Shivam Garg

Shivam Garg, Dimitris Tsipras, Percy Liang et al.

In-context learning refers to the ability of a model to condition on a prompt sequence consisting of in-context examples (input-output pairs corresponding to some task) along with a new query input, and generate the corresponding output. Crucially, in-context learning happens only at inference time without any parameter updates to the model. While large language models such as GPT-3 exhibit some ability to perform in-context learning, it is unclear what the relationship is between tasks on which this succeeds and what is present in the training data. To make progress towards understanding in-context learning, we consider the well-defined problem of training a model to in-context learn a function class (e.g., linear functions): that is, given data derived from some functions in the class, can we train a model to in-context learn "most" functions from this class? We show empirically that standard Transformers can be trained from scratch to perform in-context learning of linear functions -- that is, the trained model is able to learn unseen linear functions from in-context examples with performance comparable to the optimal least squares estimator. In fact, in-context learning is possible even under two forms of distribution shift: (i) between the training data of the model and inference-time prompts, and (ii) between the in-context examples and the query input during inference. We also show that we can train Transformers to in-context learn more complex function classes -- namely sparse linear functions, two-layer neural networks, and decision trees -- with performance that matches or exceeds task-specific learning algorithms. Our code and models are available at https://github.com/dtsip/in-context-learning .

Vasilis Kontonis, Yuchen Zeng, Shivam Garg et al. · cmu

Reasoning models think in long, unstructured streams with no mechanism for compressing or organizing their own intermediate state. We introduce MEMENTO: a method that teaches models to segment reasoning into blocks, compress each block into a memento, i.e., a dense state summary, and reason forward by attending only to mementos, reducing context, KV cache, and compute. To train MEMENTO models, we release OpenMementos, a public dataset of 228K reasoning traces derived from OpenThoughts-v3, segmented and annotated with intermediate summaries. We show that a two-stage SFT recipe on OpenMementos is effective across different model families (Qwen3, Phi-4, Olmo 3) and scales (8B--32B parameters). Trained models maintain strong accuracy on math, science, and coding benchmarks while achieving ${\sim}2.5\times$ peak KV cache reduction. We extend vLLM to support our inference method, achieving ${\sim}1.75\times$ throughput improvement while also enabling us to perform RL and further improve accuracy. Finally, we identify a dual information stream: information from each reasoning block is carried both by the memento text and by the corresponding KV states, which retain implicit information from the original block. Removing this channel drops accuracy by 15\,pp on AIME24.

Kanishk Gandhi, Shivam Garg, Noah D. Goodman et al.

Environments are the bottleneck for self-improving agents. Current terminal benchmarks were built for evaluation, not training; reinforcement learning requires a scalable pipeline, not just a dataset. We introduce Endless Terminals, a fully autonomous pipeline that procedurally generates terminal-use tasks without human annotation. The pipeline has four stages: generating diverse task descriptions, building and validating containerized environments, producing completion tests, and filtering for solvability. From this pipeline we obtain 3255 tasks spanning file operations, log management, data processing, scripting, and database operations. We train agents using vanilla PPO with binary episode level rewards and a minimal interaction loop: no retrieval, multi-agent coordination, or specialized tools. Despite this simplicity, models trained on Endless Terminals show substantial gains: on our held-out dev set, Llama-3.2-3B improves from 4.0% to 18.2%, Qwen2.5-7B from 10.7% to 53.3%, and Qwen3-8B-openthinker-sft from 42.6% to 59.0%. These improvements transfer to human-curated benchmarks: models trained on Endless Terminals show substantial gains on held out human curated benchmarks: on TerminalBench 2.0, Llama-3.2-3B improves from 0.0% to 2.2%, Qwen2.5-7B from 2.2% to 3.4%, and Qwen3-8B-openthinker-sft from 1.1% to 6.7%, in each case outperforming alternative approaches including models with more complex agentic scaffolds. These results demonstrate that simple RL succeeds when environments scale.

Charilaos Pipis, Shivam Garg, Vasilis Kontonis et al.

Reasoning models (e.g., DeepSeek-R1) generate long chains of thought to solve harder problems, but they often loop, repeating the same text at low temperatures or with greedy decoding. We study why this happens and what role temperature plays. With open reasoning models, we find that looping is common at low temperature. Larger models tend to loop less, and distilled students loop significantly even when their teachers rarely do. This points to mismatches between the training distribution and the learned model, which we refer to as errors in learning, as a key cause. To understand how such errors cause loops, we introduce a synthetic graph reasoning task and demonstrate two mechanisms. First, risk aversion caused by hardness of learning: when the correct progress-making action is hard to learn but an easy cyclic action is available, the model puts relatively more probability on the cyclic action and gets stuck. Second, even when there is no hardness, Transformers show an inductive bias toward temporally correlated errors, so the same few actions keep being chosen and loops appear. Higher temperature reduces looping by promoting exploration, but it does not fix the errors in learning, so generations remain much longer than necessary at high temperature; in this sense, temperature is a stopgap rather than a holistic solution. We end with a discussion of training-time interventions aimed at directly reducing errors in learning.

Shivam Garg, Chirag Pabbaraju, Kirankumar Shiragur et al.

We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing framework: Suppose there is a set of distributions over a discrete support of size $k$, $p_1, p_2,\ldots,p_T$, and we obtain $c$ independent draws from each distribution. Suppose the goal is to learn or test a property of the average distribution, $p_{avg}$. This setup models a number of important practical settings where the individual distributions correspond to heterogeneous entities -- either individuals, chronologically distinct time periods, spatially separated data sources, etc. From a learning standpoint, even with $c=1$ samples from each distribution, $Θ(k/\varepsilon^2)$ samples are necessary and sufficient to learn $p_{avg}$ to within error $\varepsilon$ in $\ell_1$ distance. To test uniformity or identity -- distinguishing the case that $p_{avg}$ is equal to some reference distribution, versus has $\ell_1$ distance at least $\varepsilon$ from the reference distribution, we show that a linear number of samples in $k$ is necessary given $c=1$ samples from each distribution. In contrast, for $c \ge 2$, we recover the usual sublinear sample testing guarantees of the i.i.d.\ setting: we show that $O(\sqrt{k}/\varepsilon^2 + 1/\varepsilon^4)$ total samples are sufficient, matching the optimal sample complexity in the i.i.d.\ case in the regime where $\varepsilon \ge k^{-1/4}$. Additionally, we show that in the $c=2$ case, there is a constant $ρ> 0$ such that even in the linear regime with $ρk$ samples, no tester that considers the multiset of samples (ignoring which samples were drawn from the same $p_i$) can perform uniformity testing. We also extend our techniques to the problem of testing "closeness" of two distributions.

Vaishnavi Shrivastava, Ahmed Awadallah, Vidhisha Balachandran et al. · cmu

Large language models trained with reinforcement learning with verifiable rewards tend to trade accuracy for length--inflating response lengths to achieve gains in accuracy. While longer answers may be warranted for harder problems, many tokens are merely "filler": repetitive, verbose text that makes no real progress. We introduce GFPO (Group Filtered Policy Optimization), which curbs this length explosion by sampling larger groups per problem during training and filtering responses to train on based on two key metrics: (1) response length and (2) token efficiency: reward per token ratio. By sampling more at training time, we teach models to think less at inference time. On the Phi-4-reasoning model, GFPO cuts GRPO's length inflation by 46-71% across challenging STEM and coding benchmarks (AIME 24/25, GPQA, Omni-MATH, LiveCodeBench) while maintaining accuracy. Optimizing for reward per token further increases reductions in length inflation to 71-85%. We also propose Adaptive Difficulty GFPO, which dynamically allocates more training resources to harder problems based on real-time difficulty estimates, improving the balance between computational efficiency and accuracy especially on difficult questions. GFPO demonstrates that increased training-time compute directly translates to reduced test-time compute--a simple yet effective trade-off for efficient reasoning.

Vidhisha Balachandran, Jingya Chen, Lingjiao Chen et al. · cmu

Inference-time scaling can enhance the reasoning capabilities of large language models (LLMs) on complex problems that benefit from step-by-step problem solving. Although lengthening generated scratchpads has proven effective for mathematical tasks, the broader impact of this approach on other tasks remains less clear. In this work, we investigate the benefits and limitations of scaling methods across nine state-of-the-art models and eight challenging tasks, including math and STEM reasoning, calendar planning, NP-hard problems, navigation, and spatial reasoning. We compare conventional models (e.g., GPT-4o) with models fine-tuned for inference-time scaling (e.g., o1) through evaluation protocols that involve repeated model calls, either independently or sequentially with feedback. These evaluations approximate lower and upper performance bounds and potential for future performance improvements for each model, whether through enhanced training or multi-model inference systems. Our extensive empirical analysis reveals that the advantages of inference-time scaling vary across tasks and diminish as problem complexity increases. In addition, simply using more tokens does not necessarily translate to higher accuracy in these challenging regimes. Results from multiple independent runs with conventional models using perfect verifiers show that, for some tasks, these models can achieve performance close to the average performance of today's most advanced reasoning models. However, for other tasks, a significant performance gap remains, even in very high scaling regimes. Encouragingly, all models demonstrate significant gains when inference is further scaled with perfect verifiers or strong feedback, suggesting ample potential for future improvements.

Kristian Georgiev, Roy Rinberg, Sung Min Park et al. · mit

Machine unlearning -- efficiently removing the effect of a small "forget set" of training data on a pre-trained machine learning model -- has recently attracted significant research interest. Despite this interest, however, recent work shows that existing machine unlearning techniques do not hold up to thorough evaluation in non-convex settings. In this work, we introduce a new machine unlearning technique that exhibits strong empirical performance even in such challenging settings. Our starting point is the perspective that the goal of unlearning is to produce a model whose outputs are statistically indistinguishable from those of a model re-trained on all but the forget set. This perspective naturally suggests a reduction from the unlearning problem to that of data attribution, where the goal is to predict the effect of changing the training set on a model's outputs. Thus motivated, we propose the following meta-algorithm, which we call Datamodel Matching (DMM): given a trained model, we (a) use data attribution to predict the output of the model if it were re-trained on all but the forget set points; then (b) fine-tune the pre-trained model to match these predicted outputs. In a simple convex setting, we show how this approach provably outperforms a variety of iterative unlearning algorithms. Empirically, we use a combination of existing evaluations and a new metric based on the KL-divergence to show that even in non-convex settings, DMM achieves strong unlearning performance relative to existing algorithms. An added benefit of DMM is that it is a meta-algorithm, in the sense that future advances in data attribution translate directly into better unlearning algorithms, pointing to a clear direction for future progress in unlearning.

Omar Salemohamed, Laurent Charlin, Shivam Garg et al.

We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned from scratch, and does not require careful initialization or seeding with candidate data structures/algorithms. We first apply this framework to the problem of nearest neighbor search. In several settings, we are able to reverse-engineer the learned data structures and query algorithms. For 1D nearest neighbor search, the model discovers optimal distribution (in)dependent algorithms such as binary search and variants of interpolation search. In higher dimensions, the model learns solutions that resemble k-d trees in some regimes, while in others, they have elements of locality-sensitive hashing. The model can also learn useful representations of high-dimensional data and exploit them to design effective data structures. We also adapt our framework to the problem of estimating frequencies over a data stream, and believe it could also be a powerful discovery tool for new problems.

Shivam Garg, Alexander Ihler, Sunil Kumar

An autonomous airborne network (AN) consists of multiple unmanned aerial vehicles (UAVs), which can self-configure to provide seamless, low-cost and secure connectivity. AN is preferred for applications in civilian and military sectors because it can improve the network reliability and fault tolerance, reduce mission completion time through collaboration, and adapt to dynamic mission requirements. However, facilitating seamless communication in such ANs is a challenging task due to their fast node mobility, which results in frequent link disruptions. Many existing AN-specific mobility-aware schemes restrictively assume that UAVs fly in straight lines, to reduce the high uncertainty in the mobility pattern and simplify the calculation of link lifetime (LLT). Here, LLT represents the duration after which the link between a node pair terminates. However, the application of such schemes is severely limited, which makes them unsuitable for practical autonomous ANs. In this report, a mathematical framework is described to accurately compute the \textit{LLT} value for a UAV node pair, where each node flies independently in a randomly selected smooth trajectory. In addition, the impact of random trajectory changes on LLT accuracy is also discussed.

Brian Axelrod, Shivam Garg, Yanjun Han et al.

The ``sample amplification'' problem formalizes the following question: Given $n$ i.i.d. samples drawn from an unknown distribution $P$, when is it possible to produce a larger set of $n+m$ samples which cannot be distinguished from $n+m$ i.i.d. samples drawn from $P$? In this work, we provide a firm statistical foundation for this problem by deriving generally applicable amplification procedures, lower bound techniques and connections to existing statistical notions. Our techniques apply to a large class of distributions including the exponential family, and establish a rigorous connection between sample amplification and distribution learning.

Shivam Garg, Samuele Tosatto, Yangchen Pan et al.

Policy gradient (PG) estimators are ineffective in dealing with softmax policies that are sub-optimally saturated, which refers to the situation when the policy concentrates its probability mass on sub-optimal actions. Sub-optimal policy saturation may arise from bad policy initialization or sudden changes in the environment that occur after the policy has already converged. Current softmax PG estimators require a large number of updates to overcome policy saturation, which causes low sample efficiency and poor adaptability to new situations. To mitigate this problem, we propose a novel PG estimator for softmax policies that utilizes the bias in the critic estimate and the noise present in the reward signal to escape the saturated regions of the policy parameter space. Our theoretical analysis and experiments, conducted on bandits and various reinforcement learning environments, show that this new estimator is significantly more robust to policy saturation.

Shivam Garg, Santosh S. Vempala

The success of gradient descent in ML and especially for learning neural networks is remarkable and robust. In the context of how the brain learns, one aspect of gradient descent that appears biologically difficult to realize (if not implausible) is that its updates rely on feedback from later layers to earlier layers through the same connections. Such bidirected links are relatively few in brain networks, and even when reciprocal connections exist, they may not be equi-weighted. Random Feedback Alignment (Lillicrap et al., 2016), where the backward weights are random and fixed, has been proposed as a bio-plausible alternative and found to be effective empirically. We investigate how and when feedback alignment (FA) works, focusing on one of the most basic problems with layered structure -- low-rank matrix factorization. In this problem, given a matrix $Y_{n\times m}$, the goal is to find a low rank factorization $Z_{n \times r}W_{r \times m}$ that minimizes the error $\|ZW-Y\|_F$. Gradient descent solves this problem optimally. We show that FA converges to the optimal solution when $r\ge \mbox{rank}(Y)$. We also shed light on how FA works. It is observed empirically that the forward weight matrices and (random) feedback matrices come closer during FA updates. Our analysis rigorously derives this phenomenon and shows how it facilitates convergence of FA*, a closely related variant of FA. We also show that FA can be far from optimal when $r < \mbox{rank}(Y)$. This is the first provable separation result between gradient descent and FA. Moreover, the representations found by gradient descent and FA can be almost orthogonal even when their error $\|ZW-Y\|_F$ is approximately equal. As a corollary, these results also hold for training two-layer linear neural networks when the training input is isotropic, and the output is a linear function of the input.

Sharan Vaswani, Olivier Bachem, Simone Totaro et al.

Common policy gradient methods rely on the maximization of a sequence of surrogate functions. In recent years, many such surrogate functions have been proposed, most without strong theoretical guarantees, leading to algorithms such as TRPO, PPO or MPO. Rather than design yet another surrogate function, we instead propose a general framework (FMA-PG) based on functional mirror ascent that gives rise to an entire family of surrogate functions. We construct surrogate functions that enable policy improvement guarantees, a property not shared by most existing surrogate functions. Crucially, these guarantees hold regardless of the choice of policy parameterization. Moreover, a particular instantiation of FMA-PG recovers important implementation heuristics (e.g., using forward vs reverse KL divergence) resulting in a variant of TRPO with additional desirable properties. Via experiments on simple bandit problems, we evaluate the algorithms instantiated by FMA-PG. The proposed framework also suggests an improved variant of PPO, whose robustness and efficiency we empirically demonstrate on the MuJoCo suite.

Sina Ghiassian, Andrew Patterson, Shivam Garg et al.

It is still common to use Q-learning and temporal difference (TD) learning-even though they have divergence issues and sound Gradient TD alternatives exist-because divergence seems rare and they typically perform well. However, recent work with large neural network learning systems reveals that instability is more common than previously thought. Practitioners face a difficult dilemma: choose an easy to use and performant TD method, or a more complex algorithm that is more sound but harder to tune and all but unexplored with non-linear function approximation or control. In this paper, we introduce a new method called TD with Regularized Corrections (TDRC), that attempts to balance ease of use, soundness, and performance. It behaves as well as TD, when TD performs well, but is sound in cases where TD diverges. We empirically investigate TDRC across a range of problems, for both prediction and control, and for both linear and non-linear function approximation, and show, potentially for the first time, that gradient TD methods could be a better alternative to TD and Q-learning.

Brian Axelrod, Shivam Garg, Vatsal Sharan et al.

Given data drawn from an unknown distribution, $D$, to what extent is it possible to ``amplify'' this dataset and output an even larger set of samples that appear to have been drawn from $D$? We formalize this question as follows: an $(n,m)$ $\text{amplification procedure}$ takes as input $n$ independent draws from an unknown distribution $D$, and outputs a set of $m > n$ ``samples''. An amplification procedure is valid if no algorithm can distinguish the set of $m$ samples produced by the amplifier from a set of $m$ independent draws from $D$, with probability greater than $2/3$. Perhaps surprisingly, in many settings, a valid amplification procedure exists, even when the size of the input dataset, $n$, is significantly less than what would be necessary to learn $D$ to non-trivial accuracy. Specifically we consider two fundamental settings: the case where $D$ is an arbitrary discrete distribution supported on $\le k$ elements, and the case where $D$ is a $d$-dimensional Gaussian with unknown mean, and fixed covariance. In the first case, we show that an $\left(n, n + Θ(\frac{n}{\sqrt{k}})\right)$ amplifier exists. In particular, given $n=O(\sqrt{k})$ samples from $D$, one can output a set of $m=n+1$ datapoints, whose total variation distance from the distribution of $m$ i.i.d. draws from $D$ is a small constant, despite the fact that one would need quadratically more data, $n=Θ(k)$, to learn $D$ up to small constant total variation distance. In the Gaussian case, we show that an $\left(n,n+Θ(\frac{n}{\sqrt{d}} )\right)$ amplifier exists, even though learning the distribution to small constant total variation distance requires $Θ(d)$ samples. In both the discrete and Gaussian settings, we show that these results are tight, to constant factors. Beyond these results, we formalize a number of curious directions for future research along this vein.

Shivam Garg, Vatsal Sharan, Brian Hu Zhang et al.

Given the apparent difficulty of learning models that are robust to adversarial perturbations, we propose tackling the simpler problem of developing adversarially robust features. Specifically, given a dataset and metric of interest, the goal is to return a function (or multiple functions) that 1) is robust to adversarial perturbations, and 2) has significant variation across the datapoints. We establish strong connections between adversarially robust features and a natural spectral property of the geometry of the dataset and metric of interest. This connection can be leveraged to provide both robust features, and a lower bound on the robustness of any function that has significant variance across the dataset. Finally, we provide empirical evidence that the adversarially robust features given by this spectral approach can be fruitfully leveraged to learn a robust (and accurate) model.