather than revision-specific priority as the observed source of benefit. Controlled assays, a natural-query pilot and repeated samples provide separate mechanism and robustness evidence. A legal discrepancy refutes conformance; agreement remains restricted to the recorded suite. The study establishes an auditable business-semantic revalidation profile within its authored schema and local-model scope.

  • 4 authors
·
Oct 29