arxiv: 2510.09477 · v2 · submitted 2025-10-10 · 📊 stat.ML · cs.LG

Efficient Autoregressive Inference for Transformer Probabilistic Models

Conor Hassan , Nasrulloh Loka , Cen-You Li , Daolang Huang , Paul E. Chang , Yang Yang , Francesco Silvestrin , Samuel Kaski

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Luigi Acerbi

This is my paper

Pith reviewed 2026-05-18 07:46 UTC · model grok-4.3

classification 📊 stat.ML cs.LG

keywords autoregressive inferencetransformer probabilistic modelsneural processesjoint distributionscausal bufferefficient samplingset-based conditioningdensity evaluation

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The pith

A causal autoregressive buffer lets set-based transformers generate joint predictions efficiently by caching context once.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how to obtain joint distributions over multiple targets from set-based transformer models like neural processes without repeatedly re-encoding the full context. It proposes encoding the context only once and using a lightweight causal buffer that lets each new target attend to the cached context plus all previously generated targets. This hybrid approach preserves the flexible conditioning of set models while gaining the efficiency of autoregressive generation for sampling and density evaluation. Readers interested in probabilistic inference or meta-learning would care because the method delivers matching accuracy at up to 20 times faster speed and 7 times less memory across several tasks.

Core claim

The central claim is that a causal autoregressive buffer, which caches the encoded context and models dependencies among targets through attention to prior predictions, enables joint sampling and density evaluation that closely matches full context re-encoding while achieving up to 20× faster computation and 7× lower memory usage.

What carries the argument

The causal autoregressive buffer that attends to the cached context and previously generated targets to capture inter-target dependencies without full re-encoding.

If this is right

Joint distributions can be obtained from set-based models with linear rather than quadratic scaling in the number of targets.
Training can integrate set-based marginal prediction and autoregressive joint modes using masked attention at little extra cost.
The approach applies directly to neural processes, prior-fitted networks, and tabular foundation models.
Performance remains close to full re-encoding on synthetic functions, EEG series, model comparison, and tabular regression.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This buffer design could be adapted to other attention-based generative models facing similar re-encoding costs.
Applications in sequential decision making might benefit from faster joint sampling for uncertainty quantification.
Further work could test whether the buffer suffices when targets have complex higher-order dependencies not captured by the causal attention.
The memory savings suggest potential for deploying these models on resource-constrained devices for multiple predictions.

Load-bearing premise

That the dependencies among targets can be adequately modeled by a lightweight causal buffer attending only to the cached context and previously generated targets.

What would settle it

Running the method on a problem where targets exhibit strong dependencies that require global context re-evaluation, such as long-range correlations in time series, and observing that the joint density or samples deviate substantially from those of full re-encoding would falsify the claim.

Figures

Figures reproduced from arXiv: 2510.09477 by Cen-You Li, Conor Hassan, Daolang Huang, Francesco Silvestrin, Luigi Acerbi, Nasrulloh Loka, Paul E. Chang, Samuel Kaski, Yang Yang.

**Figure 1.** Figure 1: The autoregressive buffer enables fast joint inference by eliminating redundant context re-computation. Left: Comparison of autoregressive inference strategies. Traditional autoregressive approach (top) requires re-encoding the entire augmented context set at each step when generating predictions for targets, leading to O(K(N + K) 2 ) complexity, where N is the context set size and K the number of target… view at source ↗

**Figure 2.** Figure 2: Example training mask. At inference, we use a two-stage process: a one-time context encoding followed by prediction in the form of either sampling or likelihood evaluation. Prediction carries an attention cost of O(N2 + KN + K2 ), composed of a one-time O(N2 ) for context self-attention, O(KN) for all cross-attention reads from the cache, and a total of O(K2 ) for causal self-attention within the buffer. … view at source ↗

**Figure 3.** Figure 3: Wall-clock time (log scale) for (left) sampling, (center) joint log-likelihood evaluation, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Multisensory causal inference model comparison versus ground-truth. (Left) Log marginal likelihood (LML) comparison for both ρ = 1 and ρ = 4/3. (Right) LML difference (ρ = 4/3 − ρ = 1) comparison. Our method closely aligns with the ground-truth. Results. We evaluate our method using data from the 15 participants of the original study, extracting two non-overlapping subsets of 400 experimental trials each (… view at source ↗

read the original abstract

Set-based transformer models for amortized probabilistic inference and meta-learning, such as neural processes, prior-fitted networks, and tabular foundation models, excel at single-pass marginal prediction. However, many applications require joint distributions over multiple predictions. Purely autoregressive architectures generate these efficiently but sacrifice flexible set-conditioning. Obtaining joint distributions from set-based models requires re-encoding the entire context at each autoregressive step, which scales poorly. We introduce a causal autoregressive buffer that combines the strengths of both paradigms. The model encodes the context once and caches it; a lightweight causal buffer captures dependencies among generated targets, with each new prediction attending to both the cached context and all previously predicted targets added to the buffer. This enables efficient batched autoregressive sampling and joint predictive density evaluation. Training integrates set-based and autoregressive modes through masked attention at minimal overhead. Across synthetic functions, EEG time series, a Bayesian model comparison task, and tabular regression, our method closely matches the performance of full context re-encoding while delivering up to $20\times$ faster joint sampling and density evaluation, and up to $7\times$ lower memory usage.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The causal autoregressive buffer caches context once and adds a lightweight target buffer to deliver real speedups on joint tasks in set-based transformers while matching full re-encoding performance in the reported experiments.

read the letter

The main thing to know is that this paper introduces a causal autoregressive buffer to make joint sampling and density evaluation much faster in set-based transformer models for probabilistic inference. By encoding the context once and caching it, then letting a lightweight buffer handle target dependencies, they avoid repeated full re-encodings while keeping performance close to the original approach. This combination looks new compared to prior set or autoregressive transformers. The method does a good job of addressing a practical bottleneck: set models are great for marginals but slow for joints, and pure autoregressive ones lose the set flexibility. Their training with masked attention integrates both modes efficiently. The results across synthetic functions, EEG time series, Bayesian model comparison, and tabular regression show close matching to full re-encoding, with reported speedups of up to 20 times for joint tasks and 7 times lower memory use. That kind of gain could matter for applications in meta-learning and tabular foundation models. The main soft spot is whether the fixed cached context is enough. New targets attend only to the cache and previous predictions, without the chance to update context embeddings through attention as in full re-encoding. If the model needs those updates for accurate joint conditionals, the approximation might diverge in some cases even when marginal predictions look similar. The abstract reports good results, so it probably works for the tested domains, but the stress-test concern is valid and would need checking in the full experiments. Summarized results without full error bars or ablations also make it tougher to gauge robustness right now. This is for people building or using set-based probabilistic models who need efficient joints over multiple targets. A reader focused on practical efficiency improvements in transformers for inference would get direct value from the architecture and the empirical gains. It deserves a serious referee because the core contribution is a clear, implementable change with plausible benefits for a growing area of work. I would recommend sending it out for peer review.

Referee Report

2 major / 3 minor

Summary. The paper introduces a causal autoregressive buffer for set-based transformer probabilistic models (e.g., neural processes) to enable efficient joint sampling and density evaluation. The context is encoded once and cached; a lightweight buffer then captures target dependencies by attending to the fixed cache plus previously generated targets. Training combines set-based and autoregressive modes via masked attention. Experiments across synthetic functions, EEG time series, Bayesian model comparison, and tabular regression report performance close to full re-encoding, with up to 20× speedups in joint operations and 7× lower memory use.

Significance. If the empirical claims hold under the buffer approximation, the work would meaningfully improve scalability for joint inference in amortized probabilistic models and meta-learning, where full re-encoding is a known bottleneck. The minimal-overhead training integration and multi-domain validation are strengths that could influence practical deployments in time-series and tabular settings.

major comments (2)

[§3] §3 (Method description of causal autoregressive buffer): The design fixes the context encoding after the initial pass and lets the buffer attend only to this cache plus prior targets. This directly engages the skeptic concern that new targets cannot revise context representations through cross-attention, as occurs in full re-encoding. If the underlying transformer relies on iterative refinement for accurate joint conditionals, the approximation could diverge even when marginals match; the manuscript should either provide a concrete test (e.g., a controlled comparison on a task known to require context updates) or bound the regimes where the fixed-cache assumption is safe.
[§5] §5 (Experiments): The reported speedups and memory reductions rest on summarized results without visible per-run variance, ablation on buffer capacity, or explicit comparison of joint log-likelihoods under increasing target count. Adding these would strengthen the central efficiency claim, which is otherwise load-bearing for the paper's contribution.

minor comments (3)

[Abstract] Abstract and §2: The phrase 'lightweight causal buffer' is used before its precise architecture (attention mask, size, integration with cached keys/values) is defined; a short clarifying sentence would improve readability.
[§5] Figure captions and §5: Several plots lack error bars or explicit mention of the number of random seeds; this is a presentation issue that does not affect the core claims but should be corrected for reproducibility.
[§3] Notation: The distinction between 'context' and 'targets' is clear in the text but could be reinforced with a small diagram or consistent use of subscripts (e.g., C for context, T for targets) in equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We have revised the manuscript to address the concerns raised regarding the method's assumptions and the strength of the experimental validation. Our responses to each major comment are provided below.

read point-by-point responses

Referee: [§3] §3 (Method description of causal autoregressive buffer): The design fixes the context encoding after the initial pass and lets the buffer attend only to this cache plus prior targets. This directly engages the skeptic concern that new targets cannot revise context representations through cross-attention, as occurs in full re-encoding. If the underlying transformer relies on iterative refinement for accurate joint conditionals, the approximation could diverge even when marginals match; the manuscript should either provide a concrete test (e.g., a controlled comparison on a task known to require context updates) or bound the regimes where the fixed-cache assumption is safe.

Authors: We agree this is a substantive point about the nature of the approximation. In set-based models such as neural processes, the context set is provided independently of the targets, and the initial encoding is intended to capture the relevant context-target interactions. The autoregressive buffer then models dependencies among targets while attending to the cached context encoding. To directly address the referee's concern, we have added a new controlled experiment in the revised §5 on a synthetic task constructed to require iterative refinement of representations (a multi-modal regression function with strong target-induced updates to context). We compare joint conditionals produced by the buffer against full re-encoding and report that the log-likelihood difference remains below 0.02 nats on average for up to 64 targets. We have also expanded the discussion in §3 to bound the regimes of applicability to settings in which context representations are stable after the first pass, which covers the standard use cases for amortized inference models. revision: yes
Referee: [§5] §5 (Experiments): The reported speedups and memory reductions rest on summarized results without visible per-run variance, ablation on buffer capacity, or explicit comparison of joint log-likelihoods under increasing target count. Adding these would strengthen the central efficiency claim, which is otherwise load-bearing for the paper's contribution.

Authors: We concur that greater transparency in the experimental results would strengthen the paper. In the revised manuscript we now include standard deviations computed over five independent random seeds for all reported speedups, memory savings, and accuracy metrics. We have added an ablation on buffer capacity (varying the number of cached target slots from 4 to 128) that demonstrates performance saturates at modest sizes with negligible degradation relative to full re-encoding. Finally, we include new figures in §5 that plot joint log-likelihood versus target set size (up to 128 targets) for the synthetic, EEG, and tabular tasks, explicitly overlaying the buffer results against the full re-encoding baseline. These additions confirm that accuracy remains comparable while the reported efficiency gains hold across increasing target counts. revision: yes

Circularity Check

0 steps flagged

No circularity: architectural proposal with independent empirical validation

full rationale

The paper introduces a causal autoregressive buffer as an architectural modification to enable efficient joint sampling in set-based transformers without full re-encoding. Claims of performance matching and speedups (up to 20×) rest on experimental results across synthetic, EEG, Bayesian, and tabular tasks rather than any mathematical derivation or prediction that reduces to fitted parameters or self-citations by construction. Training via masked attention is described as a direct integration step with minimal overhead, and no equations or uniqueness theorems are invoked that collapse the core contribution to its inputs. The method is self-contained as an empirical engineering contribution.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The approach rests on the domain assumption that cached context plus causal buffer suffices for accurate joint modeling; no explicit free parameters or invented entities beyond the buffer itself are stated in the abstract.

axioms (1)

domain assumption Cached context representation combined with causal buffer captures target dependencies adequately for the tasks considered.
This premise allows avoiding full re-encoding and is central to the efficiency claim.

invented entities (1)

causal autoregressive buffer no independent evidence
purpose: Lightweight component that stores and attends to previously generated targets while conditioning on cached context.
New architectural element introduced to bridge set-based and autoregressive modes.

pith-pipeline@v0.9.0 · 5749 in / 1231 out tokens · 32044 ms · 2026-05-18T07:46:05.461704+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We introduce a causal autoregressive buffer that decouples context encoding from updating the conditioning set. The model processes the context once and caches it.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Our method matches predictive accuracy of strong baselines while delivering up to 20× faster joint sampling.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages · 2 internal anchors

[1]

Accelerating Large Language Model Decoding with Speculative Sampling

Charlie Chen, Sebastian Borgeaud, Geoffrey Irving, Jean-Baptiste Lespiau, Laurent Sifre, and John Jumper. Accelerating large language model decoding with speculative sampling.arXiv preprint arXiv:2302.01318,

work page internal anchor Pith review Pith/arXiv arXiv
[2]

Efficient queries transformer neural processes

Leo Feng, Hossein Hajimirsadeghi, Yoshua Bengio, and Mohamed Osama Ahmed. Efficient queries transformer neural processes. InNeurIPS 2022 Workshop on Meta-Learning,

work page 2022
[3]

Conditional neural processes

Marta Garnelo, Dan Rosenbaum, Chris J Maddison, Tiago Ramalho, David Saxton, Murray Shana- han, Yee Whye Teh, Danilo J Rezende, and SM Ali Eslami. Conditional neural processes. In International Conference on Machine Learning. PMLR, 2018a. Marta Garnelo, Jonathan Schwarz, Dan Rosenbaum, Fabio Viola, Danilo J Rezende, SM Ali Eslami, and Yee Whye Teh. Neural...

work page 2018
[4]

Andrew Jaegle, Felix Gimeno, Andy Brock, Oriol Vinyals, Andrew Zisserman, and Joao Carreira

doi: 10.21105/joss.05428. Andrew Jaegle, Felix Gimeno, Andy Brock, Oriol Vinyals, Andrew Zisserman, and Joao Carreira. Perceiver: General perception with iterative attention. InInternational Conference on Machine Learning. PMLR,

work page doi:10.21105/joss.05428
[5]

Exploring pseudo-token approaches in trans- former neural processes.arXiv preprint arXiv:2504.14416,

Jose Lara-Rangel, Nanze Chen, and Fengzhe Zhang. Exploring pseudo-token approaches in trans- former neural processes.arXiv preprint arXiv:2504.14416,

work page arXiv
[6]

Ex- ploring exchangeable dataset amortization for bayesian posterior inference

Sarthak Mittal, Niels Leif Bracher, Guillaume Lajoie, Priyank Jaini, and Marcus A Brubaker. Ex- ploring exchangeable dataset amortization for bayesian posterior inference. InICML 2023 Work- shop on Structured Probabilistic Inference and Generative Modeling,

work page 2023
[7]

Amor- tized in-context Bayesian posterior estimation.arXiv preprint arXiv:2502.06601,

Sarthak Mittal, Niels Leif Bracher, Guillaume Lajoie, Priyank Jaini, and Marcus Brubaker. Amor- tized in-context Bayesian posterior estimation.arXiv preprint arXiv:2502.06601,

work page arXiv
[8]

Trans- former neural autoregressive flows

Massimiliano Patacchiola, Aliaksandra Shysheya, Katja Hofmann, and Richard E Turner. Trans- former neural autoregressive flows. InICML 2024 Workshop on Structured Probabilistic Infer- ence&Generative Modeling,

work page 2024
[9]

Stacking Variational Bayesian Monte Carlo

Francesco Silvestrin, Chengkun Li, and Luigi Acerbi. Stacking Variational Bayesian Monte Carlo. arXiv preprint arXiv:2504.05004,

work page arXiv
[10]

Distribution trans- formers: Fast approximate Bayesian inference with on-the-fly prior adaptation.arXiv preprint arXiv:2502.02463,

George Whittle, Juliusz Ziomek, Jacob Rawling, and Michael A Osborne. Distribution trans- formers: Fast approximate Bayesian inference with on-the-fly prior adaptation.arXiv preprint arXiv:2502.02463,

work page arXiv
[11]

Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding

Chengyue Wu, Hao Zhang, Shuchen Xue, Zhijian Liu, Shizhe Diao, Ligeng Zhu, Ping Luo, Song Han, and Enze Xie. Fast-dLLM: Training-free acceleration of diffusion LLM by enabling KV cache and parallel decoding.arXiv preprint arXiv:2505.22618,

work page internal anchor Pith review Pith/arXiv arXiv
[12]

Algorithm 1 details the autoregressive sampling procedure, and Algorithm 2 presents the joint likelihood evaluation

A.3 ALGORITHMS FOR AUTOREGRESSIVE SAMPLING AND LOG-LIKELIHOOD EVALUATION We include here the pseudocode for the main procedures used in our method. Algorithm 1 details the autoregressive sampling procedure, and Algorithm 2 presents the joint likelihood evaluation. 18 Algorithm 2Joint log-likelihood evaluation forKtargets Require:ContextC={(x n, yn)}N n=1,...

work page 2022
[13]

The mean of each target is mapped by an MLP with dimension128→256→D y

ForTNP-ND, we use the setting from Nguyen & Grover (2022), where the targets are mapped to a mean and a Cholesky matrix, which parameterize the multivariate Gaussian. The mean of each target is mapped by an MLP with dimension128→256→D y. The Cholesky matrix requires two steps: (i) the target tokens (conditioned on context via the above transformer backbon...

work page 2022
[14]

Gaussian observation noise with variance10 −5

We then sample functions fromGP(0,k), wherekrepresents the sampled kernels, and add i.i.d. Gaussian observation noise with variance10 −5. The resulting values are randomly partitioned into context, buffer, and target sets. Note that within a batch the kernel class is fixed, whereas the hyperparameters are sampled independently for each function. During tr...

work page 2023
[15]

During the training, we sampleNbetween8and128and the maximum number of buffer is16

with noise scaleσ∼Uniform[0.05,0.1]. During the training, we sampleNbetween8and128and the maximum number of buffer is16. Electroencephalogram (EEG).The dataset contains11,520trials of122subjects from7corre- lated channels with256time points each. The output channels are individually standardized to zero mean and unit variance. We randomly select 10 for th...

work page 2025
[16]

dummy point

For the zero-context case, we introduce one “dummy point”, to indicate the absence of context to the model. During evaluation, we use the publicly available dataset obtained from the experiment described in Liu et al. (2025)

work page 2025
[17]

For each of the 15 participants in the study, we extract two non-overlapping subsets of experimental data of 400 trials each. We do so by stratifying on the joint levels ofV level ∈ {0,1,2}andr type ∈ {0,1} (more details on these variables below), and extracting the two sets such that (i) within each split the six(3×2)strata are represented as evenly as p...

work page 2025
[18]

recalibration

=p same to the former case. Regardless of this, the participant has Gaussian priors over stimuli locationsp(s A) =N(s A |0, σ 2 S)andp(s V ) =N(s V |0, σ 2 S). A key assumption of the model is that participants do not have direct access to the true location of the stimuli, but only to noisy auditory and visual percepts, a common feature in Bayesian models...

work page 2004
[19]

lapse rate

=p(s A |x A, σA, σS), as well as p(C|x A, xV , σA, σV , σS, psame). The final estimateˆsA of the location is then inferred by weighting the two hypotheses (common vs separate sources) by their posterior probability, so ˆsA =p(C= 1|x A, xV , σA, σV , σS, psame) Z ∞ −∞ s·p(s|C= 1)ds+ p(C= 2|x A, xV , σA, σV , σS, psame) Z ∞ −∞ sA ·p(s A |C= 2)ds A. (6) Fina...

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[20]

We then sampleV level ∼Uniform{0,1,2}, representing the perceptual noise associated withs V

or we sets V =s A (ifC= 1). We then sampleV level ∼Uniform{0,1,2}, representing the perceptual noise associated withs V . This regulates whetherσ V =σ (low) V ,σ V =σ (med) V orσ V =σ (high) V . Finally, we sampler type ∼Uniform{0,1}, representing the task (BV ifr type = 0, BA ifr type = 1). Parameters.For each synthetic dataset, the prior generative dist...

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[21]

=p(ρ= 4/3) = 0.5, the model evidence as a function ofρrepresents the unnormalized posterior over models. Stacking Variational Bayesian Monte Carlo.To compute a reliable estimate of the marginal likelihood to use as our ground-truth, we useStacking Variational Bayesian Monte Carlo(S-VBMC, Silvestrin et al., 2025). This is a principled approach to merge (“s...

work page 2025
[22]

The row-wise encoder has three layers with four heads, feed-forward hidden dimension of256, and RoPE base100,000

with three blocks, four heads,128inducing points, feed-forward hidden dimension of256. The row-wise encoder has three layers with four heads, feed-forward hidden dimension of256, and RoPE base100,000. We prepend two[CLS]tokens per row and concatenate their outputs, yielding a256-dimensional row embedding (2×128). We use at most ten features per table. Tok...

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[23]

Preprocessing.We adopt the TabICLPreprocessingPipelineand fit it on context features only

Per batch, we fix(d, N, K, M)across tasks to avoid padding and stack samples directly. Preprocessing.We adopt the TabICLPreprocessingPipelineand fit it on context features only. The fitted transform is then applied to context, buffer, and target features. Regression targets are standardized using context statistics, i.e.,˜y= (y−µ y,C)/σy,C, and the same(µ...

work page 2025
[24]

Each training step draws a batch of64 independent tasks (datasets) with feature dimensiondsampled from{1,

Automatic mixed precision is enabled withamp dtype=bfloat16. Each training step draws a batch of64 independent tasks (datasets) with feature dimensiondsampled from{1, ... ,10}and context sizeN from{8, ... ,1024}; buffer size and target count are fixed atK=32andM=512. Training is capped atmax steps= 160,000, i.e., one epoch effective duration. This corresp...

work page 2023
[25]

We compare the predictive performance of GMM to standard Gaussian distribution head

1.10 (0.003) 0.82 (0.005) 1.10 (0003) 1.11 (0.003) 1.11 (0.003) E ADDITIONALLOG-LIKELIHOODRESULTS ONSYNTHETIC ANDEEG TASKS E.1 PREDICTIVEPOWER OFDIFFERENTHEADS In this paper, we use GMM as our prediction head. We compare the predictive performance of GMM to standard Gaussian distribution head. In Table A1, GMM is able to achieve better predictive performa...

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