Arash Gholami Davoodi

Navid Rezazadeh, Arash Gholami Davoodi · cmu

Reasoning models often generate long traces in which useful self-correction and unproductive revision are hard to distinguish. We study this distinction through backtracking dynamics: local reconsideration, retraction, or re-derivation inside long-form reasoning traces. On 6{,}000 Qwen3-8B AIME traces, we annotate segment-level backtrack severity and analyze event timing, normalized depth, and local burst structure. We find that early isolated repair is often compatible with correct reasoning, whereas incorrect traces more often show moderate-to-severe backtracks that persist and cluster late. Cross-corpus checks show the same qualitative asymmetry across additional model/domain pairs. Filtering analyses instantiate the signal as a prefix-causal selective early-exit policy: at shallow and intermediate depths, burst-aware filtering outperforms fixed length-based filtering while using only prefix-available features. Moderate length cutoffs remain strong completed-trace baselines, but burst-aware control provides a deployable mechanism for separating recoverable repair from likely instability.

Navid Rezazadeh, Arash Gholami Davoodi

Certified verification of transformer attention requires bounding the softmax function over interval constraints on the pre-softmax scores. Existing verifiers relax softmax ndependently of the downstream objective, leaving avoidable slack. We prove that the exact optimum of this score-box problem is attained at a vertex of the constraint box, and establish a threshold structure theorem showing that, after sorting the objective coefficients, the optimum lies among only linearly many candidates, yielding the Vertex-Softmax primitive with log-linear complexity in the sequence length. We further prove a formal optimality result showing that Vertex-Softmax is the tightest sound bound obtainable from score intervals alone, characterizing precisely what additional structure (score correlations, score-value coupling) is needed for further improvement. Integrated into a CROWN Convex Relaxation based Optimization for Worst-case Neurons)-style verifier with a formal soundness guarantee, Vertex-Softmax significantly improves certified rates and substantially tightens lower bounds across MNIST, Fashion-MNIST, and CIFAR-10 attention models, while consistently matching or outperforming alpha-CROWN and branch-and-bound baselines at a fraction of their cost.

Arash Gholami Davoodi, Navid Rezazadeh, Seyed Pouyan Mousavi Davoudi et al.

Large language models (LLMs) must balance diversity and creativity against logical coherence in open-ended generation. Existing truncation-based samplers are effective but largely heuristic, relying mainly on probability mass and entropy while ignoring semantic geometry of the token space. We present Top-W, a geometry-aware truncation rule that uses Wasserstein distance-defined over token-embedding geometry-to keep the cropped distribution close to the original, while explicitly balancing retained probability mass against the entropy of the kept set. Our theory yields a simple closed-form structure for the fixed-potential subset update: depending on the mass-entropy trade-off, the optimal crop either collapses to a single token or takes the form of a one-dimensional prefix that can be found efficiently with a linear scan. We implement Top-W using efficient geometry-based potentials (nearest-set or k-NN) and pair it with an alternating decoding routine that keeps the standard truncation-and-sampling interface unchanged. Extensive experiments on four benchmarks (GSM8K, GPQA, AlpacaEval, and MT-Bench) across three instruction-tuned models show that Top-W consistently outperforms prior state-of-the-art decoding approaches achieving up to 33.7% improvement. Moreover, we find that Top-W not only improves accuracy-focused performance, but also boosts creativity under judge-based open-ended evaluation.

Arash Gholami Davoodi, Seyed Pouyan Mousavi Davoudi, Pouya Pezeshkpour

Large language models (LLMs) demonstrate impressive capabilities in mathematical reasoning. However, despite these achievements, current evaluations are mostly limited to specific mathematical topics, and it remains unclear whether LLMs are genuinely engaging in reasoning. To address these gaps, we present the Mathematical Topics Tree (MaTT) benchmark, a challenging and structured benchmark that offers 1,958 questions across a wide array of mathematical subjects, each paired with a detailed hierarchical chain of topics. Upon assessing different LLMs using the MaTT benchmark, we find that the most advanced model, GPT-4, achieved a mere 54\% accuracy in a multiple-choice scenario. Interestingly, even when employing Chain-of-Thought prompting, we observe mostly no notable improvement. Moreover, LLMs accuracy dramatically reduced by up to 24.2 percentage point when the questions were presented without providing choices. Further detailed analysis of the LLMs' performance across a range of topics showed significant discrepancy even for closely related subtopics within the same general mathematical area. In an effort to pinpoint the reasons behind LLMs performances, we conducted a manual evaluation of the completeness and correctness of the explanations generated by GPT-4 when choices were available. Surprisingly, we find that in only 53.3\% of the instances where the model provided a correct answer, the accompanying explanations were deemed complete and accurate, i.e., the model engaged in genuine reasoning.

Arash Gholami Davoodi, Sean Chang, Hyun Gon Yoo et al.

In this paper, we consider the problem of classification of $M$ high dimensional queries $y^1,\cdots,y^M\in B^S$ to $N$ high dimensional classes $x^1,\cdots,x^N\in A^S$ where $A$ and $B$ are discrete alphabets and the probabilistic model that relates data to the classes $P(x,y)$ is known. This problem has applications in various fields including the database search problem in mass spectrometry. The problem is analogous to the nearest neighbor search problem, where the goal is to find the data point in a database that is the most similar to a query point. The state of the art method for solving an approximate version of the nearest neighbor search problem in high dimensions is locality sensitive hashing (LSH). LSH is based on designing hash functions that map near points to the same buckets with a probability higher than random (far) points. To solve our high dimensional classification problem, we introduce distribution sensitive hashes that map jointly generated pairs $(x,y)\sim P$ to the same bucket with probability higher than random pairs $x\sim P^A$ and $y\sim P^B$, where $P^A$ and $P^B$ are the marginal probability distributions of $P$. We design distribution sensitive hashes using a forest of decision trees and we show that the complexity of search grows with $O(N^{λ^*(P)})$ where $λ^*(P)$ is expressed in an analytical form. We further show that the proposed hashes perform faster than state of the art approximate nearest neighbor search methods for a range of probability distributions, in both theory and simulations. Finally, we apply our method to the spectral library search problem in mass spectrometry, and show that it is an order of magnitude faster than the state of the art methods.